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<journal-id journal-id-type="publisher-id">Front. Behav. Econ.</journal-id>
<journal-title>Frontiers in Behavioral Economics</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Behav. Econ.</abbrev-journal-title>
<issn pub-type="epub">2813-5296</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
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<article-meta>
<article-id pub-id-type="doi">10.3389/frbhe.2025.1499464</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Behavioral Economics</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Gender and race differences on incentivized personality measures</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name><surname>McGee</surname> <given-names>Andrew D.</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
<xref ref-type="corresp" rid="c001"><sup>&#x0002A;</sup></xref>
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<contrib contrib-type="author">
<name><surname>McGee</surname> <given-names>Peter J.</given-names></name>
<xref ref-type="aff" rid="aff3"><sup>3</sup></xref>
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<aff id="aff1"><sup>1</sup><institution>Department of Economics, University of Alberta</institution>, <addr-line>Edmonton, AB</addr-line>, <country>Canada</country></aff>
<aff id="aff2"><sup>2</sup><institution>Institute of Labor Economics (IZA)</institution>, <addr-line>Bonn</addr-line>, <country>Germany</country></aff>
<aff id="aff3"><sup>3</sup><institution>Department of Economics, University of Arkansas</institution>, <addr-line>Fayetteville, AR</addr-line>, <country>United States</country></aff>
<author-notes>
<fn fn-type="edited-by"><p>Edited by: Pedro Rey-Biel, ESADE Business School, Spain</p></fn>
<fn fn-type="edited-by"><p>Reviewed by: Christiane Schwieren, Heidelberg University, Germany</p>
<p>Pau Balart, University of the Balearic Islands, Spain</p></fn>
<corresp id="c001">&#x0002A;Correspondence: Andrew D. McGee <email>mcgee1&#x00040;ualberta.ca</email></corresp>
</author-notes>
<pub-date pub-type="epub">
<day>25</day>
<month>04</month>
<year>2025</year>
</pub-date>
<pub-date pub-type="collection">
<year>2025</year>
</pub-date>
<volume>4</volume>
<elocation-id>1499464</elocation-id>
<history>
<date date-type="received">
<day>20</day>
<month>09</month>
<year>2024</year>
</date>
<date date-type="accepted">
<day>31</day>
<month>03</month>
<year>2025</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#x000A9; 2025 McGee and McGee.</copyright-statement>
<copyright-year>2025</copyright-year>
<copyright-holder>McGee and McGee</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/"><p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p></license>
</permissions>
<abstract>
<sec>
<title>Introduction</title>
<p>Employment screening based on personalities gives applicants incentives to misrepresent themselves. Studies of group differences on personality measures primarily examine differences on measures taken without incentives for misrepresentation. Incentives may matter for group differences for at least two reasons. First, groups with different unincentivized means have different scope to distort their responses&#x02014;differences in &#x0201C;opportunity-to-fake.&#x0201D; Second, groups may differ in their notions of what constitutes a desirable personality.</p></sec>
<sec>
<title>Methods</title>
<p>We use a within-subject laboratory experiment to examine group differences on Big Five measures. Subjects first responded without incentives. A week later, subjects viewed a job ad and were informed that bonuses would be paid to subjects best fitting the hiring criteria. The treatments varied the information in the ad about desired personality traits.</p></sec>
<sec>
<title>Results</title>
<p>Controlling for opportunity-to-fake, we find evidence of racial but not gender differences in faking. Incentives attenuate gender differences on unincentivized personality measures but lead to racial differences where no differences exist on unincentivized measures. In every instance where a gap emerged on an incentivized measure where none existed on the unincentivized measure, the minority group would be disadvantaged were hiring based on the measure. We assess whether protected groups would be adversely impacted from selection on incentivized measures using the realized group differences in the experiment and the Equal Employment Opportunity Commission&#x00027;s &#x0201C;four-fifth&#x00027;s&#x0201D; rule. We find no evidence that women would be adversely affected by selection on incentivized personality measures, but racial minorities would be adversely impacted in the majority of trait-treatment comparisons.</p></sec>
<sec>
<title>Discussion</title>
<p>Given the prevalence of personality testing in employment screening, more research is needed on how the incentives for response distortion present in hiring influence racial differences on personality measures and whether any such differences influence hiring outcomes.</p></sec></abstract>
<kwd-group>
<kwd>personality</kwd>
<kwd>measurement</kwd>
<kwd>hiring</kwd>
<kwd>race</kwd>
<kwd>gender</kwd>
</kwd-group>
<contract-sponsor id="cn001">Social Sciences and Humanities Research Council<named-content content-type="fundref-id">10.13039/100021638</named-content></contract-sponsor>
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<ref-count count="54"/>
<page-count count="17"/>
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<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Behavioral Labor Economics</meta-value>
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</front>
<body>
<sec id="s1">
<title>1 Introduction</title>
<p>Meta-analyses document small to medium-sized associations between personality measures and job performance (Barrick and Mount, <xref ref-type="bibr" rid="B4">1991</xref>; Tett et al., <xref ref-type="bibr" rid="B47">1991</xref>; Salgado, <xref ref-type="bibr" rid="B45">1997</xref>; He et al., <xref ref-type="bibr" rid="B21">2019</xref>; Watrin et al., <xref ref-type="bibr" rid="B51">2023</xref>), and the use of personality tests in applicant screening has been shown to improve firm performance and selection outcomes (Ichniowski et al., <xref ref-type="bibr" rid="B29">1997</xref>; Autor and Scarborough, <xref ref-type="bibr" rid="B3">2008</xref>; Hoffman et al., <xref ref-type="bibr" rid="B22">2018</xref>). Despite their widespread use in selection, evidence concerning the effects on protected groups of personality testing in hiring is limited. Autor and Scarborough (<xref ref-type="bibr" rid="B3">2008</xref>) found that minority hiring rates at a firm&#x00027;s establishments were no different when screening was based on personality testing than when based on informal interviews, and meta-analyses in psychology have found little evidence of potential adverse impacts from personality testing on women (Hough et al., <xref ref-type="bibr" rid="B27">2001</xref>) and minorities (Foldes et al., <xref ref-type="bibr" rid="B14">2008</xref>). The studies in these meta-analyses, however, primarily examine group differences on unincentivized measures even though tests in selection are necessarily incentivized. Furthermore, the U.S. Equal Employment Opportunity Commission (EEOC) in 2018 found it probable that Best Buy adversely impacted applicants based on race through its use of personality tests (U. S. Equal Employment Opportunity Commission, <xref ref-type="bibr" rid="B49">2018</xref>).</p>
<p>This study investigates how incentives influence gender and race differences on personality tests in a within-subject, laboratory experiment. Subjects first completed Big Five personality measures without incentives.<xref ref-type="fn" rid="fn0001"><sup>1</sup></xref> About a week later, the subjects were given a job ad and took personality and IQ tests. Subjects were informed that a bonus would be paid to subjects who best met the hiring criteria. In the <italic>Extroversion</italic> (<italic>Introversion</italic>) treatment, the ad indicated that an extrovert (introvert) was desired, while in the <italic>No Priming</italic> treatment the ad contained no information about desired personality.</p>
<p>Using the unincentivized measures, women in our sample were more agreeable but less open and emotionally stable than men. Incentives, however, proved a great equalizer as we fail to reject the gender equality of the mean scores for all traits in all treatments using the incentivized measures.</p>
<p>Turning to racial differences, East Asian subjects were less extroverted, open, and emotionally stable than White subjects using the unincentivized measures. These differences, however, are not attenuated in many cases when measured with incentives. Given a clear indication of the desired personality trait in the <italic>Extroversion</italic> treatment, the East Asian-White gaps in extroversion and openness attenuate. Given no information in the <italic>No Priming</italic> treatment or counterintuitive priming in the <italic>Introversion</italic> treatment, the East Asian-White gaps fail to attenuate and in some cases gaps emerge that did not exist using the unincentivized measures.</p>
<p>Our &#x0201C;other race&#x0201D; category consists of non-White, non-East Asian subjects. These subjects were more conscientious than White subjects using the unincentivized measures, but there were no significant differences for other traits. By contrast, we find significant differences using the incentivized extroversion, agreeableness and emotional stability measures in the <italic>Introversion</italic> treatment. For conscientiousness, the gap favoring subjects of other races using the unincentivized measure reverses signs and is insignificant using the incentivized measure. Similar patterns exist in the <italic>No Priming</italic> treatment, suggesting that unusual personality requirements or the absence of cues result in incentivized measures that disadvantage subjects of other races relative to White subjects.</p>
<p>To assess whether hypothetical hiring based on incentivized measures would adversely impact women or minorities, we apply the EEOC&#x00027;s &#x0201C;four-fifths rule&#x0201D; under which a protected group is deemed adversely impacted by a hiring practice if the fraction of the protected group selected is &#x0003C; 80% of the fraction selected from the reference group. Using this rule, we find little evidence that women would be adversely impacted by selection based on any incentivized measure in any treatment. By contrast, East Asians and individuals of other races would be adversely impacted by selection on incentivized personality scores in half to two-thirds of the trait-treatment combinations in the experiment.</p>
<p>The data used in our study were originally examined in McGee and McGee (<xref ref-type="bibr" rid="B35">2024</xref>), which tested hypotheses about the correlations between incentivized and unincentivized personality measures, the influence of subject characteristics on incentivized measures, and the mediating effects of information about desired traits. That study documented that incentivized personality scores were weakly to moderately correlated with unincentivized personality scores, but the information provided in the job ads had little effect on these correlations. Most relevant for our study, McGee and McGee (<xref ref-type="bibr" rid="B35">2024</xref>) found little evidence that the subject characteristics they hypothesized would influence incentivized personality measures (e.g., IQ, Machiavellianism, impression management, willingness to lie) could explain the heterogeneity in these measures.<xref ref-type="fn" rid="fn0002"><sup>2</sup></xref> By contrast, our secondary analysis of the same data suggests that racial differences&#x02014;characteristics that were not hypothesized to influence incentivized personality measures when the experiment was conceived&#x02014;might underpin some of the heterogeneity in incentivized scores.</p>
<p>Our study makes two primary contributions. First, we contribute to the literature on non-cognitive traits by highlighting that incentives and the information available to test-takers can influence gender and race differences on personality measures. In their review of personality psychology, Almlund et al. (<xref ref-type="bibr" rid="B1">2011</xref>) stress accounting for the role of incentives and situations when measuring personality. Our findings suggest that these factors may also influence measured group differences. In this respect, the study complements (Gneezy et al., <xref ref-type="bibr" rid="B17">2019</xref>), who find that incentives influence group differences on cognitive tests between students in the United States and China.</p>
<p>Second, we demonstrate that the racial differences on incentivized Big Five measures in our sample are large enough to adversely impact minorities in hypothetical selection. Understanding the effects of personality testing on protected groups is particularly important as algorithmic screening using personality tests becomes more widespread in recruitment. While several studies evaluate the biases that machine learning may introduce in hiring (e.g., Li et al., <xref ref-type="bibr" rid="B32">2020</xref>; Cowgill, <xref ref-type="bibr" rid="B8">2020</xref>), there is little evidence on the biases that personality tests may introduce.<xref ref-type="fn" rid="fn0003"><sup>3</sup></xref> Especially noteworthy from our study is that where racial differences emerge on incentivized tests where no similar differences exist on the unincentivized tests, <italic>in every instance</italic> these racial differences would disadvantage minorities relative to their white peers. Personalities are assessed in many contexts, and selection on incentivized personality measures has been shown to influence the racial distribution of selected individuals.<xref ref-type="fn" rid="fn0004"><sup>4</sup></xref> Were our findings to generalize to other settings, racial differences in personality misrepresentation could disadvantage minorities in outcomes ranging from university admissions to promotion decisions.</p></sec>
<sec id="s2">
<title>2 Background</title>
<p>Whether personality tests adversely impact protected groups in hiring has been examined largely by extrapolating from group differences on <italic>unincentivized</italic> tests (e.g., Feingold, <xref ref-type="bibr" rid="B11">1994</xref>; Goldberg et al., <xref ref-type="bibr" rid="B19">1998</xref>; Weisberg et al., <xref ref-type="bibr" rid="B53">2011</xref>). The standardized mean gender and race differences in these studies tend to be small. Hough et al. (<xref ref-type="bibr" rid="B27">2001</xref>) report in a meta-analysis that women were less extroverted (<italic>d</italic> &#x0003D; &#x02212;0.09), open to experience (<italic>d</italic> &#x0003D; &#x02212;0.07), and emotionally stable (<italic>d</italic> &#x0003D; &#x02212;0.24) than men but more conscientious (<italic>d</italic> &#x0003D; 0.08) and agreeable (<italic>d</italic> &#x0003D; 0.39). Also in a meta-analysis, Foldes et al. (<xref ref-type="bibr" rid="B14">2008</xref>) find that Blacks and Hispanics are more conscientious than Whites (<italic>d</italic> &#x0003D; 0.17 and <italic>d</italic> &#x0003D; 0.20, respectively), while Asians were more agreeable (<italic>d</italic> &#x0003D; 0.63) and open (<italic>d</italic> &#x0003D; 0.11), but less extroverted (<italic>d</italic> &#x0003D; &#x02212;0.07) and emotionally stable (<italic>d</italic> &#x0003D; &#x02212;0.16) than Whites. While the meta-analyses in Hough et al. (<xref ref-type="bibr" rid="B27">2001</xref>) and Foldes et al. (<xref ref-type="bibr" rid="B14">2008</xref>) include a few incentivized applicant samples, the incentivized samples in Foldes et al. (<xref ref-type="bibr" rid="B14">2008</xref>), for instance, made up only 14% of their database.</p>
<p>Incentives for misrepresentation may matter for group differences for at least two reasons. First, groups may have different notions about optimal personalities (Hofstede and McRae, <xref ref-type="bibr" rid="B23">2004</xref>; Ryan et al., <xref ref-type="bibr" rid="B42">2021</xref>) that result in differences in faking (Fell and K&#x000F6;nig, <xref ref-type="bibr" rid="B12">2016</xref>). Second, group differences in traits result in differences in &#x0201C;opportunity-to-fake&#x0201D; (McFarland and Ryan, <xref ref-type="bibr" rid="B34">2000</xref>; Tett and Simonet, <xref ref-type="bibr" rid="B48">2011</xref>). That is, members of a group with lower scores can increase their scores by more on average than members of the higher scoring group given that the scores are bounded above. This dynamic should attenuate group differences when personalities are measured with incentives for misrepresentation. Leveraging its within-subject design, ours is the first study to document how opportunity-to-fake dynamics influence gender and race gaps on incentivized personality measures.</p>
<p>A within-subject experiment also identifies the effects of incentives without the sampling variation present when comparing applicant and incumbent samples (e.g., Hough et al., <xref ref-type="bibr" rid="B25">1990</xref>; Rosse et al., <xref ref-type="bibr" rid="B40">1998</xref>; Weekley et al., <xref ref-type="bibr" rid="B52">2004</xref>). Hu and Connelly (<xref ref-type="bibr" rid="B28">2021</xref>) identified only ten published and seven unpublished within-subject studies comparing incentivized responses in selection settings to unincentivized responses in low-stakes settings&#x02014;what might be considered the ideal experiment. Studies such as Griffith et al. (<xref ref-type="bibr" rid="B20">2007</xref>), Ellingson et al. (<xref ref-type="bibr" rid="B10">2007</xref>), and Isaacson et al. (<xref ref-type="bibr" rid="B30">2009</xref>) highlight the difficulties of this research: small samples, high non-response rates, and idiosyncratic settings. Ellingson et al. (<xref ref-type="bibr" rid="B10">2007</xref>), for example, identify 218 individuals who took tests in a development setting and when applying for actual jobs, but the tests were for different jobs and taken as much as seven years apart.</p>
