An approximate critical point for a test in the growth curve model: a conditional approach

A test proposed by Seid Hamid & von Rosen (2005b) is considered. The critical point is calculated using a conditional approach. The conditional distributions under the null and alternative hypotheses are shown to be represented as sums of weighted central and non central chi-square random variables, respectively. Under the null hypothesis, the Satterth- waite approximation is used to a get an approximate critical point. An approximate estimated power is given using a Satterthwaite kind of approximation together with some new ideas. A numerical example is given to illustrate the results