Assessment & Research

Concerning the statistical procedures enumerated by Gentile et al.: another perspective.

Keselman et al. (1974) · Journal of applied behavior analysis 1974
★ The Verdict

Swap ANOVA for Bonferroni t tests on correlated single-case data to keep power and control error.

✓ Read this if BCBAs who run statistical checks on single-case graphs.
✗ Skip if Practitioners who rely only on visual inspection and never run inferential tests.

01Research in Context

01

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.

02

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.

03

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.

04

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.

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Re-analyze your last ABAB data with Bonferroni t instead of ANOVA and compare p values.

02At a glance

Intervention
not applicable
Design
theoretical
Finding
not reported

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