<p>In the only within-subject study we are aware to examine racial differences on incentivized measures, Isaacson et al. (<xref ref-type="bibr" rid="B30">2009</xref>) find no Black&#x02013;White difference in faking on a conscientiousness measure among individuals completing the measure both in a job application and for research purposes.<xref ref-type="fn" rid="fn0005"><sup>5</sup></xref> They report that men faked more frequently than women, but they do not report means under the honest-reporting conditions making it impossible to assess the role of opportunity-to-fake. By contrast, our study assesses whether faking differs by gender and race on all Big Five traits while accounting for differences in opportunity-to-fake.</p>
<p>We are aware of only two studies that adopt the EEOC&#x00027;s &#x0201C;four-fifths&#x0201D; rule to assess the potential for adverse impacts from personality tests on women and racial minorities. Powell et al. (<xref ref-type="bibr" rid="B37">2011</xref>) assess whether women applying for positions at an oil refinery would be adversely impacted by selection on extroversion and conscientiousness scores or the related facet scores. While they find the potential for adverse gender impacts from selection on facet scores, they find little such evidence using the factor scores&#x02014;suggesting that gender differences at the facet level cancel each other out when aggregated to the factor-level. We likewise find little evidence of the potential for adverse gender impacts based on the incentivized factor measures. In our case, however, the absence of adverse impacts appears to stem from opportunity-to-fake dynamics that attenuate gender differences in the unincentivized measures.</p>
<p>Finally, Foldes et al. (<xref ref-type="bibr" rid="B14">2008</xref>) evaluate whether adverse impacts on racial minorities are likely to arise when selection is based on each of the Big Five factors using the standardized mean differences from their meta-analysis and assuming standard normal distributions. They find evidence of advantages for Blacks and Hispanics when selection is based on conscientiousness measures&#x02014;similar to our findings for non-White, non-East Asian subjects&#x02014;but conclude that there is some potential for adverse impacts on Blacks when selection is based on emotional stability or extroversion scores. For Asians, they find some potential for adverse impact using emotional stability, but again their inferences are based largely on studies using unincentivized measures.</p></sec>
<sec id="s3">
<title>3 Experimental design</title>
<p>The study conducts an exploratory analysis using data from the experiment in McGee and McGee (<xref ref-type="bibr" rid="B35">2024</xref>). Subjects participated in two sessions. In the Baseline session lasting &#x0007E;15 min, subjects responded to a Big Five assessment (DeYoung et al., <xref ref-type="bibr" rid="B9">2007</xref>), other psychometric instruments detailed in the <xref ref-type="supplementary-material" rid="SM1">Appendix</xref>, and demographic questions.<xref ref-type="fn" rid="fn0006"><sup>6</sup></xref><sup>,</sup><xref ref-type="fn" rid="fn0007"><sup>7</sup></xref> The demographic questions including race and gender were part of a standard code module we used when initiating experiments, but we did not ex ante have hypotheses regarding the relationships between race and gender and incentivized personality measures. Subjects earned $7 for participating. Afterwards, subjects were invited to sign up for the Evaluation session a week later.</p>
<p>In the Evaluation session lasting approximately an hour, subjects received a job ad and completed the same personality test and Raven&#x00027;s Progressive Matrices (RPM) (Raven, <xref ref-type="bibr" rid="B39">1998</xref>), an intelligence test. The instructions informed subjects that after these tests a $25 bonus would be awarded to one subject in each group of four subjects. After the bonus was awarded, subjects completed other psychometric instruments, a risk preferences measure (Holt and Laury, <xref ref-type="bibr" rid="B24">2002</xref>), and questions about work experiences.</p>
<p>The treatments varied the job description in the Evaluation session given that applicants are often routed to tests from ads, and the information in ads likely influences applicants&#x00027; understanding of personality demands.<xref ref-type="fn" rid="fn0008"><sup>8</sup></xref> In the <italic>Extroversion</italic> treatment, the instructions indicated that &#x0201C;All members of a group will receive the same job description. We will then administer an intelligence test and a personality test to determine who to &#x0201C;hire&#x0201D; for the job. We will weigh these two tests according to some criteria and one subject within each group who best meets these criteria will receive a bonus of $25; the remaining subjects in each group will not receive any bonus.&#x0201D; Subjects received an ad for a &#x0201C;client services representative&#x0201D; based on an actual ad. To indicate that an extrovert was desired, the job description incorporated words and phrases associated with extroversion such as &#x0201C;outgoing&#x0201D; and &#x0201C;able to take initiative, be assertive&#x0201D; while attempting to avoid indicating that the firm sought other personality traits.</p>
<p>Subjects in the <italic>Introversion</italic> and <italic>No Priming</italic> treatments received the same instructions. In the <italic>Introversion</italic> treatment, the ad indicated that an introvert was desired through the use of words and phrases associated with introversion such as &#x0201C;contemplative&#x0201D; and &#x0201C;reserved.&#x0201D; In the <italic>No Priming</italic> treatment, the ad contained little detail beyond listing tasks and requirements common to all of the ads. In contrast to much of the psychology literature on faking, at no point did we direct subjects to fake or suggest strategies for responding.<xref ref-type="fn" rid="fn0009"><sup>9</sup></xref> For each trait, the incentivized measure from the Evaluation session minus the unincentivized measure from the Baseline session serves as our measure of faking.<xref ref-type="fn" rid="fn0010"><sup>10</sup></xref></p>
<p>Concerning the differences in incentives between subjects and job applicants, we argue that these incentives are reasonably similar. Most job applicants take personality tests at the same time that they submit resum&#x000E9;s and other application materials. Job boards hosting job ads in some cases even provide employers with personality tests for applicants, who presumably take these tests not long after reading the job ad. Similar to our instructions, employers do not explicitly reveal how this information (i.e., resum&#x000E9;s, references, test scores) will be used, but applicants understand that a decision will be reached using this information: they will either hear back from the employer or they will not. Personality tests at this stage are unlikely to be used to select applicants to hire so much as to eliminate applicants from consideration.<xref ref-type="fn" rid="fn0011"><sup>11</sup></xref> Applicants likely understand that in order to be hired, they must avoid being in that fraction of the applicant pool eliminated from consideration based on these early signals to employers in order to advance to the next stage of hiring (typically job interviews). Similarly, subjects in our experiment understand that they must be in the top quartile within their group to win the group. Both applicants and subjects likely view personality testing as a hurdle to be passed, and their test-taking strategies presumably reflect this.<xref ref-type="fn" rid="fn0012"><sup>12</sup></xref></p>
<p>The client services representative occupation was selected as the sort of job to which young graduates might apply. In the 2016 American Community Survey, 25% of respondents in the services sales representative occupation were age 30 or less and 91% had a bachelor&#x00027;s degree or less (authors&#x00027; calculations). Bren&#x0010D;i&#x0010D; and McGee (<xref ref-type="bibr" rid="B6">2023</xref>) find in a sample of job ads that 42% of ads in this occupation signaled a demand for extroverts through terms associated with extroversion (nearly twice the proportion expressing demands for any other trait), while less than 1% of such ads indicated a demand for introversion. At the same time, 36% of ads for this occupation used no terms associated with desired personality traits. As such, we view the <italic>Extroversion</italic> and <italic>No Priming</italic> treatments as representative of the ads job seekers in this occupation encounter.<xref ref-type="fn" rid="fn0013"><sup>13</sup></xref></p>
<p>In addition to a $7 participation fee and (if applicable) the $25 bonus, subjects were paid $0.20 for each correct answer on the RPM and earnings from one randomly selected realization of a paired lottery of the risk preference instrument.</p></sec>
<sec id="s4">
<title>4 Experimental sample</title>
<p>Between 2014 and 2016, 474 undergraduates at Simon Fraser University participated in both a Baseline and Evaluation session: 167 in the <italic>Extroversion</italic> treatment, 160 in the <italic>Introversion</italic> treatment, and 147 in the <italic>No Priming</italic> treatment. Subjects were recruited <italic>via</italic> email from the registered subject pool at Simon Fraser&#x00027;s experimental lab consisting of students from all majors. Subjects self-reported their gender and race with 48% of the sample identifying as men. Subjects who identified as White were coded as such, while subjects who identified as Chinese, Filipino, Japanese, Korean, or Asian were categorized as East Asian. All remaining subjects identifying as Indian, Pakistani, Black, Latino, or an unspecified race were placed in the &#x0201C;other race&#x0201D; category.<xref ref-type="fn" rid="fn0014"><sup>14</sup></xref> In the sample, 23% of subjects reported being White, 49% East Asian, and 28% another race.<xref ref-type="fn" rid="fn0015"><sup>15</sup></xref><sup>,</sup> <xref ref-type="fn" rid="fn0016"><sup>16</sup></xref></p>
<p>The experiment did not attempt to balance the treatments by gender and race. In the <italic>Extroversion</italic> treatment, 57% of subjects indicated that they were women, 19% White, and 59% East Asian. In the <italic>No Priming</italic> (<italic>Introversion</italic>) treatment, 49% (51%) indicated that they were women, 25% (29%) White, and 50% (36%) East Asian. Using Pearson chi-squared tests, we fail to reject the hypothesis of independence between gender and treatment (<italic>p</italic> &#x0003D; 0.67), but we reject the independence hypothesis between the race categories and treatment (<italic>p</italic> &#x0003D; 0.001). This lack of balance primarily affects our statistical power to detect small group differences, an issue we elaborate on in the Discussion section. See <xref ref-type="supplementary-material" rid="SM1">Appendix A Tables 1</xref>&#x02013;<xref ref-type="supplementary-material" rid="SM1">4</xref> for summary statistics for all measures by treatment and group.</p></sec>
<sec id="s5">
<title>5 Results</title>
<sec>
<title>5.1 Gender</title>
<p>The first row in Panel A of <xref ref-type="table" rid="T1">Table 1</xref> reports standardized effect sizes&#x02014;the mean for women minus the mean for men divided by the full sample standard deviation&#x02014;for each personality trait pooling Baseline scores from all treatments. Women were more agreeable (0.29), less open to experience (&#x02212;0.28), and less emotionally stable (&#x02212;0.40) than men. Standardized effects of 0.2, 0.5, and 0.8 standard deviations are considered small, medium, and large, respectively, in the psychology literature (Cohen, <xref ref-type="bibr" rid="B7">1988</xref>), and thus these gender differences would be viewed as small to medium-sized. Moreover, the gender differences in mean agreeableness, openness, and emotional stability are statistically significant even after correcting for the 40 hypotheses in Panel A using Benjamini et al.&#x00027;s (<xref ref-type="bibr" rid="B5">2006</xref>) sharpened <italic>q-</italic>values given that the data were not collected to test for gender differences.<xref ref-type="fn" rid="fn0017"><sup>17</sup></xref></p>
<table-wrap position="float" id="T1">
<label>Table 1</label>
<caption><p>Standardized effect sizes (<italic>d</italic>), power calculations and sample sizes.</p></caption>
<table frame="box" rules="all">
<thead>
<tr style="background-color:#8f9496;color:#ffffff">
<th valign="top" align="center" colspan="6"><bold>Personality trait</bold></th>
</tr>
</thead>
<tbody>
<tr style="background-color:#8f9496;color:#ffffff">
<td/>
<td valign="top" align="center"><bold>Extroversion</bold></td>
<td valign="top" align="center"><bold>Conscientious</bold>.</td>
<td valign="top" align="center"><bold>Agreeableness</bold></td>
<td valign="top" align="center"><bold>Openness</bold></td>
<td valign="top" align="center"><bold>Em. Stab</bold>.</td>
</tr>
<tr style="background-color:#8f9496;color:#ffffff">
<td/>
<td valign="top" align="center"><bold>(1)</bold></td>
<td valign="top" align="center"><bold>(2)</bold></td>
<td valign="top" align="center"><bold>(3)</bold></td>
<td valign="top" align="center"><bold>(4)</bold></td>
<td valign="top" align="center"><bold>(5)</bold></td>
</tr> <tr style="background-color:#dee1e1;">
<td valign="top" align="left" colspan="6"><bold>Panel A. Women-men standardized differences</bold></td>
</tr> <tr>
<td valign="top" align="left">Pooled baseline</td>
<td valign="top" align="center">&#x02212;0.09</td>
<td valign="top" align="center">0.01</td>
<td valign="top" align="center"><italic><bold>0.29</bold></italic><sup>&#x02020;</sup></td>
<td valign="top" align="center"><italic><bold>&#x02212;0.28</bold></italic><sup>&#x02020;</sup></td>
<td valign="top" align="center"><italic><bold>&#x02212;0.40!</bold></italic></td>
</tr> <tr>
<td valign="top" align="left">Pooled evaluation</td>
<td valign="top" align="center">0.01</td>
<td valign="top" align="center">&#x02212;0.04</td>
<td valign="top" align="center">&#x02212;0.01</td>
<td valign="top" align="center">&#x02212;0.09</td>
<td valign="top" align="center">&#x02212;0.12</td>
</tr> <tr>
<td valign="top" align="left">(<italic>E</italic>) Baseline</td>
<td valign="top" align="center">0.04</td>
<td valign="top" align="center">0.00</td>
<td valign="top" align="center">0.11</td>
<td valign="top" align="center">&#x02212;0.17</td>
<td valign="top" align="center"><italic>&#x02212;0.28</italic></td>
</tr> <tr>
<td valign="top" align="left">(<italic>E</italic>) Evaluation</td>
<td valign="top" align="center">0.08</td>
<td valign="top" align="center">&#x02212;0.03</td>
<td valign="top" align="center">&#x02212;0.15</td>
<td valign="top" align="center">&#x02212;0.03</td>
<td valign="top" align="center">&#x02212;0.13</td>
</tr> <tr>
<td valign="top" align="left">(<italic>NP</italic>) Baseline</td>
<td valign="top" align="center">&#x02212;0.19</td>
<td valign="top" align="center">0.10</td>
<td valign="top" align="center"><italic><bold>0.49</bold></italic><sup>&#x02020;</sup></td>
<td valign="top" align="center"><bold>&#x02212;0.37</bold></td>
<td valign="top" align="center"><italic><bold>&#x02212;0.67!</bold></italic></td>
</tr> <tr>
<td valign="top" align="left">(<italic>NP</italic>) Evaluation</td>
<td valign="top" align="center">&#x02212;0.11</td>
<td valign="top" align="center">&#x02212;0.06</td>
<td valign="top" align="center">0.20</td>
<td valign="top" align="center">&#x02212;0.15</td>
<td valign="top" align="center">&#x02212;0.26</td>
</tr> <tr>
<td valign="top" align="left">(<italic>I</italic>) Baseline</td>
<td valign="top" align="center">&#x02212;0.13</td>
<td valign="top" align="center">&#x02212;0.12</td>
<td valign="top" align="center"><italic>0.28</italic></td>
<td valign="top" align="center"><italic>&#x02212;0.29</italic></td>
<td valign="top" align="center"><italic>&#x02212;0.29</italic></td>
</tr> <tr>
<td valign="top" align="left">(<italic>I</italic>) Evaluation</td>
<td valign="top" align="center">&#x02212;0.08</td>
<td valign="top" align="center">&#x02212;0.06</td>
<td valign="top" align="center">&#x02212;0.07</td>
<td valign="top" align="center">&#x02212;0.20</td>
<td valign="top" align="center">&#x02212;0.06</td>
</tr> <tr style="background-color:#dee1e1;">
<td valign="top" align="left" colspan="6"><bold>Panel B. East Asian-White standardized differences</bold></td>
</tr> <tr>
<td valign="top" align="left">Pooled baseline</td>
<td valign="top" align="center"><italic><bold>&#x02212;0.45!</bold></italic></td>
<td valign="top" align="center">0.07</td>
<td valign="top" align="center">&#x02212;0.14</td>
<td valign="top" align="center"><italic><bold>&#x02212;0.56!</bold></italic></td>
<td valign="top" align="center"><italic><bold>&#x02212;0.35</bold></italic><sup>&#x02020;</sup></td>
</tr> <tr>
<td valign="top" align="left">Pooled evaluation</td>
<td valign="top" align="center">0.06</td>
<td valign="top" align="center"><italic><bold>&#x02212;0.32</bold></italic><sup>&#x02020;</sup></td>
<td valign="top" align="center"><italic><bold>&#x02212;0.48!</bold></italic></td>
<td valign="top" align="center"><bold>&#x02212;0.23</bold></td>
<td valign="top" align="center"><italic><bold>&#x02212;0.39</bold></italic><sup>&#x02020;</sup></td>
</tr> <tr>
<td valign="top" align="left">(<italic>E</italic>) Baseline</td>
<td valign="top" align="center"><italic><bold>&#x02212;0.60</bold></italic><sup>&#x02020;</sup></td>
<td valign="top" align="center">&#x02212;0.10</td>
<td valign="top" align="center">&#x02212;0.14</td>
