Time Series Analysis in Forecasting Mental Addition and Summation Performance - Abdul-Rahman, Anmar (Frontiers in Psychology, 2020)
An ideal performance evaluation metric would be predictive, objective, easy to administer, estimate the variance in performance and provide a confidence interval for the level of uncertainty. Time series forecasting may provide objective metrics for predictive performance in mental arithmetic. Addition and summation (addition combined with subtraction) using the Japanese Soroban computation system was undertaken over 60 days. The median calculation time in seconds (sec) for adding 10 sequential 6 digit numbers (CTAdd) was 63 sec (interquartile range (IQR)=12, range 48 to 127 sec), while that for summation (CTSum) was 70 sec (IQR=14, range 53 to 108 sec), and the difference between these times was statistically significant p<0.0001. Using the mean absolute percentage error (MAPE) to measure forecast accuracy, the autoregressive integrated moving average (ARIMA) model predicted a further reduction in both CTAdd to a mean of 51.51±13.21 sec (AIC=5403.13) with an error of 6.32%, and CTSum to a mean of 54.57±15.37 sec (AIC=3852.61) with an error of 8.02% over an additional 100 forecasted trials. When the testing was repeated, the actual mean performance differed by 1.35 and 4.41 seconds for each of the tasks respectively from the ARIMA point forecast value. There was no difference between the ARIMA model and actual performance values (p-value CTAdd=1.0, CTSum=0.054). This is in contrast to both Wright’s model and linear regression (p-value < 0.0001). By accounting for both variability in performance over time and task difficulty, forecasting mental arithmetic performance may be possible using an ARIMA model, with an accuracy exceeding that of both Wright’s model and univariate linear regression.