Our research plans to use one-way ANOVA, but upon encountering the assumptions of it, we had to conduct the test for normality and homoscedasticity. We're going to compare 3 populations(Grade 10,11,12 students) with 2 dependent variables(parental perfectionism, career indecision) to be done separately.
I have decided upon using the Anderson-Darling Test, but my problem is, will I be testing each population for each dependent variable, or combine the three populations for each dependent variable and perform the Anderson-Darling test?
The assumption for a general linear model is that the data are marginally normal. That is, that the distributions of errors from the model are normally distributed. So, you want to take the residuals from the model, and assess those for normality.
I recommend against using a test to assess normality in the way you are suggesting. The problem is that these tests are sensitive to sample size and will find a significant deviation from normal for a large data set even if the deviation is small.
You are better off using visual methods. Your eyes and brain are a better judge. You can use a quantile-quantile plot or a histogram of residuals that you can compare to a normal distribution.
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