Non-central t distribution and the power of the t test : A rejoinder

coincides with the standard (central) tν distribution. In the following, represents the effect size; by convention, a of 0.5 is considered a "medium" effect size. In Figure 1 are shown three instances of the t′ density envelope for ν = 10, one with δ = 0 (a standard t), and two with δ = 3 and δ = 6 : one may note that, whereas t10(δ = 0) is centered at 0 and symmetrical, the non-central t′’s are displaced toward δ, their variance is increased and they are skewed. The probability density function for is (Levy & Narula, 1974) :