<td valign="top" align="center"><bold>&#x02212;0.45</bold><sup><bold>&#x00023;</bold></sup></td>
<td valign="top" align="center">&#x02212;0.32</td>
</tr> <tr>
<td valign="top" align="left">(<italic>E</italic>) Evaluation</td>
<td valign="top" align="center">&#x02212;0.23</td>
<td valign="top" align="center">&#x02212;0.13</td>
<td valign="top" align="center"><italic><bold>&#x02212;0.61</bold></italic><sup>&#x02020;</sup></td>
<td valign="top" align="center">&#x02212;0.05</td>
<td valign="top" align="center">&#x02212;0.32</td>
</tr> <tr>
<td valign="top" align="left">(<italic>NP</italic>) Baseline</td>
<td valign="top" align="center"><italic>&#x02212;0.41</italic></td>
<td valign="top" align="center">0.16</td>
<td valign="top" align="center">0.08</td>
<td valign="top" align="center"><italic><bold>&#x02212;0.65</bold></italic><sup>&#x02020;</sup></td>
<td valign="top" align="center"><italic>&#x02212;0.38</italic></td>
</tr> <tr>
<td valign="top" align="left">(<italic>NP</italic>) Evaluation</td>
<td valign="top" align="center">&#x02212;0.15</td>
<td valign="top" align="center"><italic>&#x02212;0.34</italic></td>
<td valign="top" align="center">&#x02212;0.25</td>
<td valign="top" align="center"><italic>&#x02212;0.41</italic></td>
<td valign="top" align="center"><bold>&#x02212;0.49</bold><sup><bold>&#x00023;</bold></sup></td>
</tr> <tr>
<td valign="top" align="left">(<italic>I</italic>) Baseline</td>
<td valign="top" align="center">&#x02212;0.30</td>
<td valign="top" align="center">0.03</td>
<td valign="top" align="center">&#x02212;0.29</td>
<td valign="top" align="center"><italic><bold>&#x02212;0.52</bold></italic><sup>&#x02020;</sup></td>
<td valign="top" align="center"><italic>&#x02212;0.39</italic></td>
</tr> <tr>
<td valign="top" align="left">(<italic>I</italic>) Evaluation</td>
<td valign="top" align="center">0.10</td>
<td valign="top" align="center"><bold>&#x02212;0.46</bold><italic><sup><bold>&#x00023;</bold></sup></italic></td>
<td valign="top" align="center"><bold>&#x02212;0.49</bold><sup><bold>&#x00023;</bold></sup></td>
<td valign="top" align="center"><italic><bold>&#x02212;0.54</bold></italic><sup>&#x02020;</sup></td>
<td valign="top" align="center"><italic><bold>&#x02212;0.55</bold></italic><sup>&#x02020;</sup></td>
</tr> <tr style="background-color:#dee1e1;">
<td valign="top" align="left" colspan="6"><bold>Panel C. Other race-White standardized differences</bold></td>
</tr> <tr>
<td valign="top" align="left">Pooled baseline</td>
<td valign="top" align="center">&#x02212;0.05</td>
<td valign="top" align="center"><bold>0.30</bold><sup>&#x00023;</sup></td>
<td valign="top" align="center">0.02</td>
<td valign="top" align="center">&#x02212;0.13</td>
<td valign="top" align="center">&#x02212;0.20</td>
</tr> <tr>
<td valign="top" align="left">Pooled evaluation</td>
<td valign="top" align="center">0.08</td>
<td valign="top" align="center">&#x02212;0.11</td>
<td valign="top" align="center"><bold>&#x02212;0.30</bold><sup><bold>&#x00023;</bold></sup></td>
<td valign="top" align="center">&#x02212;0.13</td>
<td valign="top" align="center"><italic><bold>&#x02212;0.39</bold></italic><sup>&#x02020;</sup></td>
</tr> <tr>
<td valign="top" align="left">(<italic>E</italic>) Baseline</td>
<td valign="top" align="center">&#x02212;0.09</td>
<td valign="top" align="center">&#x02212;0.20</td>
<td valign="top" align="center">0.12</td>
<td valign="top" align="center">&#x02212;0.09</td>
<td valign="top" align="center"><bold>&#x02212;0.56</bold><sup><bold>&#x00023;</bold></sup></td>
</tr> <tr>
<td valign="top" align="left">(<italic>E</italic>) Evaluation</td>
<td valign="top" align="center">&#x02212;0.13</td>
<td valign="top" align="center">0.21</td>
<td valign="top" align="center">&#x02212;0.23</td>
<td valign="top" align="center">0.10</td>
<td valign="top" align="center">&#x02212;0.30</td>
</tr> <tr>
<td valign="top" align="left">(<italic>NP</italic>) Baseline</td>
<td valign="top" align="center">&#x02212;0.05</td>
<td valign="top" align="center"><bold>0.58</bold><sup><bold>&#x00023;</bold></sup></td>
<td valign="top" align="center">0.07</td>
<td valign="top" align="center">&#x02212;0.14</td>
<td valign="top" align="center">0.07</td>
</tr> <tr>
<td valign="top" align="left">(<italic>NP</italic>) Evaluation</td>
<td valign="top" align="center">&#x02212;0.24</td>
<td valign="top" align="center">&#x02212;0.21</td>
<td valign="top" align="center">&#x02212;0.12</td>
<td valign="top" align="center">&#x02212;0.26</td>
<td valign="top" align="center"><bold>&#x02212;0.46</bold><sup><bold>&#x00023;</bold></sup></td>
</tr> <tr>
<td valign="top" align="left">(<italic>I</italic>) Baseline</td>
<td valign="top" align="center">0.22</td>
<td valign="top" align="center"><bold>0.45</bold><sup><bold>&#x00023;</bold></sup></td>
<td valign="top" align="center">&#x02212;0.10</td>
<td valign="top" align="center">&#x02212;0.15</td>
<td valign="top" align="center">&#x02212;0.16</td>
</tr> <tr>
<td valign="top" align="left">(<italic>I</italic>) Evaluation</td>
<td valign="top" align="center"><bold>0.49</bold><sup><bold>&#x00023;</bold></sup></td>
<td valign="top" align="center">&#x02212;0.26</td>
<td valign="top" align="center"><bold>&#x02212;0.50</bold><sup><bold>&#x00023;</bold></sup></td>
<td valign="top" align="center">&#x02212;0.23</td>
<td valign="top" align="center"><bold>&#x02212;0.43</bold><sup><bold>&#x00023;</bold></sup></td>
</tr> <tr style="background-color:#dee1e1;">
<td valign="top" align="left" colspan="6"><bold>Panel D: Power calculations and sample sizes</bold></td>
</tr> <tr>
<td/>
<td valign="top" align="center"><italic><bold>d</bold> <bold>&#x0003D;</bold></italic> <bold>0.2</bold></td>
<td valign="top" align="center"><italic><bold>d</bold> <bold>&#x0003D;</bold></italic> <bold>0.5</bold></td>
<td valign="top" align="center"><italic><bold>d</bold> <bold>&#x0003D;</bold></italic> <bold>0.8</bold></td>
<td/>
<td/>
</tr> <tr style="background-color:#dee1e1;">
<td/>
<td valign="top" align="center" colspan="3"><bold>Women-men</bold></td>
<td valign="top" align="center"><italic><bold>N</bold></italic> <bold>(Men)</bold></td>
<td valign="top" align="center"><italic><bold>N</bold></italic> <bold>(Women)</bold></td>
</tr> <tr>
<td valign="top" align="left">Pooled scores</td>
<td valign="top" align="center">0.58</td>
<td valign="top" align="center">1.00</td>
<td valign="top" align="center">1.00</td>
<td valign="top" align="center">228</td>
<td valign="top" align="center">256</td>
</tr> <tr>
<td valign="top" align="left"><italic>Extroversion</italic></td>
<td valign="top" align="center">0.25</td>
<td valign="top" align="center">0.89</td>
<td valign="top" align="center">1.00</td>
<td valign="top" align="center">74</td>
<td valign="top" align="center">93</td>
</tr> <tr>
<td valign="top" align="left"><italic>No Priming</italic></td>
<td valign="top" align="center">0.23</td>
<td valign="top" align="center">0.85</td>
<td valign="top" align="center">1.00</td>
<td valign="top" align="center">75</td>
<td valign="top" align="center">72</td>
</tr> <tr>
<td valign="top" align="left"><italic>Introversion</italic></td>
<td valign="top" align="center">0.24</td>
<td valign="top" align="center">0.88</td>
<td valign="top" align="center">1.00</td>
<td valign="top" align="center">79</td>
<td valign="top" align="center">91</td>
</tr> <tr style="background-color:#dee1e1;">
<td/>
<td valign="top" align="center" colspan="3"><bold>East Asian-White</bold></td>
<td valign="top" align="center"><italic><bold>N</bold></italic> <bold>(White)</bold></td>
<td valign="top" align="center"><italic><bold>N</bold></italic> <bold>(Asian)</bold></td>
</tr> <tr>
<td valign="top" align="left">Pooled scores</td>
<td valign="top" align="center">0.41</td>
<td valign="top" align="center">0.99</td>
<td valign="top" align="center">1.00</td>
<td valign="top" align="center">113</td>
<td valign="top" align="center">230</td>
</tr> <tr>
<td valign="top" align="left"><italic>Extroversion</italic></td>
<td valign="top" align="center">0.16</td>
<td valign="top" align="center">0.67</td>
<td valign="top" align="center">0.97</td>
<td valign="top" align="center">31</td>
<td valign="top" align="center">98</td>
</tr> <tr>
<td valign="top" align="left"><italic>No Priming</italic></td>
<td valign="top" align="center">0.16</td>
<td valign="top" align="center">0.68</td>
<td valign="top" align="center">0.97</td>
<td valign="top" align="center">36</td>
<td valign="top" align="center">74</td>
</tr> <tr>
<td valign="top" align="left"><italic>Introversion</italic></td>
<td valign="top" align="center">0.17</td>
<td valign="top" align="center">0.71</td>
<td valign="top" align="center">0.98</td>
<td valign="top" align="center">46</td>
<td valign="top" align="center">58</td>
</tr>
<tr style="background-color:#dee1e1;">
<td/>
<td valign="top" align="center" colspan="3"><bold>Other race-white</bold></td>
<td valign="top" align="center"><italic><bold>N</bold></italic> <bold>(White)</bold></td>
<td valign="top" align="center"><italic><bold>N</bold></italic> <bold>(Other)</bold></td>
</tr>  <tr>
<td valign="top" align="left">Pooled scores</td>
<td valign="top" align="center">0.34</td>
<td valign="top" align="center">0.97</td>
<td valign="top" align="center">1.00</td>
<td valign="top" align="center">113</td>
<td valign="top" align="center">131</td>
</tr> <tr>
<td valign="top" align="left"><italic>Extroversion</italic></td>
<td valign="top" align="center">0.13</td>
<td valign="top" align="center">0.53</td>
<td valign="top" align="center">0.90</td>
<td valign="top" align="center">31</td>
<td valign="top" align="center">38</td>
</tr> <tr>
<td valign="top" align="left"><italic>No Priming</italic></td>
<td valign="top" align="center">0.13</td>
<td valign="top" align="center">0.56</td>
<td valign="top" align="center">0.92</td>
<td valign="top" align="center">36</td>
<td valign="top" align="center">37</td>
</tr> <tr>
<td valign="top" align="left"><italic>Introversion</italic></td>
<td valign="top" align="center">0.17</td>
<td valign="top" align="center">0.70</td>
<td valign="top" align="center">0.98</td>
<td valign="top" align="center">46</td>
<td valign="top" align="center">56</td>
</tr></tbody>
</table>
<table-wrap-foot>
<p>Panels A, B and C report the difference between the group means specified in a cell (i.e., the mean for women minus the mean for men or the minority group mean minus the white mean) divided by the standard deviation of the pooled scores from the same session (Baseline or Evaluation) and treatment or across treatments where the table refers to pooled scores. E indicates the Extroversion treatment, NP the No Priming treatment, and I the Introversion treatment. Panels A, B, and C also report significance levels for two-sided t-tests of the equality of means. For d-statistics in italics, we reject the equality at the 10% significance level. In bold, we reject the equality at the 5% significance level. In bold and italics, we reject the equality at the 1% significance level. Beside each d-statistic, we report the significance level for the same tests using sharpened q-values to account for the 40 hypotheses in Panel A and the 80 hypotheses in Panels B and C. Significance levels: <sup>!</sup>p &#x0003C; 0.01,<sup>&#x02020;</sup>p &#x0003C; 0.05, <sup>&#x00023;</sup>p &#x0003C; 0.10. Panel D reports power calculations for a significance level of 0.05 for effect sizes of 0.2, 0.5, and 0.8 for the groups given in the panels while also reporting the sample sizes for each group by treatment informing these power calculations. The calculations assume that the groups&#x00027; scores have common variance, which we assume equals one so that the effects correspond to the standardized effects in the upper panels.</p>
</table-wrap-foot>
</table-wrap>
<p>The second row of Panel A reports standardized effect sizes for each personality trait pooling the Evaluation scores from all treatments. McGee and McGee (<xref ref-type="bibr" rid="B35">2024</xref>) fail to reject the equality of the correlations between the incentivized and unincentivized personality measures across treatments&#x02014;suggesting that the information in the job ads has only second-order effects on responding behavior relative to the effects of the incentives themselves. Notably, all of the standardized gender differences in the pooled Evaluation scores are &#x0003C; 0.12 in absolute value, and none are statistically significant even before the multiple hypotheses corrections. At first glance, incentives for misrepresentation alone appear sufficient to attenuate the gender differences in personality trait measures.</p>
<p>The remainder of Panel A reports the standardized gender differences by trait and treatment for the Baseline and Evaluation scores, but we would reach similar conclusions analyzing the scores by treatment. The Baseline gender differences by treatment are mostly consistent with the pooled differences, but the variability in magnitudes highlights the role of sampling variance in smaller treatment-specific samples and the importance of within-subject designs. Turning to the Evaluation measures, the gender differences for every trait in every treatment are uniformly small. Eight of the 15 treatment-specific gender differences in the Evaluation measures are &#x0003C; 0.1 in absolute value, while only one is &#x0003E;0.2.</p>
<p><xref ref-type="fig" rid="F1">Figure 1</xref> displays by treatment the mean faking levels by gender and the quartile in which the subject falls of the pooled Baseline score distribution for each trait. Two things are apparent. First, opportunity-to-fake matters as mean faking levels decrease monotonically moving from the lowest to the highest quartile of Baseline scores. Second, one can infer from the confidence intervals that we fail to reject the gender equality of mean faking in virtually every quartile for every trait in every treatment.</p>
<fig id="F1" position="float">
<label>Figure 1</label>
<caption><p>Mean faking by gender, trait, quartile and treatment. Each graph depicts the gender-specific mean changes in trait scores from the Baseline to Evaluation sessions for subjects in a given quartile of the Baseline trait score distribution (pooling subjects across treatments) along with 95% confidence intervals for the gender-specific means. For the treatment specified in the column and the Big Five trait specified in the row, we regress the change in scores (i.e., Evaluation score minus Baseline score) on indicators for the quartile of the pooled, Baseline score distribution in which the subject fell and interactions between these quartile indicators and the indicator for being a woman with the intercept omitted. Below each plot we report the <italic>p-</italic>value from a heteroscedasticity-robust F-test of the null hypothesis that the quartile-female interactions are jointly significant followed after a comma by the sharpened <italic>q-</italic>values for the same hypothesis test accounting for the 15 hypotheses tested. <bold>(A)</bold> Extroversion. <bold>(B)</bold> No priming. <bold>(C)</bold> Introversion.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="frbhe-04-1499464-g0001.tif"/>
</fig>
<p>To test for gender differences in responses to incentives accounting for opportunity-to-fake, we regress each subject&#x00027;s change in scores on indicators for the quartile in which the subject falls of the pooled Baseline score distribution for a given trait along with interactions between the indicator for being a woman and the quartile indicators. Below each plot in <xref ref-type="fig" rid="F1">Figure 1</xref>, we report the <italic>p-</italic>values from heteroskedasticity-robust F-tests of the joint significance of the woman-quartile interactions for each regression along with sharpened <italic>q-</italic>values to account for the 15 hypotheses tested in <xref ref-type="fig" rid="F1">Figure 1</xref>. Using either the <italic>p-</italic> or <italic>q-</italic>values, we fail to reject the joint insignificance of the woman-quartile interactions for all 15 hypotheses. Men and women appear to respond similarly to incentives when misrepresenting themselves.<xref ref-type="fn" rid="fn0018"><sup>18</sup></xref></p>
<p>To test whether incentives or the combination of incentives and information attenuate the gender differences in the Baseline scores, we estimate for each trait:</p>
<disp-formula id="E1"><mml:math id="M1"><mml:mtable columnalign="center"><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>&#x0002B;</mml:mo><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mi>W</mml:mi><mml:mi>o</mml:mi><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x0002B;</mml:mo><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mi>E</mml:mi><mml:mi>v</mml:mi><mml:mi>a</mml:mi><mml:mi>l</mml:mi><mml:mi>u</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>i</mml:mi><mml:mi>o</mml:mi><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>&#x0002B;</mml:mo><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mi>W</mml:mi><mml:mi>o</mml:mi><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mtext>&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;</mml:mtext><mml:mo>*</mml:mo><mml:mtext>&#x000A0;</mml:mtext><mml:mi>E</mml:mi><mml:mi>v</mml:mi><mml:mi>a</mml:mi><mml:mi>l</mml:mi><mml:mi>u</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>i</mml:mi><mml:mi>o</mml:mi><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>&#x0002B;</mml:mo><mml:msub><mml:mrow><mml:mi>&#x003B5;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mtext>&#x000A0;</mml:mtext></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>where <italic>T</italic><sub><italic>i, j, k</italic></sub> is the raw (i.e., non-standardized) score for trait <italic>i</italic> for respondent <italic>j</italic> from session <italic>k</italic> (i.e., Baseline or Evaluation), <italic>Woman</italic><sub><italic>j</italic></sub> and <italic>Evaluation</italic><sub><italic>k</italic></sub> indicators for whether a subject is a woman and the score from the Evaluation session, respectively, and &#x003B5;<sub><italic>i, j, k</italic></sub> an econometric error term. These estimates are reported in the odd-numbered columns of <xref ref-type="table" rid="T2">Table 2</xref> for each trait. We test the hypothesis that <italic>a</italic><sub>1</sub>&#x0002B;<italic>a</italic><sub>3</sub> &#x0003D; 0. The null hypothesis is that the gender difference in Baseline scores for a given trait is completely attenuated by the incentives in the Evaluation session. This hypothesis can be violated in many ways (e.g., partial attenuation, exacerbation of gender differences, reversals of gender differences), but for every trait we fail to reject the null that incentives completely attenuate the gender differences in unincentivized personality measures.</p>
