Concerning the statistical procedures enumerated by Gentile et al.: another perspective.
Swap ANOVA for Bonferroni t tests on correlated single-case data to keep power and control error.
01Research in Context
What this study did
Périkel et al. (1974) wrote a short, sharp note about statistics. They said stop using ANOVA F tests on single-case data. Use Bonferroni-corrected t tests instead.
The paper is pure method talk. No kids, no rats, just math advice for behavior analysts.
What they found
Bonferroni t keeps the family-wise error low and keeps power high when your data points are correlated. ANOVA loses power in that same spot.
How this fits with other research
Moeyaert et al. (2014) extends the same worry to meta-analysis. They show how to build design matrices that respect within-case correlation, giving cleaner effect sizes.
Alsop (2004) also warns about bias, but in signal-detection estimates. Both papers say routine fixes can mislead if you ignore how behavioral data behave.
Kessel (2004) offers a concrete fix for noisy records: Wiener filtering. It sharpens transfer-function estimates, echoing the 1974 call for cleaner quantification.
Why it matters
Next time you run a reversal or multiple-baseline graph, skip the ANOVA button. Run separate t tests with a simple Bonferroni correction. You keep power and stay honest about Type I error. It takes one extra line in Excel or R and gives you stronger evidence for your visual analysis.
Want CEUs on This Topic?
The ABA Clubhouse has 60+ free CEUs — live every Wednesday. Ethics, supervision & clinical topics.
Join Free →Re-analyze your last ABAB data with Bonferroni t instead of ANOVA and compare p values.
02At a glance
03Original abstract
The thrust of this paper is to bring to the attention of operant researchers statistical procedures that are appropriate for correlated data. In addition to specifying these statistical procedures consideration is given to the question of using individual comparison statistics rather than omnibus F tests. Specifically, it is recommended that a more powerful test of the experimental hypotheses can be obtained by performing Bonferroni t statistics rather than analysis of variance F tests.
Journal of applied behavior analysis, 1974 · doi:10.1901/jaba.1974.7-643