A further consideration in the application of an analysis-of-variance model for the intrasubject replication design.

Lydersen et al. (1974) wrote a theory paper. They checked if ANOVA fits single-subject reversal designs. They showed the math breaks the independence rule. Data points in one phase depend on the point before them.

They said: use your eyes, not F-tests. Graphs and phase lines give the answer.

The authors found a clear flaw. ANOVA needs each score to be independent. In A-B-A designs, scores next to each other rise and fall together. That linkage spoils the test.

They urged behavior analysts to stay with visual checks and simple phase mean shifts.

Christophersen et al. (1972) had pushed the opposite view: ANOVA can work on reversal data. Lydersen et al. (1974) and Mulvaney et al. (1974) shot that idea down in the same journal issue. Both pairs of critics agreed: serial correlation kills the test.

DeHart et al. (2019) later offered a fix. Mixed-effects models handle the correlation and still give p-values. Their method keeps each subject’s raw data, so it respects single-case logic while adding stats.

Reid et al. (1999) and Nasr et al. (2000) widened the fight. They asked if any number-crunching summary of single cases is fair. The field still splits: some teams defend meta-analysis, others stay visual-only like T et al.

If you run reversal or multiple-baseline graphs, skip ANOVA. The rows of dots are linked like a chain; the test assumes they are not. Plot the data, draw phase lines, and look for level or trend changes. If you need a statistic for a grant or journal, try mixed-effects or randomization tests instead. Your graphs stay clean and your stats stay honest.