<table-wrap position="float" id="T2">
<label>Table 2</label>
<caption><p>Testing for attenuation of gender gaps in evaluation scores.</p></caption>
<table frame="box" rules="all">
<thead>
<tr style="background-color:#8f9496;color:#ffffff">
<th valign="top" align="center" colspan="11"><bold>Dependent variable</bold></th>
</tr>
</thead>
<tbody>
<tr style="background-color:#8f9496;color:#ffffff">
<td/>
<td valign="top" align="center" colspan="2"><bold>Ext</bold>.</td>
<td valign="top" align="center" colspan="2"><bold>Con</bold>.</td>
<td valign="top" align="center" colspan="2"><bold>Agr</bold>.</td>
<td valign="top" align="center" colspan="2"><bold>Ope</bold>.</td>
<td valign="top" align="center" colspan="2"><bold>Em. Stab</bold>.</td>
</tr>
<tr style="background-color:#8f9496;color:#ffffff">
<td valign="top" align="left"><bold>Controls</bold></td>
<td valign="top" align="center"><bold>(1)</bold></td>
<td valign="top" align="center"><bold>(2)</bold></td>
<td valign="top" align="center"><bold>(3)</bold></td>
<td valign="top" align="center"><bold>(4)</bold></td>
<td valign="top" align="center"><bold>(5)</bold></td>
<td valign="top" align="center"><bold>(6)</bold></td>
<td valign="top" align="center"><bold>(7)</bold></td>
<td valign="top" align="center"><bold>(8)</bold></td>
<td valign="top" align="center"><bold>(9)</bold></td>
<td valign="top" align="center"><bold>(10)</bold></td>
</tr> <tr>
<td valign="top" align="left">Woman (<italic>a</italic><sub>1</sub>)</td>
<td valign="top" align="center">&#x02212;1.1</td>
<td/>
<td valign="top" align="center">0.1</td>
<td/>
<td valign="top" align="center">2.7<sup>!</sup></td>
<td/>
<td valign="top" align="center">&#x02212;2.6<sup>!</sup></td>
<td/>
<td valign="top" align="center">&#x02212;5.1<sup>!</sup></td>
<td/>
</tr> <tr>
<td/>
<td valign="top" align="center">(1.1)</td>
<td/>
<td valign="top" align="center">(1.0)</td>
<td/>
<td valign="top" align="center">(0.9)</td>
<td/>
<td valign="top" align="center">(0.9)</td>
<td/>
<td valign="top" align="center">(1.1)</td>
<td/>
</tr> <tr>
<td valign="top" align="left">Evaluation (<italic>a</italic><sub>2</sub>)</td>
<td valign="top" align="center">9.4<sup>!</sup></td>
<td/>
<td valign="top" align="center">14.6<sup>!</sup></td>
<td/>
<td valign="top" align="center">7.1<sup>!</sup></td>
<td/>
<td valign="top" align="center">7.3<sup>!</sup></td>
<td/>
<td valign="top" align="center">15.7<sup>!</sup></td>
<td/>
</tr> <tr>
<td/>
<td valign="top" align="center">(1.1)</td>
<td/>
<td valign="top" align="center">(1.0)</td>
<td/>
<td valign="top" align="center">(0.9)</td>
<td/>
<td valign="top" align="center">(0.9)</td>
<td/>
<td valign="top" align="center">(1.2)</td>
<td/>
</tr> <tr>
<td valign="top" align="left">Woman<sup>&#x0002A;</sup></td>
<td valign="top" align="center">1.2</td>
<td/>
<td valign="top" align="center">&#x02212;0.5</td>
<td/>
<td valign="top" align="center">&#x02212;2.7<sup>&#x02020;</sup></td>
<td/>
<td valign="top" align="center">1.8</td>
<td/>
<td valign="top" align="center">3.4<sup>&#x02020;</sup></td>
<td/>
</tr> <tr>
<td valign="top" align="left">Evaluation (<italic>a</italic><sub>3</sub>)</td>
<td valign="top" align="center">(1.6)</td>
<td/>
<td valign="top" align="center">(1.5)</td>
<td/>
<td valign="top" align="center">(1.2)</td>
<td/>
<td valign="top" align="center">(1.2)</td>
<td/>
<td valign="top" align="center">(1.7)</td>
<td/>
</tr> <tr>
<td valign="top" align="left">No Priming (<italic>b</italic><sub>1</sub>)</td>
<td/>
<td valign="top" align="center">2.8</td>
<td/>
<td valign="top" align="center">&#x02212;3.3<sup>&#x00023;</sup></td>
<td/>
<td valign="top" align="center">&#x02212;2.0</td>
<td/>
<td valign="top" align="center">1.9</td>
<td/>
<td valign="top" align="center">1.4</td>
</tr> <tr>
<td/>
<td/>
<td valign="top" align="center">(1.9)</td>
<td/>
<td valign="top" align="center">(1.8)</td>
<td/>
<td valign="top" align="center">(1.5)</td>
<td/>
<td valign="top" align="center">(1.6)</td>
<td/>
<td valign="top" align="center">(2.0)</td>
</tr> <tr>
<td valign="top" align="left">Introversion (<italic>b</italic><sub>2</sub>)</td>
<td/>
<td valign="top" align="center">3.4<sup>&#x00023;</sup></td>
<td/>
<td valign="top" align="center">&#x02212;0.7</td>
<td/>
<td valign="top" align="center">&#x02212;0.1</td>
<td/>
<td valign="top" align="center">2.8<sup>&#x00023;</sup></td>
<td/>
<td valign="top" align="center">0.9</td>
</tr> <tr>
<td/>
<td/>
<td valign="top" align="center">(1.9)</td>
<td/>
<td valign="top" align="center">(1.5)</td>
<td/>
<td valign="top" align="center">(1.5)</td>
<td/>
<td valign="top" align="center">(1.5)</td>
<td/>
<td valign="top" align="center">(1.9)</td>
</tr> <tr>
<td valign="top" align="left">Extroversion<sup>&#x0002A;</sup></td>
<td/>
<td valign="top" align="center">0.5</td>
<td/>
<td valign="top" align="center">0.0</td>
<td/>
<td valign="top" align="center">1.0</td>
<td/>
<td valign="top" align="center">&#x02212;1.7</td>
<td/>
<td valign="top" align="center">&#x02212;3.5<sup>&#x00023;</sup></td>
</tr> <tr>
<td valign="top" align="left">Woman (<italic>b</italic><sub>3</sub>)</td>
<td/>
<td valign="top" align="center">(1.9)</td>
<td/>
<td valign="top" align="center">(1.7)</td>
<td/>
<td valign="top" align="center">(1.4)</td>
<td/>
<td valign="top" align="center">(1.6)</td>
<td/>
<td valign="top" align="center">(2.0)</td>
</tr> <tr>
<td valign="top" align="left">No Priming<sup>&#x0002A;</sup></td>
<td/>
<td valign="top" align="center">&#x02212;2.1</td>
<td/>
<td valign="top" align="center">1.1</td>
<td/>
<td valign="top" align="center">4.6<sup>!</sup></td>
<td/>
<td valign="top" align="center">&#x02212;3.5<sup>&#x02020;</sup></td>
<td/>
<td valign="top" align="center">&#x02212;8.8<sup>!</sup></td>
</tr> <tr>
<td valign="top" align="left">Woman (<italic>b</italic><sub>4</sub>)</td>
<td/>
<td valign="top" align="center">(1.9)</td>
<td/>
<td valign="top" align="center">(1.8)</td>
<td/>
<td valign="top" align="center">(1.5)</td>
<td/>
<td valign="top" align="center">(1.6)</td>
<td/>
<td valign="top" align="center">(2.1)</td>
</tr> <tr>
<td valign="top" align="left">Introversion<sup>&#x0002A;</sup></td>
<td/>
<td valign="top" align="center">&#x02212;1.4</td>
<td/>
<td valign="top" align="center">&#x02212;1.2</td>
<td/>
<td valign="top" align="center">2.7<sup>&#x00023;</sup></td>
<td/>
<td valign="top" align="center">&#x02212;2.6<sup>&#x00023;</sup></td>
<td/>
<td valign="top" align="center">&#x02212;3.5<sup>&#x00023;</sup></td>
</tr> <tr>
<td valign="top" align="left">Woman (<italic>b</italic><sub>5</sub>)</td>
<td/>
<td valign="top" align="center">(1.7)</td>
<td/>
<td valign="top" align="center">(1.6)</td>
<td/>
<td valign="top" align="center">(1.5)</td>
<td/>
<td valign="top" align="center">(1.4)</td>
<td/>
<td valign="top" align="center">(1.9)</td>
</tr> <tr>
<td valign="top" align="left">Extroversion<sup>&#x0002A;</sup></td>
<td/>
<td valign="top" align="center">16.8<sup>!</sup></td>
<td/>
<td valign="top" align="center">14.5<sup>!</sup></td>
<td/>
<td valign="top" align="center">7.2<sup>!</sup></td>
<td/>
<td valign="top" align="center">11.2<sup>!</sup></td>
<td/>
<td valign="top" align="center">20.0<sup>!</sup></td>
</tr> <tr>
<td valign="top" align="left">Evaluation (<italic>b</italic><sub>6</sub>)</td>
<td/>
<td valign="top" align="center">(2.1)</td>
<td/>
<td valign="top" align="center">(1.7)</td>
<td/>
<td valign="top" align="center">(1.5)</td>
<td/>
<td valign="top" align="center">(1.7)</td>
<td/>
<td valign="top" align="center">(2.0)</td>
</tr> <tr>
<td valign="top" align="left">No Priming<sup>&#x0002A;</sup></td>
<td/>
<td valign="top" align="center">8.3<sup>!</sup></td>
<td/>
<td valign="top" align="center">13.9<sup>!</sup></td>
<td/>
<td valign="top" align="center">5.8<sup>!</sup></td>
<td/>
<td valign="top" align="center">6.2<sup>!</sup></td>
<td/>
<td valign="top" align="center">13.2<sup>!</sup></td>
</tr> <tr>
<td valign="top" align="left">Evaluation (<italic>b</italic><sub>7</sub>)</td>
<td/>
<td valign="top" align="center">(1.9)</td>
<td/>
<td valign="top" align="center">(1.9)</td>
<td/>
<td valign="top" align="center">(1.5)</td>
<td/>
<td valign="top" align="center">(1.5)</td>
<td/>
<td valign="top" align="center">(2.1)</td>
</tr> <tr>
<td valign="top" align="left">Introversion<sup>&#x0002A;</sup></td>
<td/>
<td valign="top" align="center">3.4<sup>&#x00023;</sup></td>
<td/>
<td valign="top" align="center">15.3<sup>!</sup></td>
<td/>
<td valign="top" align="center">8.2<sup>!</sup></td>
<td/>
<td valign="top" align="center">4.7<sup>!</sup></td>
<td/>
<td valign="top" align="center">14.1<sup>!</sup></td>
</tr> <tr>
<td valign="top" align="left">Evaluation (<italic>b</italic><sub>8</sub>)</td>
<td/>
<td valign="top" align="center">(1.7)</td>
<td/>
<td valign="top" align="center">(1.6)</td>
<td/>
<td valign="top" align="center">(1.5)</td>
<td/>
<td valign="top" align="center">(1.3)</td>
<td/>
<td valign="top" align="center">(2.0)</td>
</tr> <tr>
<td valign="top" align="left">Evaluation<sup>&#x0002A;</sup>Woman</td>
<td/>
<td valign="top" align="center">0.6</td>
<td/>
<td valign="top" align="center">&#x02212;0.4</td>
<td/>
<td valign="top" align="center">&#x02212;2.2</td>
<td/>
<td valign="top" align="center">1.4</td>
<td/>
<td valign="top" align="center">1.9</td>
</tr> <tr>
<td valign="top" align="left"><sup>&#x0002A;</sup>Extroversion (<italic>b</italic><sub>9</sub>)</td>
<td/>
<td valign="top" align="center">(2.8)</td>
<td/>
<td valign="top" align="center">(2.4)</td>
<td/>
<td valign="top" align="center">(2.0)</td>
<td/>
<td valign="top" align="center">(2.2)</td>
<td/>
<td valign="top" align="center">(2.8)</td>
</tr> <tr>
<td valign="top" align="left">Evaluation<sup>&#x0002A;</sup>Woman</td>
<td/>
<td valign="top" align="center">0.8</td>
<td/>
<td valign="top" align="center">&#x02212;1.8</td>
<td/>
<td valign="top" align="center">&#x02212;2.8</td>
<td/>
<td valign="top" align="center">2.0</td>
<td/>
<td valign="top" align="center">4.9</td>
</tr> <tr>
<td valign="top" align="left"><sup>&#x0002A;</sup>No Priming (<italic>b</italic><sub>10</sub>)</td>
<td/>
<td valign="top" align="center">(2.7)</td>
<td/>
<td valign="top" align="center">(2.7)</td>
<td/>
<td valign="top" align="center">(2.1)</td>
<td/>
<td valign="top" align="center">(2.2)</td>
<td/>
<td valign="top" align="center">(3.2)</td>
</tr> <tr>
<td valign="top" align="left">Evaluation<sup>&#x0002A;</sup>Woman</td>
<td/>
<td valign="top" align="center">0.5</td>
<td/>
<td valign="top" align="center">0.5</td>
<td/>
<td valign="top" align="center">&#x02212;3.4</td>
<td/>
<td valign="top" align="center">1.0</td>
<td/>
<td valign="top" align="center">2.8</td>
</tr> <tr>
<td valign="top" align="left"><sup>&#x0002A;</sup>Introversion (<italic>b</italic><sub>11</sub>)</td>
<td/>
<td valign="top" align="center">(2.5)</td>
<td/>
<td valign="top" align="center">(2.5)</td>
<td/>
<td valign="top" align="center">(2.1)</td>
<td/>
<td valign="top" align="center">(1.9)</td>
<td/>
<td valign="top" align="center">(2.9)</td>
</tr> <tr>
<td valign="top" align="left">Constant</td>
<td valign="top" align="center">68.9<sup>!</sup></td>
<td valign="top" align="center">66.8<sup>!</sup></td>
<td valign="top" align="center">66.4<sup>!</sup></td>
<td valign="top" align="center">67.7<sup>!</sup></td>
<td valign="top" align="center">72.9<sup>!</sup></td>
<td valign="top" align="center">73.6<sup>!</sup></td>
<td valign="top" align="center">73.5<sup>!</sup></td>
<td valign="top" align="center">71.9<sup>!</sup></td>
<td valign="top" align="center">64.4<sup>!</sup></td>
<td valign="top" align="center">63.6<sup>!</sup></td>
</tr> <tr>
<td/>
<td valign="top" align="center">(0.8)</td>
<td valign="top" align="center">(1.4)</td>
<td valign="top" align="center">(0.7)</td>
<td valign="top" align="center">(1.2)</td>
<td valign="top" align="center">(0.6)</td>
<td valign="top" align="center">(1.1)</td>
<td valign="top" align="center">(0.6)</td>
<td valign="top" align="center">(1.2)</td>
<td valign="top" align="center">(0.8)</td>
<td valign="top" align="center">(1.5)</td>
</tr> <tr>
<td valign="top" align="left">R<sup>2</sup></td>
<td valign="top" align="center">0.14</td>
<td valign="top" align="center">0.21</td>
<td valign="top" align="center">0.29</td>
<td valign="top" align="center">0.30</td>
<td valign="top" align="center">0.10</td>
<td valign="top" align="center">0.11</td>
<td valign="top" align="center">0.17</td>
<td valign="top" align="center">0.19</td>
<td valign="top" align="center">0.32</td>
<td valign="top" align="center">0.34</td>
</tr> <tr style="background-color:#dee1e1;">
<td valign="top" align="left" colspan="6"><bold>Hypothesis tests (</bold><italic><bold>p</bold></italic><bold>-value, sharpened</bold> <italic><bold>q-</bold></italic><bold>value)</bold></td>
</tr> <tr>
<td valign="top" align="left">(1) <italic>a</italic><sub>1</sub>&#x0002B;<italic>a</italic><sub>3</sub> &#x0003D; 0</td>
<td valign="top" align="center">(0.93, 1.00)</td>
<td valign="top" align="center">(0.68, 1.00)</td>
<td valign="top" align="center">(0.95, 1.00)</td>
<td valign="top" align="center">(0.32, 1.00)</td>
<td valign="top" align="center">(0.18, 1.00)</td>
</tr> <tr>
<td valign="top" align="left">(2) <italic>b</italic><sub>3</sub>&#x0002B;<italic>b</italic><sub>9</sub> &#x0003D; 0</td>
<td valign="top" align="center">(0.61, 1.00)</td>
<td valign="top" align="center">(0.83, 1.00)</td>
<td valign="top" align="center">(0.36, 1.00)</td>
<td valign="top" align="center">(0.87, 1.00)</td>
<td valign="top" align="center">(0.42, 1.00)</td>
</tr> <tr>
<td valign="top" align="left">(3) <italic>b</italic><sub>4</sub>&#x0002B;<italic>b</italic><sub>10</sub> &#x0003D; 0</td>
<td valign="top" align="center">(0.51, 1.00)</td>
<td valign="top" align="center">(0.73, 1.00)</td>
<td valign="top" align="center">(0.23, 1.00)</td>
<td valign="top" align="center">(0.36, 1.00)</td>
<td valign="top" align="center">(0.11, 1.00)</td>
</tr> <tr>
<td valign="top" align="left">(4) <italic>b</italic><sub>5</sub>&#x0002B;<italic>b</italic><sub>11</sub> &#x0003D; 0</td>
<td valign="top" align="center">(0.62, 1.00)</td>
<td valign="top" align="center">(0.69, 1.00)</td>
<td valign="top" align="center">(0.67, 1.00)</td>
<td valign="top" align="center">(0.21, 1.00)</td>
<td valign="top" align="center">(0.71, 1.00)</td>
</tr> <tr>
<td valign="top" align="left">(2) &#x00026; (3) &#x00026; (4)</td>
<td valign="top" align="center">(0.81, 1.00)</td>
<td valign="top" align="center">(0.96, 1.00)</td>
<td valign="top" align="center">(0.47, 1.00)</td>
<td valign="top" align="center">(0.49, 1.00)</td>
<td valign="top" align="center">(0.34, 1.00)</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<p>The odd-numbered columns report coefficients from regressions of the scores for the personality trait indicated in the column on indicators for whether the subject was a woman, whether the score comes from an Evaluation session, and the interaction between the woman and Evaluation indicators. The omitted category represents Baseline scores for men pooled across treatments. The even-numbered columns report coefficients from regressions of the scores for the personality trait indicated in the column on indicators for whether the score comes from the No Priming or Introversion treatments, interactions between the indicator for being a woman and three treatment indicators, interactions between the treatment indicators and the indicator for scores from Evaluation sessions, and the triple interaction terms for the woman-treatment-Evaluation combinations. The omitted category represents Baseline scores for men in the Extroversion treatment. Heteroskedasticity-robust standard errors are given in parentheses. Significance levels: <sup>!</sup>p &#x0003C; 0.01,<sup>&#x02020;</sup>p &#x0003C; 0.05, <sup>&#x00023;</sup>p &#x0003C; 0.10. The bottom of the table reports p-values and sharpened q-values accounting for the 25 hypotheses tested for the hypothesis indicated in the row for the regression given in the column. The hypothesis &#x0201C;(2), (3), and (4)&#x0201D; refers to the joint hypothesis test for the hypotheses as numbered in the table. <sup>&#x0002A;</sup>is the multiplication operator, indicating that the coefficient in the row is the coefficient of an interaction between two or more variables (i.e., they are multiplied together).</p>
</table-wrap-foot>
</table-wrap>
<p>Pooling the Evaluation sessions, however, may obscure differences across treatments given the different priming in the job ads. To evaluate this possibility, we estimate for each trait:</p>
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<p>These estimates are reported in the even-numbered columns of <xref ref-type="table" rid="T2">Table 2</xref>. Here we test the hypotheses of complete attenuation of the treatment-specific gender differences in Baseline scores in the Evaluation scores for the same treatment: <italic>b</italic><sub>3</sub>&#x0002B;<italic>b</italic><sub>9</sub> &#x0003D; 0, <italic>b</italic><sub>4</sub>&#x0002B;<italic>b</italic><sub>10</sub> &#x0003D; 0, and <italic>b</italic><sub>5</sub>&#x0002B;<italic>b</italic><sub>11</sub> &#x0003D; 0. Similar to the tests pooling the treatments, however, we fail to reject the complete attenuation of the unincentivized gender differences for every trait and treatment combination when measured with incentives. We also fail to reject the joint hypothesis of complete attenuation in all three treatments. For women, incentives for misrepresentation alone appear sufficient to attenuate gender differences in unincentivized personality trait measures.</p>
