An experiment is planned in which we have a set of regressors X 1 and one addition regressor X 2 will be created with values 0 for subjects that get a control treatment and 1 for subjects that get the...

An experiment is planned in which we have a set of regressors X₁
and one addition regressor X₂
will be created with values 0 for subjects that get a control treatment and 1 for subjects that get the experimental treatment. Treatment assignment will be done at random, with half of the subjects getting the experimental treatment. The test for a treatment effect will be done at level α = 0.05, and it desired to make the experiment large enough to have 90% power. An estimate of σ is required, and suppose that setting σ = 0.5 is reasonable. Use a sample size calculator such as that of Lenth (2006–2009) to determine the sample size if the smallest meaningful treatment effect is equal to 1.0. Repeat for effect sizes of 0.5 and 2.0.