I have problems to understand when a non-centrality parameter is relevant. As far as I understood, if the t distribution is not centered on 0, a non-central t distribution is used. For example, in power analysis, it is assumed that an effect is present, therefore, a non-central t is used to calculate the probabilities. Now to my application: If I carry out a t test where the null hypothesis is not that the difference is 0, eg:
H0: μ1 − μ2 ≤ 3
H1: μ1 − μ2 > 3
Do I need a noncentral t distribution here to calculate the pvalue for H0? Is this non-centrality parameter = 3?
Does anyone have an good source for the relevance of non-central distributions in social sciences?
Thanks for your answers! (and patience!)