</sec>
<sec>
<title>5.2 Race</title>
<p>Panels B and C of <xref ref-type="table" rid="T1">Table 1</xref> report the standardized mean differences between East Asian and White subjects and between subjects of other races and White subjects, respectively. East Asian subjects were moderately less extroverted (&#x02212;0.45), open to experience (&#x02212;0.56), and emotionally stable (&#x02212;0.35) than White subjects pooling Baseline scores, and similar differences exist in most treatments. Subjects of other races were more conscientious (0.30) than White subjects in the pooled Baseline scores (though not in the <italic>Extroversion</italic> treatment), but we observe no other significant differences.</p>
<p>More intriguing are the racial differences in incentivized scores. Pooling the Evaluation scores across treatments, the East Asian-White differences in conscientiousness, agreeableness, and emotional stability are statistically significant after accounting for multiple hypotheses using the sharpened <italic>q-</italic>values. Indeed, only the East Asian-White difference in extroversion is not significant prior to accounting for multiple hypotheses, but this is also the trait for which pooling the Evaluation scores is problematic given the countervailing priming in the <italic>Extroversion</italic> and <italic>Introversion</italic> treatments. Notably, the East Asian-White differences in conscientiousness and agreeableness were not present in the Baseline scores. Likewise, statistically significant differences between White subjects and subjects of other races in agreeableness and emotional stability emerge using the pooled Evaluation scores where no similar differences existed in the pooled Baseline scores.</p>
<p>That incentives do not appear to attenuate racial differences in the unincentivized scores is also apparent when looking at the treatment-specific standardized differences. Where there were seven significant gender differences in Baseline scores by treatment in Panel A, none of the gender differences were significant using the Evaluation scores. By contrast, four (three) East Asian-White (other race-White) Baseline score differences by treatment are significant in Panels B and C, but six (four) differences in Evaluation scores are significant. Moreover, five (four) of these East Asian-White (other race-White) Evaluation differences occur where no significant difference in Baseline scores existed. Where only small differences between subjects of other races and White subjects exist in the pooled Baseline scores, many of the differences in Evaluation scores would be described as medium-sized, and all would disadvantage subjects of other races.<xref ref-type="fn" rid="fn0019"><sup>19</sup></xref></p>
<p>To formally test whether incentives attenuate racial differences in unincentivized scores, we estimate regressions similar to those described in <xref ref-type="table" rid="T2">Table 2</xref> replacing the indicator for being a woman with indicators for being East Asian or another race. Pooling the treatments and interacting the race indicators with only an indicator for the Evaluation session in the odd-numbered columns of <xref ref-type="table" rid="T3">Table 3</xref>, we reject the hypotheses of complete attenuation of the East Asian-White differences in unincentivized measures when measured with incentives for every trait except extroversion even after correcting for multiple hypotheses. Likewise we reject the complete attenuation of the other race-White differences for agreeableness and emotional stability pooling the treatments. Disaggregating the Evaluation sessions and including treatment indicators in the second set of regressions in the even-numbered columns of <xref ref-type="table" rid="T3">Table 3</xref>, we continue to reject the complete attenuation hypotheses in the majority of trait-treatment-group comparisons. After accounting for the 55 hypotheses tested in <xref ref-type="table" rid="T3">Table 3</xref>, we reject 28 of these hypotheses at the 10% significance level using the sharpened <italic>q-</italic>values.</p>
<table-wrap position="float" id="T3">
<label>Table 3</label>
<caption><p>Testing for attenuation of racial gaps in evaluation scores.</p></caption>
<table frame="box" rules="all">
<thead>
<tr style="background-color:#8f9496;color:#ffffff">
<th valign="top" align="center" colspan="11"><bold>Dependent variable</bold></th>
</tr>
</thead>
<tbody>
<tr style="background-color:#8f9496;color:#ffffff">
<td/>
<td valign="top" align="center" colspan="2"><bold>Ext</bold>.</td>
<td valign="top" align="center" colspan="2"><bold>Con</bold>.</td>
<td valign="top" align="center" colspan="2"><bold>Agr</bold>.</td>
<td valign="top" align="center" colspan="2"><bold>Ope</bold>.</td>
<td valign="top" align="center" colspan="2"><bold>Em. Stab</bold>.</td>
</tr>
<tr style="background-color:#8f9496;color:#ffffff">
<td valign="top" align="left"><bold>Controls</bold></td>
<td valign="top" align="center"><bold>(1)</bold></td>
<td valign="top" align="center"><bold>(2)</bold></td>
<td valign="top" align="center"><bold>(3)</bold></td>
<td valign="top" align="center"><bold>(4)</bold></td>
<td valign="top" align="center"><bold>(5)</bold></td>
<td valign="top" align="center"><bold>(6)</bold></td>
<td valign="top" align="center"><bold>(7)</bold></td>
<td valign="top" align="center"><bold>(8)</bold></td>
<td valign="top" align="center"><bold>(9)</bold></td>
<td valign="top" align="center"><bold>(10)</bold></td>
</tr>
<tr>
<td valign="top" align="left">East Asian (a<sub>1</sub>)</td>
<td valign="top" align="center">&#x02212;5.2<sup>!</sup></td>
<td/>
<td valign="top" align="center">0.8</td>
<td/>
<td valign="top" align="center">&#x02212;1.3</td>
<td/>
<td valign="top" align="center">&#x02212;5.3<sup>!</sup></td>
<td/>
<td valign="top" align="center">&#x02212;4.5<sup>!</sup></td>
</tr>
<tr>
<td valign="top" align="left">(1.3)</td>
<td/>
<td valign="top" align="center">(1.2)</td>
<td/>
<td valign="top" align="center">(1.2)</td>
<td/>
<td valign="top" align="center">(1.0)</td>
<td/>
<td valign="top" align="center">(1.5)</td>
</tr>
<tr>
<td valign="top" align="left">Other race (a<sub>2</sub>)</td>
<td valign="top" align="center">0.5</td>
<td/>
<td valign="top" align="center">3.3<sup>&#x02020;</sup></td>
<td/>
<td valign="top" align="center">0.2</td>
<td/>
<td valign="top" align="center">&#x02212;1.2</td>
<td/>
<td valign="top" align="center">&#x02212;2.5</td>
</tr>
<tr>
<td valign="top" align="left">(1.4)</td>
<td/>
<td valign="top" align="center">(1.5)</td>
<td/>
<td valign="top" align="center">(1.3)</td>
<td/>
<td valign="top" align="center">(1.2)</td>
<td/>
<td valign="top" align="center">(1.6)</td>
</tr>
<tr>
<td valign="top" align="left">Evaluation (a<sub>3</sub>)</td>
<td valign="top" align="center">6.9<sup>!</sup></td>
<td/>
<td valign="top" align="center">17.8<sup>!</sup></td>
<td/>
<td valign="top" align="center">7.9<sup>!</sup></td>
<td/>
<td valign="top" align="center">6.7<sup>!</sup></td>
<td/>
<td valign="top" align="center">18.8<sup>!</sup></td>
</tr>
<tr>
<td valign="top" align="left">(1.7)</td>
<td/>
<td valign="top" align="center">(1.5)</td>
<td/>
<td valign="top" align="center">(1.4)</td>
<td/>
<td valign="top" align="center">(1.1)</td>
<td/>
<td valign="top" align="center">(1.7)</td>
</tr>
<tr>
<td valign="top" align="left">East Asian&#x0002A;</td>
<td valign="top" align="center">6.0<sup>!</sup></td>
<td/>
<td valign="top" align="center">&#x02212;4.6<sup>&#x02020;</sup></td>
<td/>
<td valign="top" align="center">&#x02212;3.0<sup>&#x00023;</sup></td>
<td/>
<td valign="top" align="center">3.1<sup>&#x02020;</sup></td>
<td/>
<td valign="top" align="center">&#x02212;1.0</td>
</tr>
<tr>
<td valign="top" align="left">Evaluation (a<sub>4</sub>)</td>
<td valign="top" align="center">(2.1)</td>
<td/>
<td valign="top" align="center">(1.8)</td>
<td/>
<td valign="top" align="center">(1.6)</td>
<td/>
<td valign="top" align="center">(1.5)</td>
<td/>
<td valign="top" align="center">(2.1)</td>
</tr>
<tr>
<td valign="top" align="left">Other race&#x0002A;</td>
<td valign="top" align="center">0.5</td>
<td/>
<td valign="top" align="center">&#x02212;4.6<sup>&#x02020;</sup></td>
<td/>
<td valign="top" align="center">&#x02212;2.9</td>
<td/>
<td valign="top" align="center">0.0</td>
<td/>
<td valign="top" align="center">&#x02212;2.8</td>
</tr>
<tr>
<td valign="top" align="left">Evaluation (a<sub>5</sub>)</td>
<td valign="top" align="center">(2.1)</td>
<td/>
<td valign="top" align="center">(2.1)</td>
<td/>
<td valign="top" align="center">(1.9)</td>
<td/>
<td valign="top" align="center">(1.6)</td>
<td/>
<td valign="top" align="center">(2.3)</td>
</tr>
<tr>
<td valign="top" align="left">No Priming (b<sub>1</sub>)</td>
<td/>
<td valign="top" align="center">&#x02212;0.6</td>
<td/>
<td valign="top" align="center">&#x02212;6.3<sup>&#x02020;</sup></td>
<td/>
<td valign="top" align="center">&#x02212;1.4</td>
<td/>
<td valign="top" align="center">1.7</td>
<td/>
<td valign="top" align="center">&#x02212;2.8</td>
</tr>
<tr>
<td valign="top" align="left">(2.9)</td>
<td/>
<td valign="top" align="center">(2.6)</td>
<td/>
<td valign="top" align="center">(2.7)</td>
<td/>
<td valign="top" align="center">(2.2)</td>
<td/>
<td valign="top" align="center">(3.3)</td>
</tr>
<tr>
<td valign="top" align="left">Introversion (b<sub>2</sub>)</td>
<td/>
<td valign="top" align="center">&#x02212;1.8</td>
<td/>
<td valign="top" align="center">&#x02212;4.2<sup>&#x00023;</sup></td>
<td/>
<td valign="top" align="center">1.6</td>
<td/>
<td valign="top" align="center">1.7</td>
<td/>
<td valign="top" align="center">&#x02212;0.5</td>
</tr>
<tr>
<td valign="top" align="left">(3.0)</td>
<td/>
<td valign="top" align="center">(2.5)</td>
<td/>
<td valign="top" align="center">(2.7)</td>
<td/>
<td valign="top" align="center">(2.1)</td>
<td/>
<td valign="top" align="center">(3.0)</td>
</tr>
<tr>
<td valign="top" align="left">Extroversion&#x0002A;</td>
<td/>
<td valign="top" align="center">&#x02212;7.4<sup>!</sup></td>
<td/>
<td valign="top" align="center">&#x02212;1.1</td>
<td/>
<td valign="top" align="center">&#x02212;1.3</td>
<td/>
<td valign="top" align="center">&#x02212;4.5<sup>&#x02020;</sup></td>
<td/>
<td valign="top" align="center">&#x02212;4.1</td>
</tr>
<tr>
<td valign="top" align="left">East Asian (b<sub>3</sub>)</td>
<td/>
<td valign="top" align="center">(2.7)</td>
<td/>
<td valign="top" align="center">(2.1)</td>
<td/>
<td valign="top" align="center">(2.2)</td>
<td/>
<td valign="top" align="center">(2.0)</td>
<td/>
<td valign="top" align="center">(2.6)</td>
</tr>
<tr>
<td valign="top" align="left">No Priming&#x0002A;</td>
<td/>
<td valign="top" align="center">&#x02212;4.6<sup>&#x02020;</sup></td>
<td/>
<td valign="top" align="center">1.7</td>
<td/>
<td valign="top" align="center">0.8</td>
<td/>
<td valign="top" align="center">&#x02212;6.2<sup>!</sup></td>
<td/>
<td valign="top" align="center">&#x02212;5.0<sup>&#x00023;</sup></td>
</tr>
<tr>
<td valign="top" align="left">East Asian (b<sub>4</sub>)</td>
<td/>
<td valign="top" align="center">(2.2)</td>
<td/>
<td valign="top" align="center">(2.1)</td>
<td/>
<td valign="top" align="center">(2.1)</td>
<td/>
<td valign="top" align="center">(1.7)</td>
<td/>
<td valign="top" align="center">(2.8)</td>
</tr>
<tr>
<td valign="top" align="left">Introversion&#x0002A;</td>
<td/>
<td valign="top" align="center">&#x02212;3.3</td>
<td/>
<td valign="top" align="center">0.3</td>
<td/>
<td valign="top" align="center">&#x02212;2.8</td>
<td/>
<td valign="top" align="center">&#x02212;4.6<sup>!</sup></td>
<td/>
<td valign="top" align="center">&#x02212;4.8&#x00023;$</td>
</tr>
<tr>
<td valign="top" align="left">East Asian (b<sub>5</sub>)</td>
<td/>
<td valign="top" align="center">(2.2)</td>
<td/>
<td valign="top" align="center">(2.1)</td>
<td/>
<td valign="top" align="center">(2.1)</td>
<td/>
<td valign="top" align="center">(1.7)</td>
<td/>
<td valign="top" align="center">(2.5)</td>
</tr>
<tr>
<td valign="top" align="left">Extroversion&#x0002A;</td>
<td/>
<td valign="top" align="center">&#x02212;1.1</td>
<td/>
<td valign="top" align="center">&#x02212;2.2</td>
<td/>
<td valign="top" align="center">1.1</td>
<td/>
<td valign="top" align="center">&#x02212;0.9</td>
<td/>
<td valign="top" align="center">&#x02212;7.2<sup>&#x02020;</sup></td>
</tr>
<tr>
<td valign="top" align="left">Other race (b<sub>6</sub>)</td>
<td/>
<td valign="top" align="center">(2.9)</td>
<td/>
<td valign="top" align="center">(2.9)</td>
<td/>
<td valign="top" align="center">(2.5)</td>
<td/>
<td valign="top" align="center">(2.5)</td>
<td/>
<td valign="top" align="center">(3.0)</td>
</tr>
<tr>
<td valign="top" align="left">No Priming&#x0002A;</td>
<td/>
<td valign="top" align="center">&#x02212;0.5</td>
<td/>
<td valign="top" align="center">6.2<sup>&#x02020;</sup></td>
<td/>
<td valign="top" align="center">0.6</td>
<td/>
<td valign="top" align="center">&#x02212;1.3</td>
<td/>
<td valign="top" align="center">1.0</td>
</tr>
<tr>
<td valign="top" align="left">Other race (b<sub>7</sub>)</td>
<td/>
<td valign="top" align="center">(2.2)</td>
<td/>
<td valign="top" align="center">(2.7)</td>
<td/>
<td valign="top" align="center">(2.4)</td>
<td/>
<td valign="top" align="center">(2.1)</td>
<td/>
<td valign="top" align="center">(3.2)</td>
</tr>
<tr>
<td valign="top" align="left">Introversion&#x0002A;</td>
<td/>
<td valign="top" align="center">2.4</td>
<td/>
<td valign="top" align="center">4.7<sup>&#x02020;</sup></td>
<td/>
<td valign="top" align="center">&#x02212;1.0</td>
<td/>
<td valign="top" align="center">&#x02212;1.3</td>
<td/>
<td valign="top" align="center">&#x02212;2.0</td>
</tr>
<tr>
<td valign="top" align="left">Other race (b<sub>8</sub>)</td>
<td/>
<td valign="top" align="center">(2.3)</td>
<td/>
<td valign="top" align="center">(2.1)</td>
<td/>
<td valign="top" align="center">(2.1)</td>
<td/>
<td valign="top" align="center">(1.7)</td>
<td/>
<td valign="top" align="center">(2.5)</td>
</tr>
<tr>
<td valign="top" align="left">Extroversion&#x0002A;</td>
<td/>
<td valign="top" align="center">14.7<sup>!</sup></td>
<td/>
<td valign="top" align="center">13.5<sup>!</sup></td>
<td/>
<td valign="top" align="center">8.9<sup>!</sup></td>
<td/>
<td valign="top" align="center">9.3<sup>!</sup></td>
<td/>
<td valign="top" align="center">20.3<sup>!</sup></td>
</tr>
<tr>
<td valign="top" align="left">Evaluation (b<sub>9</sub>)</td>
<td/>
<td valign="top" align="center">(3.5)</td>
<td/>
<td valign="top" align="center">(2.5)</td>
<td/>
<td valign="top" align="center">(2.5)</td>
<td/>
<td valign="top" align="center">(2.3)</td>
<td/>
<td valign="top" align="center">(2.9)</td>
</tr>
<tr>
<td valign="top" align="left">No Priming&#x0002A;</td>
<td/>
<td valign="top" align="center">7.9<sup>!</sup></td>
<td/>
<td valign="top" align="center">18.3<sup>!</sup></td>
<td/>
<td valign="top" align="center">6.4<sup>!</sup></td>
<td/>
<td valign="top" align="center">6.4<sup>!</sup></td>
<td/>
<td valign="top" align="center">18.8<sup>!</sup></td>
</tr>
<tr>
<td valign="top" align="left">Evaluation (b<sub>10</sub>)</td>
<td/>
<td valign="top" align="center">(2.5)</td>
<td/>
<td valign="top" align="center">(2.7)</td>
<td/>
<td valign="top" align="center">(2.4)</td>
<td/>
<td valign="top" align="center">(2.1)</td>
<td/>
<td valign="top" align="center">(3.2)</td>
</tr>
<tr>
<td valign="top" align="left">Introversion&#x0002A;</td>
<td/>
<td valign="top" align="center">0.9</td>
<td/>
<td valign="top" align="center">20.3<sup>!</sup></td>
<td/>
<td valign="top" align="center">8.5<sup>!</sup></td>
<td/>
<td valign="top" align="center">5.3<sup>!</sup></td>
<td/>
<td valign="top" align="center">17.8<sup>!</sup></td>
</tr>
<tr>
<td valign="top" align="left">Evaluation (b<sub>11</sub>)</td>
<td/>
<td valign="top" align="center">(2.6)</td>
<td/>
<td valign="top" align="center">(2.5)</td>
<td/>
<td valign="top" align="center">(2.4)</td>
<td/>
<td valign="top" align="center">(1.7)</td>
<td/>
<td valign="top" align="center">(2.6)</td>
</tr>
<tr>
<td valign="top" align="left">Evaluation&#x0002A;Asian</td>
<td/>
<td valign="top" align="center">4.4</td>
<td/>
<td valign="top" align="center">&#x02212;0.3</td>
<td/>
<td valign="top" align="center">&#x02212;3.9</td>
<td/>
<td valign="top" align="center">4.0</td>
<td/>
<td valign="top" align="center">0.0</td>
</tr>
<tr>
<td valign="top" align="left">&#x0002A;Extroversion (b<sub>12</sub>)</td>
<td/>
<td valign="top" align="center">(4.0)</td>
<td/>
<td valign="top" align="center">(2.9)</td>
<td/>
<td valign="top" align="center">(2.8)</td>
<td/>
<td valign="top" align="center">(2.8)</td>
<td/>
<td valign="top" align="center">(3.5)</td>
</tr>
<tr>
<td valign="top" align="left">Evaluation&#x0002A;Asian</td>
<td/>
<td valign="top" align="center">2.7</td>
<td/>
<td valign="top" align="center">&#x02212;6.0&#x00023;$</td>
<td/>
<td valign="top" align="center">&#x02212;3.0</td>
<td/>
<td valign="top" align="center">2.2</td>
<td/>
<td valign="top" align="center">&#x02212;2.3</td>
</tr>
<tr>
<td valign="top" align="left">&#x0002A;No Priming (b<sub>13</sub>)</td>
<td/>
<td valign="top" align="center">(3.3)</td>
<td/>
<td valign="top" align="center">(3.3)</td>
<td/>
<td valign="top" align="center">(2.8)</td>
<td/>
<td valign="top" align="center">(2.6)</td>
<td/>
<td valign="top" align="center">(4.0)</td>
</tr>
<tr>
<td valign="top" align="left">Evaluation&#x0002A;Asian</td>
<td/>
<td valign="top" align="center">4.4</td>
<td/>
<td valign="top" align="center">&#x02212;5.8&#x00023;$</td>
<td/>
<td valign="top" align="center">&#x02212;1.8</td>
<td/>
<td valign="top" align="center">0.3</td>
<td/>
