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?
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$\begingroup$ Perhaps you can explain why you expect "parental perfectionism" and "career indecision" to be distributed normally in the first place. $\endgroup$– Nick CoxCommented Aug 29, 2017 at 13:37
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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.
answered Aug 29, 2017 at 12:45
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2$\begingroup$ A bigger problem is not having a power of 1.0 so missing non-normality when n is small. It is better practice to just use nonparametric tests if you are not somewhat certain of normal residuals. Checking the data to find out how to model the data can distort statistical inference. $\endgroup$ Commented Aug 29, 2017 at 12:47
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$\begingroup$ So visual methods of a combination of 3 populations for each dependent variable? Sorry but our school only taught us until Pearson Correlation Coefficient, all of these were my part of my personal research. $\endgroup$ Commented Aug 29, 2017 at 13:32
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$\begingroup$ @FrankHarrell Use Kruskal-Wallis Test instead?(the non-parametric equivalent of ANOVA) $\endgroup$ Commented Aug 29, 2017 at 13:32
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$\begingroup$ Our sample size is n=20, still too sensitive to non-normality? $\endgroup$ Commented Aug 29, 2017 at 13:35
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$\begingroup$ Yes, combo of samples for each DV, but you want to look at the residuals from the analysis, not the original data. You should also take to heart @Frank Harrell 's comment. Especially if your dependent variables aren't really continuous variables, a nonparametric test may be more appropriate (Kruskal-Wallis perhaps). For what you're doing if you're not real comfortable looking at the assumptions of anova, probably K-W with a Dunn test post-hoc will be easy, familiar to readers, and will serve you well. $\endgroup$ Commented Aug 29, 2017 at 13:53