This is a general question so I am not supplying details of my experiment. When I search for information on whether to conduct ANCOVA/ANOVA or multiple regression, in many sources including this forum people say they are "the same thing". Yet when I conduct a power analysis for a two way ANOVA and compare that with my power analysis for a multiple regression with 2 predictors, the estimated necessary sample size for my multiple regression is much smaller than for the ANOVA. The specifications in Gpower (effect size, power level etc) are the same. So, why, if they are based on the same model, should they require vastly different sample sizes to be adequately powered?
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$\begingroup$ Anova and multiple regression are not based on the same model. $\endgroup$– user10619Mar 7, 2018 at 10:47
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I don't know Gpower, but my guess is that your usage of ANCOVA/ANOVA includes interaction terms and the multiple regression does not. To detect a significant interaction would require a larger sample size. Maybe you can list the desired interaction terms in the regression model and get the same suggested sample size.
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$\begingroup$ The interaction to be significant is not guaranteed by larger sample-size. $\endgroup$– user10619Mar 7, 2018 at 10:50