<td valign="top" align="center">&#x02212;2.5</td>
</tr>
<tr>
<td valign="top" align="left">&#x0002A;Introversion (b<sub>14</sub>)</td>
<td/>
<td valign="top" align="center">(3.2)</td>
<td/>
<td valign="top" align="center">(3.2)</td>
<td/>
<td valign="top" align="center">(2.8)</td>
<td/>
<td valign="top" align="center">(2.3)</td>
<td/>
<td valign="top" align="center">(3.6)</td>
</tr>
<tr>
<td valign="top" align="left">Evaluation&#x0002A;Other</td>
<td/>
<td valign="top" align="center">&#x02212;0.5</td>
<td/>
<td valign="top" align="center">4.4</td>
<td/>
<td valign="top" align="center">&#x02212;3.0</td>
<td/>
<td valign="top" align="center">1.9</td>
<td/>
<td valign="top" align="center">3.4</td>
</tr>
<tr>
<td valign="top" align="left">&#x0002A;Extroversion (b<sub>15</sub>)</td>
<td/>
<td valign="top" align="center">(4.2)</td>
<td/>
<td valign="top" align="center">(3.9)</td>
<td/>
<td valign="top" align="center">(3.1)</td>
<td/>
<td valign="top" align="center">(3.3)</td>
<td/>
<td valign="top" align="center">(3.9)</td>
</tr>
<tr>
<td valign="top" align="left">Evaluation<sup>&#x0002A;</sup>Other</td>
<td/>
<td valign="top" align="center">&#x02212;2.4</td>
<td/>
<td valign="top" align="center">&#x02212;8.8<sup>&#x02020;</sup></td>
<td/>
<td valign="top" align="center">&#x02212;1.7</td>
<td/>
<td valign="top" align="center">&#x02212;1.2</td>
<td/>
<td valign="top" align="center">&#x02212;7.8<sup>&#x00023;</sup></td>
</tr> <tr>
<td valign="top" align="left"><sup>&#x0002A;</sup>No Priming (<italic>b</italic><sub>16</sub>)</td>
<td/>
<td valign="top" align="center">(3.4)</td>
<td/>
<td valign="top" align="center">(3.9)</td>
<td/>
<td valign="top" align="center">(3.2)</td>
<td/>
<td valign="top" align="center">(3.0)</td>
<td/>
<td valign="top" align="center">(4.5)</td>
</tr> <tr>
<td valign="top" align="left">Evaluation<sup>&#x0002A;</sup>Other</td>
<td/>
<td valign="top" align="center">3.2</td>
<td/>
<td valign="top" align="center">&#x02212;7.8<sup>&#x02020;</sup></td>
<td/>
<td valign="top" align="center">&#x02212;3.7</td>
<td/>
<td valign="top" align="center">&#x02212;0.5</td>
<td/>
<td valign="top" align="center">&#x02212;3.8</td>
</tr> <tr>
<td valign="top" align="left"><sup>&#x0002A;</sup>Introversion (<italic>b</italic><sub>17</sub>)</td>
<td/>
<td valign="top" align="center">(3.2)</td>
<td/>
<td valign="top" align="center">(3.2)</td>
<td/>
<td valign="top" align="center">(2.9)</td>
<td/>
<td valign="top" align="center">(2.3)</td>
<td/>
<td valign="top" align="center">(3.5)</td>
</tr> <tr>
<td valign="top" align="left">Constant</td>
<td valign="top" align="center">70.7<sup>!</sup></td>
<td valign="top" align="center">71.6<sup>!</sup></td>
<td valign="top" align="center">65.2<sup>!</sup></td>
<td valign="top" align="center">68.9<sup>!</sup></td>
<td valign="top" align="center">74.8<sup>!</sup></td>
<td valign="top" align="center">74.6<sup>!</sup></td>
<td valign="top" align="center">75.0<sup>!</sup></td>
<td valign="top" align="center">73.8<sup>!</sup></td>
<td valign="top" align="center">64.6<sup>!</sup></td>
<td valign="top" align="center">65.7<sup>!</sup></td>
</tr> <tr>
<td/>
<td valign="top" align="center">(1.1)</td>
<td valign="top" align="center">(2.4)</td>
<td valign="top" align="center">(1.0)</td>
<td valign="top" align="center">(1.8)</td>
<td valign="top" align="center">(1.1)</td>
<td valign="top" align="center">(2.0)</td>
<td valign="top" align="center">(0.8)</td>
<td valign="top" align="center">(1.7)</td>
<td valign="top" align="center">(1.2)</td>
<td valign="top" align="center">(2.3)</td>
</tr> <tr>
<td valign="top" align="left"><italic>R</italic><sup>2</sup></td>
<td valign="top" align="center">0.17</td>
<td valign="top" align="center">0.24</td>
<td valign="top" align="center">0.30</td>
<td valign="top" align="center">0.32</td>
<td valign="top" align="center">0.11</td>
<td valign="top" align="center">0.12</td>
<td valign="top" align="center">0.19</td>
<td valign="top" align="center">0.21</td>
<td valign="top" align="center">0.32</td>
<td valign="top" align="center">0.34</td>
</tr> <tr style="background-color:#dee1e1;">
<td valign="top" align="left" colspan="6"><bold>Hypothesis tests (</bold><italic><bold>p</bold></italic><bold>-value, sharpened</bold> <italic><bold>q-</bold></italic><bold>value)</bold></td>
</tr> <tr>
<td valign="top" align="left">(1) <italic>a</italic><sub>1</sub>&#x0002B;<italic>a</italic><sub>4</sub> &#x0003D; 0</td>
<td valign="top" align="center">(0.61, 0.41)</td>
<td valign="top" align="center">(0.01, 0.02)</td>
<td valign="top" align="center">(0.00, 0.01)</td>
<td valign="top" align="center">(0.03, 0.06)</td>
<td valign="top" align="center">(0.00, 0.01)</td>
</tr> <tr>
<td valign="top" align="left">(2) <italic>a</italic><sub>2</sub>&#x0002B;<italic>a</italic><sub>5</sub> &#x0003D; 0</td>
<td valign="top" align="center">(0.52, 0.36)</td>
<td valign="top" align="center">(0.39, 0.29)</td>
<td valign="top" align="center">(0.02, 0.05)</td>
<td valign="top" align="center">(0.27, 0.23)</td>
<td valign="top" align="center">(0.00, 0.01)</td>
</tr> <tr>
<td valign="top" align="left">(1) &#x00026; (2)</td>
<td valign="top" align="center">(0.81, 0.51)</td>
<td valign="top" align="center">(0.01, 0.04)</td>
<td valign="top" align="center">(0.00, 0.01)</td>
<td valign="top" align="center">(0.10, 0.11)</td>
<td valign="top" align="center">(0.00, 0.01)</td>
</tr> <tr>
<td valign="top" align="left">(3) <italic>b</italic><sub>3</sub>&#x0002B;<italic>b</italic><sub>12</sub> &#x0003D; 0</td>
<td valign="top" align="center">(0.31, 0.26)</td>
<td valign="top" align="center">(0.49, 0.35)</td>
<td valign="top" align="center">(0.00, 0.01)</td>
<td valign="top" align="center">(0.81, 0.51)</td>
<td valign="top" align="center">(0.07, 0.10)</td>
</tr> <tr>
<td valign="top" align="left">(4) <italic>b</italic><sub>4</sub>&#x0002B;<italic>b</italic><sub>13</sub> &#x0003D; 0</td>
<td valign="top" align="center">(0.46, 0.34)</td>
<td valign="top" align="center">(0.09, 0.11)</td>
<td valign="top" align="center">(0.23, 0.22)</td>
<td valign="top" align="center">(0.04, 0.06)</td>
<td valign="top" align="center">(0.01, 0.03)</td>
</tr> <tr>
<td valign="top" align="left">(5) <italic>b</italic><sub>5</sub>&#x0002B;<italic>b</italic><sub>14</sub> &#x0003D; 0</td>
<td valign="top" align="center">(0.63, 0.41)</td>
<td valign="top" align="center">(0.02, 0.05)</td>
<td valign="top" align="center">(0.02, 0.04)</td>
<td valign="top" align="center">(0.00, 0.02)</td>
<td valign="top" align="center">(0.00, 0.02)</td>
</tr> <tr>
<td valign="top" align="left">(3) &#x00026; (4) &#x00026; (5)</td>
<td valign="top" align="center">(0.61, 0.41)</td>
<td valign="top" align="center">(0.04, 0.06)</td>
<td valign="top" align="center">(0.00, 0.01)</td>
<td valign="top" align="center">(0.01, 0.02)</td>
<td valign="top" align="center">(0.00, 0.01)</td>
</tr> <tr>
<td valign="top" align="left">(6) <italic>b</italic><sub>6</sub>&#x0002B;<italic>b</italic><sub>15</sub> &#x0003D; 0</td>
<td valign="top" align="center">(0.60, 0.41)</td>
<td valign="top" align="center">(0.38, 0.29)</td>
<td valign="top" align="center">(0.32, 0.26)</td>
<td valign="top" align="center">(0.64, 0.41)</td>
<td valign="top" align="center">(0.15, 0.16)</td>
</tr> <tr>
<td valign="top" align="left">(7) <italic>b</italic><sub>7</sub>&#x0002B;<italic>b</italic><sub>16</sub> &#x0003D; 0</td>
<td valign="top" align="center">(0.27, 0.23)</td>
<td valign="top" align="center">(0.37, 0.29)</td>
<td valign="top" align="center">(0.61, 0.41)</td>
<td valign="top" align="center">(0.24, 0.22)</td>
<td valign="top" align="center">(0.03, 0.06)</td>
</tr> <tr>
<td valign="top" align="left">(8) <italic>b</italic><sub>8</sub>&#x0002B;<italic>b</italic><sub>17</sub> &#x0003D; 0</td>
<td valign="top" align="center">(0.01, 0.04)</td>
<td valign="top" align="center">(0.19, 0.19)</td>
<td valign="top" align="center">(0.02, 0.04)</td>
<td valign="top" align="center">(0.24, 0.22)</td>
<td valign="top" align="center">(0.02, 0.04)</td>
</tr> <tr>
<td valign="top" align="left">(6) &#x00026; (7) &#x00026; (8)</td>
<td valign="top" align="center">(0.05, 0.07)</td>
<td valign="top" align="center">(0.35, 0.28)</td>
<td valign="top" align="center">(0.08, 0.10)</td>
<td valign="top" align="center">(0.39, 0.29)</td>
<td valign="top" align="center">(0.01, 0.02)</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<p>The odd-numbered columns report coefficients from regressions of the scores for the personality trait indicated in the column on indicators for being East Asian or other race, whether the score comes from an Evaluation session, and the interaction between the race indicators and the Evaluation indicator. The omitted category represents Baseline scores for White subjects pooled across treatments. The even-numbered columns report coefficients from regressions of the scores for the personality trait indicated in the column on indicators for whether the score comes from the No Priming or Introversion treatments, interactions between the race indicators and three treatment indicators, interactions between the treatment indicators and the indicator for scores from Evaluation sessions, and the triple interaction terms for the race-treatment-Evaluation combinations. The omitted category represents Baseline scores for White subjects in the Extroversion treatment. Heteroskedasticity-robust standard errors are given in parentheses. Significance levels: <sup>!</sup>p &#x0003C; 0.01,<sup>&#x02020;</sup>p &#x0003C; 0.05, <sup>&#x00023;</sup>p &#x0003C; 0.10. The bottom of the table reports p-values and sharpened q-values accounting for the 55 hypotheses tested for the hypothesis indicated in the row for the regression given in the column. The hypothesis &#x0201C;(1) &#x00026; (2)&#x0201D;, &#x0201C;(3) &#x00026; (4) &#x00026; (5)&#x0201D;, and &#x0201C;(6) &#x00026; (7) &#x00026; (8)&#x0201D; refer to the joint hypothesis tests for the hypotheses as numbered in the table. <sup>&#x0002A;</sup>is the multiplication operator, indicating that the coefficient in the row is the coefficient of an interaction between two or more variables (i.e., they are multiplied together).</p>
</table-wrap-foot>
</table-wrap>
<p>The failure of so many of the racial differences to attenuate strongly suggests racial differences in responses to the incentives and treatment manipulations. To test for racial differences in faking relative to White subjects accounting for opportunity-to-fake, we again regress the change in trait scores on indicators for the quartile in which the subject falls of the pooled Baseline score distribution for a given trait along with interactions between these quartile indicators and the East Asian and other race indicators. <xref ref-type="fig" rid="F2">Figure 2</xref> displays the quartile-by-race mean faking levels for each trait and treatment while also reporting the <italic>p-</italic>values and sharpened <italic>q-</italic>values for tests of the joint significance of the race-quartile interactions. Using the <italic>p-</italic>values, we reject the joint insignificance of the race-quartile interactions for 13 of the 30 hypotheses at the 10% level and 10 of the 30 hypotheses at the 5% level. At either significance level, we reject far more of the hypotheses than one would expect by chance, but some rejections are likely Type I errors given the number of hypotheses tested. Using the sharpened <italic>q-</italic>values, we reject at the 10% level 10 out of the 30 null hypotheses tested&#x02014;still more than one would expect by chance.<xref ref-type="fn" rid="fn0020"><sup>20</sup></xref></p>
<fig id="F2" position="float">
<label>Figure 2</label>
<caption><p>Mean faking by race, trait, quartile and treatment. Each graph depicts the mean changes in trait scores from the Baseline to Evaluation sessions for subjects in a given race category in a given quartile of the Baseline trait score distribution (pooling subjects across treatments) along with 95% confidence intervals for the race-specific means. For the treatment specified in the column and the Big Five trait specified in the row, we regress the change in scores on indicators for the quartile of the pooled, Baseline score distribution in which a subject fell and interactions between these quartile indicators and the East Asian and other race indicators with the intercept omitted. Below each plot we report first the <italic>p-</italic>value from a heteroscedasticity-robust <italic>F</italic>-test of the null hypothesis that the quartile-race interactions are jointly significant followed (after a comma) by the sharpened <italic>q-</italic>values for the same hypothesis test accounting for the 30 hypotheses tested (&#x0201C;A:&#x0201D; for the East Asian-White <italic>p-</italic> and <italic>q-</italic> values and &#x0201C;O:&#x0201D; for the other race-white <italic>p-</italic> and <italic>q-</italic>values). <bold>(A)</bold> Extroversion. <bold>(B)</bold> No priming. <bold>(C)</bold> Introversion.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="frbhe-04-1499464-g0002.tif"/>
</fig>
</sec>
<sec>
<title>5.3 Would the differences matter for selection?</title>
<p>In the experiment, racial differences on incentivized personality measures were clearly consequential. White subjects were more likely to win the bonus and had higher earnings than East Asian subjects and subjects of other races in all treatments. Pooling the treatments, the East Asian-White and other race-White differences in winning the bonus and earnings are significant at the 1% level.<xref ref-type="fn" rid="fn0021"><sup>21</sup></xref></p>
<p>To assess the potential for adverse impacts in the labor market, we assume as in Foldes et al. (<xref ref-type="bibr" rid="B14">2008</xref>) that the trait scores for each group are drawn from standard normal distributions with the mean differences as given in <xref ref-type="table" rid="T1">Table 1</xref>. For each trait and for majority group selection ratios (i.e., the share of majority group members selected) ranging from 1% to 99%, we identify the cut-off score associated with the selection ratio. We then calculate the share of members from the protected group that would be selected given this cutoff.<xref ref-type="fn" rid="fn0022"><sup>22</sup></xref></p>
<p><xref ref-type="table" rid="T4">Table 4</xref> reports the majority group selection ratios below which the share of protected group applicants would be less than four-fifths of the majority group selection ratio for each trait and protected vs. majority group comparison by treatment using both unincentivized and incentivized scores. When small mean differences imply that the share of protected group applicants selected would never be less than four-fifths of the majority group selection ratio, <xref ref-type="table" rid="T4">Table 4</xref> indicates that adverse impacts are &#x0201C;unlikely.&#x0201D; For other comparisons, the mean differences imply that the protected group would enjoy an advantage were hiring based on the trait scores in the cell. For these comparisons (indicated by the &#x0201C;&#x0002B;&#x0201D; prefix), we report the majority group selection ratios below which the share of the protected group selected would be more than 1.25 times the majority group selection ratio.</p>
<table-wrap position="float" id="T4">
<label>Table 4</label>
<caption><p>Evaluating the potential for adverse impacts using incentivized and unincentivized scores.</p></caption>
<table frame="box" rules="all">
<thead>
<tr style="background-color:#8f9496;color:#ffffff">
<th valign="top" align="center" colspan="6"><bold>Personality trait on which hypothetical selection based</bold></th>
</tr>
</thead>
<tbody>
<tr style="background-color:#8f9496;color:#ffffff">
<td valign="top" align="left"><bold>Treatment</bold></td>
<td valign="top" align="center"><bold>Extroversion</bold></td>
<td valign="top" align="center"><bold>Conscientiousness</bold></td>
<td valign="top" align="center"><bold>Agreeableness</bold></td>
<td valign="top" align="center"><bold>Openness</bold></td>
<td valign="top" align="center"><bold>Emotional stability</bold></td>
</tr>
<tr style="background-color:#8f9496;color:#ffffff">
<td/>
<td valign="top" align="center"><bold>(1)</bold></td>
<td valign="top" align="center"><bold>(2)</bold></td>
<td valign="top" align="center"><bold>(3)</bold></td>
<td valign="top" align="center"><bold>(4)</bold></td>
<td valign="top" align="center"><bold>(5)</bold></td>
</tr> <tr style="background-color:#dee1e1;">
<td valign="top" align="left" colspan="6"><bold>Panel A. Female&#x02013;male</bold></td>
</tr> <tr>
<td valign="top" align="left">Baseline</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.02</td>
<td valign="top" align="center">Unlikely</td>
<td valign="top" align="center">&#x0002B;SR &#x0003C; 0.46</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.56</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.73</td>
</tr> <tr>
<td valign="top" align="left">Evaluation</td>
<td valign="top" align="center">Unlikely</td>
<td valign="top" align="center">Unlikely</td>
<td valign="top" align="center">Unlikely</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.02</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.09</td>
</tr> <tr>
<td valign="top" align="left">(<italic>E</italic>) Baseline</td>
<td valign="top" align="center">Unlikely</td>
<td valign="top" align="center">Unlikely</td>
<td valign="top" align="center">&#x0002B;SR &#x0003C; 0.04</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.26</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.56</td>
</tr> <tr>
<td valign="top" align="left">(<italic>E</italic>) Evaluation</td>
<td valign="top" align="center">Unlikely</td>
<td valign="top" align="center">Unlikely</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.20</td>
<td valign="top" align="center">Unlikely</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.13</td>
</tr> <tr>
<td valign="top" align="left">(<italic>NP</italic>) Baseline</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.33</td>
