Question

1. It is not possible to use ANCOVA to increase statistical power, only decrease it.

   True

   False

Answer 1

this is true that It is not possible to use ANCOVA to increase statistical power, only decrease it.

basically ANCOVA is mostly used to

(1) explains an ANOVA’s within-group variance,

(2) controls confounding factors. and ANOVA is splits into two variances i.e. explained and unexplained variances

The ANCOVA tries to explain some of unexplained variance with the covariates. Thus it increases the power of the ANOVA by explaining more variability in the model. since  just like in regression analysis and all linear models, over-fitting might occur. That is, the more covariates you enter into the ANCOVA, the more variance it will explain, but the fewer degrees of freedom the model has. Thus entering a weak covariate into the ANCOVA decreases the statistical power of the analysis instead of increasing it.