Logarithmic Versus Linear Change in Step Size When Using an Adaptive Threshold-Seeking Procedure in a Frequency Discrimination Task: Does It Matter?

Abstract

Different rules for changing step sizes (e.g., logarithmic, linear) are alternately used in adaptive threshold-seeking procedures, with no clear justification. We hypothesized that the linear rule may yield more accurate thresholds for poor performers because the step sizes are predetermined and fixed across listeners and thus can be small, in contrast to the logarithmic rule, in which step sizes are changed with respect to the listener's performance. Purpose The aim of this study was to test the effect of logarithmic and linear rules on frequency discrimination (FD) thresholds. Method Three experiments involving human subjects and Monte Carlo computer simulations were designed and conducted. In the 1st experiment, FD thresholds were estimated in 40 young adults with either 3-interval 2-alternative forced choice (3I2AFC; n = 19) or 2-interval 2AFC ( n = 21) in a within-subject design. In the 2nd experiment, thresholds were estimated in 16 children (7–8 years old) in a within-subject design, using 3I2AFC. In the 3rd experiment, thresholds were estimated in 30 young adults in a between-subjects design using 3I2AFC. Results No significant differences were shown between the 2 rules, regardless of age group, method, or level of FD performance. Computer simulations supported the empirical findings, predicting similar FD thresholds for both rules in the majority of runs. However, they also yielded more accurate thresholds with the linear rule, but with a larger number of outliers, which increased as the listener's attention level decreased. Conclusion Overall, the use of a particular rule has little influence on FD thresholds. Possible outliers may be minimized by monitoring the participant's attention at the beginning of the run.