<td valign="top" align="center">&#x0002B;SR &#x0003C; 0.02</td>
<td valign="top" align="center">&#x0002B;SR &#x0003C; 0.64</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.70</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.90</td>
</tr> <tr>
<td valign="top" align="left">(<italic>NP</italic>) Evaluation</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.07</td>
<td valign="top" align="center">Unlikely</td>
<td valign="top" align="center">&#x0002B;SR &#x0003C; 0.28</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.20</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.52</td>
</tr> <tr>
<td valign="top" align="left">(<italic>I</italic>) Baseline</td>
<td valign="top" align="center">&#x0002B;SR &#x0003C; 0.09</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.09</td>
<td valign="top" align="center">&#x0002B;SR &#x0003C; 0.44</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.58</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.58</td>
</tr> <tr>
<td valign="top" align="left">(<italic>I</italic>) Evaluation</td>
<td valign="top" align="center">Unlikely</td>
<td valign="top" align="center">Unlikely</td>
<td valign="top" align="center">Unlikely</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.36</td>
<td valign="top" align="center">Unlikely</td>
</tr> <tr style="background-color:#dee1e1;">
<td valign="top" align="left" colspan="6"><bold>Panel B. East Asian-White</bold></td>
</tr> <tr>
<td valign="top" align="left">Baseline</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.78</td>
<td valign="top" align="center">Unlikely</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.16</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.85</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.68</td>
</tr> <tr>
<td valign="top" align="left">Evaluation</td>
<td valign="top" align="center">Unlikely</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.63</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.80</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.45</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.72</td>
</tr> <tr>
<td valign="top" align="left">(<italic>E</italic>) Baseline</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.87</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.04</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.16</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.78</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.63</td>
</tr> <tr>
<td valign="top" align="left">(<italic>E</italic>) Evaluation</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.45</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.13</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.87</td>
<td valign="top" align="center">Unlikely</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.63</td>
</tr> <tr>
<td valign="top" align="left">(<italic>NP</italic>) Baseline</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.74</td>
<td valign="top" align="center">&#x0002B;SR &#x0003C; 0.18</td>
<td valign="top" align="center">Unlikely</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.89</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.71</td>
</tr> <tr>
<td valign="top" align="left">(<italic>NP</italic>) Evaluation</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.20</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.66</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.50</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.74</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.81</td>
</tr> <tr>
<td valign="top" align="left">(<italic>I</italic>) Baseline</td>
<td valign="top" align="center">&#x0002B;SR &#x0003C; 0.47</td>
<td valign="top" align="center">Unlikely</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.58</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.83</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.72</td>
</tr> <tr>
<td valign="top" align="left">(<italic>I</italic>) Evaluation</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.04</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.79</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.81</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.84</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.85</td>
</tr> <tr style="background-color:#dee1e1;">
<td valign="top" align="left" colspan="6"><bold>Panel C. Other race-White</bold></td>
</tr> <tr>
<td valign="top" align="left">Baseline</td>
<td valign="top" align="center">Unlikely</td>
<td valign="top" align="center">&#x0002B;SR &#x0003C; 0.47</td>
<td valign="top" align="center">Unlikely</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.13</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.36</td>
</tr> <tr>
<td valign="top" align="left">Evaluation</td>
<td valign="top" align="center">Unlikely</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.07</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.60</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.13</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.72</td>
</tr> <tr>
<td valign="top" align="left">(<italic>E</italic>) Baseline</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.02</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.36</td>
<td valign="top" align="center">&#x0002B;SR &#x0003C; 0.07</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.02</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.85</td>
</tr> <tr>
<td valign="top" align="left">(<italic>E</italic>) Evaluation</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.13</td>
<td valign="top" align="center">&#x0002B;SR &#x0003C; 0.30</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.45</td>
<td valign="top" align="center">&#x0002B;SR &#x0003C; 0.02</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.60</td>
</tr> <tr>
<td valign="top" align="left">(<italic>NP</italic>) Baseline</td>
<td valign="top" align="center">Unlikely</td>
<td valign="top" align="center">&#x0002B;SR &#x0003C; 0.68</td>
<td valign="top" align="center">Unlikely</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.16</td>
<td valign="top" align="center">Unlikely</td>
</tr> <tr>
<td valign="top" align="left">(<italic>NP</italic>) Evaluation</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.47</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.39</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.09</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.52</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.79</td>
</tr> <tr>
<td valign="top" align="left">(<italic>I</italic>) Baseline</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.42</td>
<td valign="top" align="center">&#x0002B;SR &#x0003C; 0.62</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.04</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.20</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.23</td>
</tr> <tr>
<td valign="top" align="left">(<italic>I</italic>) Evaluation</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.81</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.52</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.82</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.45</td>
<td valign="top" align="center">&#x02013;SR &#x0003C; 0.76</td>
</tr></tbody>
</table>
<table-wrap-foot>
<p>We use the standardized mean differences reported in <xref ref-type="table" rid="T1">Table 1</xref> assuming standard normal distributions to evaluate at which reference group selection ratios members of the protected group would be adversely or positively impacted by selection based on the trait specified in the column. When preceded by &#x0201C;&#x02013;&#x0201D;, the share of the protected group selected would be &#x0003C; 80% of the share of the reference group selected at all selection ratios less than the selection ratio given in the cell. When preceded by a &#x0201C;&#x0002B;&#x0201D;, the share of the protected group selected would be more than 1.25 times the share of the reference group at all selection ratios less than the selection ratio given in the cell. E indicates the Extroversion treatment, NP indicates the No Priming treatment, and I indicates the Introversion treatment. The first two rows in each panel use the pooled Baseline or Evaluation scores across all treatments.</p>
</table-wrap-foot>
</table-wrap>
<p>Interpreting <xref ref-type="table" rid="T4">Table 4</xref>, however, requires understanding how employers use personality tests to cull their applicant pools. Low selection ratios and high cutoff scores are more likely to identify good fits if personality tests are predictive of performance, but they also make adverse impacts more likely if there are differences in distributions across groups. Test providers highlight this tradeoff when marketing their services to employers.<xref ref-type="fn" rid="fn0023"><sup>23</sup></xref> Given that personality tests are likely noisy signals used in combination with other assessments, we suspect that selection ratios for personality tests are seldom very low. Indeed, small standardized differences between groups of 0.2&#x02014;comparable in magnitude to some of the racial differences documented in Foldes et al. (<xref ref-type="bibr" rid="B14">2008</xref>)&#x02014;under our assumptions would result in adverse impacts at selection ratios up to 0.36. Given that firms are wary of adverse impacts, firms would probably not be so selective when using personality tests to screen applicants.<xref ref-type="fn" rid="fn0024"><sup>24</sup></xref> As such, we focus on trait-treatment cells in <xref ref-type="table" rid="T4">Table 4</xref> in which adverse impacts would occur at selection ratios &#x0003E;0.5, but we acknowledge that this threshold is somewhat arbitrary.</p>
<p>Regardless of what one believes plausible selection ratios to be, however, focusing on instances when adverse impact would occur at selection ratios &#x0003E;0.5 is a conservative approach to identifying trait-treatment cells where adverse impact might occur. If an adverse impact would occur at a selection ratio above 0.5 using our approach, it will also occur at <italic>all lower</italic> selection ratios when assuming both distributions are standard normal distributions. This is because, when a small number of applicants are selected at low selection ratios, these will be drawn first from the right-tail of the distribution with the higher mean. Effectively what we report in <xref ref-type="table" rid="T4">Table 4</xref> is the highest selection ratio at which adverse impact would occur.</p>
<p>Panel A of <xref ref-type="table" rid="T4">Table 4</xref> reports this analysis for women (the protected group) and men (the majority group). Women would experience adverse impacts at selection ratios &#x0003E;0.5 from selection on openness and emotional stability given the mean differences on the unincentivized scores pooling treatments and in the <italic>No Priming</italic> and <italic>Introversion</italic> treatments. Using the pooled incentivized scores, however, women would only be adversely impacted at selection ratios &#x0003C; 0.1 for openness and emotional stability. In the trait-treatment cells, women would only be adversely impacted at selection ratios &#x0003E;0.5 from selection on emotional stability in the <italic>No Priming</italic> treatment.</p>
<p>By contrast, the potential for adverse impacts on East Asians relative to Whites from selection on incentivized personality scores is readily apparent in Panel B. Were applicants&#x00027; scores drawn from the unincentivized score distributions, adverse impacts on East Asians would occur at selection ratios &#x0003E;0.5 in 9 of 15 trait-treatment cases. In six of these cases, adverse impacts would persist at selection ratios &#x0003E;0.5 using the incentivized scores. Of the five trait-treatment cases in which selection on unincentivized scores would be unlikely to result in adverse impacts or occur only at selection ratios &#x0003C; 0.2, adverse impacts would occur at selection ratios &#x0003E;0.5 in four of these cases from selection on incentivized scores. Overall, adverse impacts on East Asians relative to Whites would occur at selection ratios &#x0003E;0.5 from selection on incentivized scores in 10 of the 15 trait-treatment cases. Using the pooled Evaluation scores, adverse impacts on East Asians would occur at selection ratios &#x0003E;0.5 for conscientiousness, agreeableness and emotional stability.</p>
<p>The potential for adverse impacts on individuals of other races relative to Whites is also apparent in Panel C. Adverse impacts would occur at selection ratios &#x0003E;0.5 for none of the traits using the pooled Baseline scores and in only one of 15 trait-treatment cases were applicants&#x00027; scores drawn from the unincentivized score distributions. By contrast, adverse impacts would occur at selection ratios &#x0003E;0.5 for agreeableness and emotional stability using the pooled Evaluation scores and in seven of 15 trait-treatment cases were applicants&#x00027; scores drawn from the incentivized score distributions. Overall, our findings imply that selection on incentivized personality scores would adversely impact East Asians and individuals of other races at selection ratios &#x0003E;0.5 in half to two-thirds of the trait-treatment combinations in the experiment.<xref ref-type="fn" rid="fn0025"><sup>25</sup></xref></p>
</sec>
</sec>
<sec id="s6">
<title>6 Discussion</title>
<p>We investigate how incentives influence gender and race differences on personality measures. Gender gaps on unincentivized measures essentially disappear when subjects have incentives for misrepresentation. The attenuating effect of incentives highlights the importance of &#x0201C;opportunity-to-fake&#x0201D; dynamics: if two groups respond to incentives similarly (as we show that men and women do), then the lower scoring group on unincentivized measures will tend to close the gap when incentives are provided because they have more scope to manipulate their responses.</p>
<p>Incentives have very different effects on racial gaps. For East Asian subjects and subjects of other races, gaps relative to white subjects on unincentivized measures are in many cases not attenuated by incentives, or gaps appear where no similar gaps existed in the unincentivized scores. It should give researchers pause that <italic>in every instance</italic> where racial differences appear on incentivized personality measures where none existed on unincentivized measures, racial minorities would be adversely affected relative to Whites were hiring based on these measures.</p>
<p>In the experiment, most racial differences on incentivized measures occur where cues are absent or counterintuitive, which might reflect differences in norms and expectations concerning ideal personalities. Differences in cultural norms have been shown to contribute to personality differences in cross-country studies (Hofstede and McRae, <xref ref-type="bibr" rid="B23">2004</xref>). Likewise, Ryan et al. (<xref ref-type="bibr" rid="B42">2021</xref>) find evidence of cultural differences in the social desirability of personality traits for Confucian Asian and South Asian contexts relative to Germanic and Eastern Europe. Future research should investigate why racial differences on incentivized personality measures emerge. A potential implication for employers wishing to avoid adverse impacts is that they should be explicit about what they are looking for when screening applicants using personality tests&#x02014;a suggestion that echoes Ziegler&#x00027;s (<xref ref-type="bibr" rid="B54">2011</xref>) observation that providing job information before personality tests may be necessary to &#x0201C;level the playing field&#x0201D; given differences in applicants&#x00027; prior knowledge of jobs.</p>
<p>We note two important limitations of our study. First, the experiment was not designed to study the effects of incentives on gender and race differences. As a consequence, our exploratory analysis is underpowered for identifying small group differences (i.e., <italic>d</italic> &#x02264; 0.2), but we have power &#x0003E;0.5 to detect medium-sized group differences as indicated by the power calculations reported in Panel D of <xref ref-type="table" rid="T1">Table 1</xref>. In our view, the lack of power to detect plausible but small group differences is a second-order concern given that such differences are less likely to influence hiring. More important is the fact that the racial differences that emerge with incentives in many cases are as large as half of a standard deviation and would almost certainly influence selection.</p>
<p>Second, differences between the laboratory and hiring limit the external validity of our findings. Subjects&#x00027; incentives were not the same as those of actual job applicants, and our subjects may not resemble the applicants for any given job. We attempted to minimize these concerns by using ads based on an actual ad for a job to which young graduates might apply without directing subjects to fake.</p>
<p>In view of these limitations, we conclude by stressing the need for additional evidence regarding whether personality testing in hiring adversely impacts minorities. Evidence from a single firm as in Autor and Scarborough (<xref ref-type="bibr" rid="B3">2008</xref>) cannot settle the issue given the importance of information, applicant populations, and other factors.<xref ref-type="fn" rid="fn0026"><sup>26</sup></xref> Likewise the evidence from this study is not definitive. Research using larger, more diverse samples ideally in a hiring setting is necessary. Larger samples would offer greater power to identify small racial differences while also permitting the investigation of differences among racial groups under-represented in our study.</p></sec>
<sec id="s7">
<title>7 Materials and methods</title>
