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Although the consequences of ignoring a nested factor on decisions to reject the null hypothesis of no treatment effects have been discussed in the literature, typically researchers in applied psychology and education ignore treatment providers (often a nested factor) when comparing the efficacy of treatments. The incorrect analysis, however, not only invalidates tests of hypotheses, but it also overestimates the treatment effect. Formulas were derived and a Monte Carlo study was conducted to estimate the degree to which the F statistic and treatment effect size measures are inflated by ignoring the effects due to providers of treatments. These untoward effects are illustrated with examples from psychotherapeutic treatments.
Wampold et al. (Sat,) studied this question.