<p>The project was approved by Simon Fraser University&#x00027;s Research Ethics Board (2012s0590). The experimental method is described in the Section 3. Further materials can be found in the <xref ref-type="supplementary-material" rid="SM1">Appendices</xref>. <xref ref-type="supplementary-material" rid="SM1">Appendix A</xref> reports additional summary statistics. <xref ref-type="supplementary-material" rid="SM1">Appendix B</xref> provides the instructions, job ads, and the instruments used in the experiment. <xref ref-type="supplementary-material" rid="SM1">Appendix C</xref> discusses the potential for adverse impacts from hypothetical selection using the realized distributions of subjects&#x00027; scores rather than assuming that the scores are drawn from standard normal distributions as in the main text.</p></sec>
</body>
<back>
<sec sec-type="data-availability" id="s8">
<title>Data availability statement</title>
<p>The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession number(s) can be found below: Andrew D. McGee ECIN Replication Package for &#x0201C;Whoever you want me to be: personality and incentives.&#x0201D; Ann Arbor, MI: Inter-university Consortium for Political and Social Research [distributor], 2024-02-05. <ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3886/E194887V5">https://doi.org/10.3886/E194887V5</ext-link>.</p>
</sec>
<sec sec-type="ethics-statement" id="s9">
<title>Ethics statement</title>
<p>The studies involving humans were approved by Simon Fraser University Research Ethics Board. The studies were conducted in accordance with the local legislation and institutional requirements. The participants provided their written informed consent to participate in this study.</p>
</sec>
<sec sec-type="author-contributions" id="s10">
<title>Author contributions</title>
<p>AM: Conceptualization, Formal analysis, Funding acquisition, Methodology, Project administration, Writing &#x02013; original draft, Writing &#x02013; review &#x00026; editing. PM: Conceptualization, Data curation, Methodology, Writing &#x02013; review &#x00026; editing.</p>
</sec>
<sec sec-type="funding-information" id="s11">
<title>Funding</title>
<p>The author(s) declare that financial support was received for the research and/or publication of this article. AM gratefully acknowledges financial support from a Social Sciences and Humanities Research Council Insight Development Grant (&#x00023;430-2013-00700).</p>
</sec>
<sec sec-type="COI-statement" id="conf1">
<title>Conflict of interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
<p>The author(s) declared that they were an editorial board member of Frontiers, at the time of submission. This had no impact on the peer review process and the final decision.</p>
</sec>
<sec sec-type="disclaimer" id="s12">
<title>Publisher&#x00027;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
<sec sec-type="supplementary-material" id="s13">
<title>Supplementary material</title>
<p>The Supplementary Material for this article can be found online at: <ext-link ext-link-type="uri" xlink:href="https://www.frontiersin.org/articles/10.3389/frbhe.2025.1499464/full#supplementary-material">https://www.frontiersin.org/articles/10.3389/frbhe.2025.1499464/full#supplementary-material</ext-link></p>
<supplementary-material xlink:href="Supplementary_file_1.docx" id="SM1" mimetype="application/vnd.openxmlformats-officedocument.wordprocessingml.document" xmlns:xlink="http://www.w3.org/1999/xlink"/></sec>
<fn-group>
<fn id="fn0001"><p><sup>1</sup>The Five Factor Model (Goldberg, <xref ref-type="bibr" rid="B18">1992</xref>) organizes personality into five broad traits: extroversion, conscientiousness, agreeableness, openness/intellect, and neuroticism. According to McCrae and John (<xref ref-type="bibr" rid="B33">1992</xref>), individuals high in extroversion tend to be more energetic, outgoing, ambitious, and assertive. Individuals high in conscientiousness tend to be diligent, well-organized, and neat. Individuals high in agreeableness tend to be more trusting, modest, and compliant. Individuals high in openness/intellect have greater need for varied and novel experiences, greater aesthetic sensitivity, and greater curiosity. Individuals high in neuroticism experience more depression, feelings of guilt, and anxiety.</p></fn>
<fn id="fn0002"><p><sup>2</sup>McGee and McGee (<xref ref-type="bibr" rid="B35">2024</xref>) found that IQ and locus of control beliefs were correlated with incentivized scores in some instances. In particular, IQ was correlated with incentivized extroversion scores in the <italic>Extroversion</italic> and <italic>Introversion</italic> treatments when the ad provided information concerning the desired degree of extroversion, suggesting that IQ influenced the incentivized extroversion scores through an information acquisition or processing channel.</p></fn>
<fn id="fn0003"><p><sup>3</sup>Raghavan et al. (<xref ref-type="bibr" rid="B38">2020</xref>) note that vendors may have difficulty establishing the effects of screening tools outside of testing samples in applicant samples given that protected attributes may not be collected in the hiring process.</p></fn>
<fn id="fn0004"><p><sup>4</sup>Arcidiacono et al. (<xref ref-type="bibr" rid="B2">2020</xref>) show that Asian applicants to Harvard received lower &#x0201C;personal ratings&#x0201D; than other applicants despite being stronger on characteristics correlated with the personal rating. Incorporating this rating explains about half of the admissions &#x0201C;penalty&#x0201D; that they find imposed on Asian applicants.</p></fn>
<fn id="fn0005"><p><sup>5</sup>Only 6% of applicants responded to the research survey.</p></fn>
<fn id="fn0006"><p><sup>6</sup>The experiment was conducted using z-Tree (Fischbacher, <xref ref-type="bibr" rid="B13">2007</xref>).</p></fn>
<fn id="fn0007"><p><sup>7</sup>DeYoung et al.&#x00027;s (<xref ref-type="bibr" rid="B9">2007</xref>) Big Five assessment asks subjects to indicate how well a statement describes them using a 5-point Likert scale. Each trait score sums the values of the 20 items associated with that trait, resulting in scores between 20 and 100. We reverse the neuroticism scale and refer to it as emotional stability.</p></fn>
<fn id="fn0008"><p><sup>8</sup>K&#x000F6;nig et al. (<xref ref-type="bibr" rid="B31">2012</xref>) report that applicants reference the expectations of organizations when describing faking strategies. Roulin and Krings (<xref ref-type="bibr" rid="B41">2020</xref>) find that individuals adapt their responses to match an organization&#x00027;s culture.</p></fn>
<fn id="fn0009"><p><sup>9</sup>In so-called &#x0201C;fake good&#x0201D; studies, subjects are explicitly directed to misrepresent themselves in favorable ways or to fake as they think workers in particular occupations would (e.g., Velicer and Weiner, <xref ref-type="bibr" rid="B50">1975</xref>; Furnham, <xref ref-type="bibr" rid="B15">1990</xref>, <xref ref-type="bibr" rid="B16">1997</xref>; McFarland and Ryan, <xref ref-type="bibr" rid="B34">2000</xref>).</p></fn>
<fn id="fn0010"><p><sup>10</sup>Using the difference between incentivized and unincentivized scores as a measure of faking could be problematic if subjects attempt to match a desired personality profile without regard to their own personalities. In this case, the incentivized scores would be uncorrelated with the unincentivized scores, but this is not what we observe. The correlations between the incentivized and non-incentivized scores reported in McGee and McGee (<xref ref-type="bibr" rid="B35">2024</xref>) range between 0.4 and 0.6 for every trait and treatment. Likewise, if subjects attempt to match a desired profile without using their actual personalities as a reference point, the incentivized scores might be greater than or less than the non-incentivized scores. In the scatterplots of the incentivized scores against the non-incentivized scores reported in McGee and McGee (<xref ref-type="bibr" rid="B35">2024</xref>), however, the incentivized scores almost never lie below the 45&#x000B0; line. That is, subjects inflate their unincentivized responses.</p></fn>
<fn id="fn0011"><p><sup>11</sup>Hoffman et al. (<xref ref-type="bibr" rid="B22">2018</xref>), for instance, study a firm that used test scores to produce &#x0201C;green-yellow-red&#x0201D; recommendations to hiring managers concerning applicants. Approximately 21% of applicants received red scores indicating the lowest potential; these applicants had a probability of being hired of just 0.08.</p></fn>
<fn id="fn0012"><p><sup>12</sup>Another concern regarding incentives is that actual job applicants might worry about their &#x0201C;fit&#x0201D; for a position when faking if they actually have to fill the position to which they are applying. Individuals worried about fit, however, can choose not to apply for a position. Likewise, advancing to later stages of hiring does not require applicants to take a job for which they determine they would be a bad fit. Allowing fit concerns to influence one&#x00027;s responses at this stage would not seem very sensible given that applicants have assessed this fit and chosen to apply. Undoubtedly some applicants prefer to be honest when responding, but some subjects in our experiment also exhibit this preference for honest responding.</p></fn>
<fn id="fn0013"><p><sup>13</sup>The counterintuitive priming in the <italic>Introversion</italic> treatment was used to investigate the mediating effect of information about desired personalities on the correlates of faking behavior in McGee and McGee (<xref ref-type="bibr" rid="B35">2024</xref>).</p></fn>
<fn id="fn0014"><p><sup>14</sup>Subjects of Indian or Pakistani heritage make up 60% of our &#x0201C;other race&#x0201D; category, Black subjects 15%, Latino subjects 5%, and subjects who selected the &#x0201C;Other&#x0201D; category 20%.</p></fn>
<fn id="fn0015"><p><sup>15</sup>The racial distribution of subjects is similar to the representation of these groups in Burnaby, British Columbia, where Simon Fraser University is located (Statistics Canada, <xref ref-type="bibr" rid="B46">2017</xref>).</p></fn>
<fn id="fn0016"><p><sup>16</sup>Subjects were not obliged to participate in the Evaluation session, but 80% did so. There were no significant differences between non-returnees and returnees; see McGee and McGee (<xref ref-type="bibr" rid="B35">2024</xref>). Most importantly, the gender and race distributions of returnees and non-returnees were nearly identical. Among subjects who participated in only a Baseline session, 21% identified as White, 50% as East Asian, and 29% another race, while 49% identified as men.</p></fn>
<fn id="fn0017"><p><sup>17</sup>Sharpened <italic>q-</italic>values control the false discovery rate, the proportion of rejections that are Type I errors. In the first step, the <italic>p-</italic>values are sorted by magnitude. The largest <italic>p-</italic>value is compared to the acceptable proportion of false positives times the ratio of the number of tests with <italic>p-</italic>values no larger than the current <italic>p-</italic>value to the total number of tests. The procedure then rejects all hypotheses with <italic>p-</italic>values less than or equal to this product. The second step repeats this process but adjusts the acceptable number of false positives to account for the hypotheses rejected in the first stage. The process ends when the number of hypotheses rejected in the first stage is zero. This algorithm indicates which hypotheses should be rejected for a given false discovery rate, but obtaining the smallest possible rate at which the hypothesis is rejected involves running the algorithm for every possible rate, e.g., 1, 0.99, 0.98, &#x02026;, 0 and reporting the value at which the test ceases to be rejected, which is the reported <italic>q-</italic>value.</p></fn>
<fn id="fn0018"><p><sup>18</sup>Alternatively we might fail to reject the null hypotheses that faking does not depend on gender after accounting for opportunity to fake due to a lack of statistical power. Our power calculations, however, suggest that we could detect changes in the <italic>R</italic><sup>2</sup> of &#x0007E;0.03 at the five percent significance level with 80% power depending on the treatment and the <italic>R</italic><sup>2</sup> in the regressions without the gender-quartile interactions. Effect sizes of this magnitude are common for the regressions used to construct <xref ref-type="fig" rid="F2">Figure 2</xref>. In the regressions used to generate <xref ref-type="fig" rid="F1">Figure 1</xref>, however, the <italic>R</italic><sup>2</sup> increases by &#x0003C; 0.01 in most cases. Thus while it is true that we are underpowered to detect effect sizes of this magnitude, the reality is that the observed changes in <italic>R</italic><sup>2</sup> suggest that gender has little explanatory power where faking is concerned, which is consistent with what we observe in <xref ref-type="fig" rid="F1">Figure 1</xref>.</p></fn>
<fn id="fn0019"><p><sup>19</sup>The positive other race-White difference in incentivized extroversion in the <italic>Introversion</italic> treatment would adversely affect subjects of other races as the ad indicated that the firm sought an introvert.</p></fn>
<fn id="fn0020"><p><sup>20</sup>Racial differences in effort or attentiveness when responding on the unincentivized measures could produce differences in faking. In this case, opportunity-to-fake arises not from differences in the underlying traits (as we assume) but from differences in effort in the Baseline: subjects who supply low effort and reply randomly or with little attentiveness have greater scope to improve their scores when incentivized. To assess this possibility, we constructed two measures to identify subjects who supplied low Baseline effort. Notably, all of our results are robust to simply excluding subjects who supplied low effort in the Baseline. Furthermore, East Asian subjects and subjects of other races were <italic>more</italic> likely than White subjects to supply low effort according to these measures, implying that they had more scope for improving their scores relative to white subjects on the incentivized tests. As such, racial differences in effort or attentiveness in the Baseline cannot explain the differences in faking that we observe. See <xref ref-type="supplementary-material" rid="SM1">Appendix A Table 5</xref> for these summary statistics. In <xref ref-type="supplementary-material" rid="SM1">Appendix A Table 6</xref>, we also demonstrate that other measured subject characteristics cannot explain the racial differences in faking. This is largely unsurprising given that McGee and McGee (<xref ref-type="bibr" rid="B35">2024</xref>) found that most of these characteristics were uncorrelated with the incentivized scores.</p></fn>
<fn id="fn0021"><p><sup>21</sup>These differences in earnings and the probability of winning the bonus could reflect racial differences in IQ given that both were influenced directly by IQ scores. In regressions of earnings and an indicator for winning the bonus on the race indicators, however, the race coefficients are significant at the 1% level even after controlling for IQ.</p></fn>
<fn id="fn0022"><p><sup>22</sup>Firms may use tests to identify workers with a particular trait (Hough and Oswald, <xref ref-type="bibr" rid="B26">2000</xref>), but they might also create composite scores from multiple measures to mitigate group differences on any one measure. We follow Foldes et al. (<xref ref-type="bibr" rid="B14">2008</xref>) and Powell et al. (<xref ref-type="bibr" rid="B37">2011</xref>) in considering adverse impacts on a trait-by-trait basis because such composite measures are firm-specific. Moreover, Sackett and Ellingson (<xref ref-type="bibr" rid="B44">1997</xref>) show that it is difficult to add measures to a selection test to mitigate large group differences (i.e., <italic>d</italic> = 1.0)&#x02014;an observation confirmed in studies of personality testing such as Ryan et al. (<xref ref-type="bibr" rid="B43">1998</xref>). While the standardized effects in our study are not that large, it would still be difficult to mitigate effects of the sizes in our study (<italic>d</italic> = 0.6 in some cases) given the correlations between measures.</p></fn>
<fn id="fn0023"><p><sup>23</sup>See, for instance, <ext-link ext-link-type="uri" xlink:href="https://www.testpartnership.com/blog/impact-cut-off-scores-recruitment.html">https://www.testpartnership.com/blog/impact-cut-off-scores-recruitment.html</ext-link>.</p></fn>
<fn id="fn0024"><p><sup>24</sup>Unfortunately, little evidence on how employers use personality tests exists. Applicants to the retail firm studied by Hoffman et al. (<xref ref-type="bibr" rid="B22">2018</xref>) received &#x0201C;green&#x02013;yellow&#x02013;red&#x0201D; scores from job tests with 21% receiving &#x0201C;red&#x0201D; scores indicating low potential candidates, which suggests a selection ratio of around 0.8. On the other hand, Ock and Oswald (<xref ref-type="bibr" rid="B36">2018</xref>) use values of 0.1, 0.2, and 0.4 as plausible selection ratios in a simulation study of selection decisions.</p></fn>
<fn id="fn0025"><p><sup>25</sup>In <xref ref-type="supplementary-material" rid="SM1">Appendix C</xref>, we investigate the potential for adverse impacts from hypothetical selection using the <italic>realized</italic> distributions of subjects&#x00027; scores following Powell et al. (<xref ref-type="bibr" rid="B37">2011</xref>) rather than assuming that the scores are drawn from standard normal distributions. We reach similar conclusions regarding the prospects for adverse impacts.</p></fn>
<fn id="fn0026"><p><sup>26</sup>In over a decade since Autor and Scarborough published their study, not a single paper citing their study has estimated the effects of personality testing on minority hiring outcomes.</p></fn>
</fn-group>
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