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I have an independent variable with 4 levels. Lets say Group A, B, C and D. When i see for the normality in my dependent variables, i can see, some dependent variables are normal in Group A, B and C but not in D (Shapiro-Wilk Test, p<0.05), Some variables shows normality for Group A and C but not for Group B and D and like wise for all possible combinations. According to the assumption, the dependent variable should be normally distributed in each of the groups.

What should i do in this case where some groups shows normality and some do not. Shall i continue with the traditional ANOVA or need to use Non-parametric alternative? Please suggest.

NK2112
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  • The residuals, not the dependent variable, should be checked for normality, see for example https://stats.stackexchange.com/a/6351/27276. – hplieninger Jul 26 '17 at 10:27
  • Suppose Height is my dependent variable for which i have to check for Normality. After applying Shapiro-Wilk test (in SPSS), i can see, height is normal for group A, B and C (p=0.913, 0.078 and 0.612 respectively) but non normal for group D (p=0.002). I want to test mean height across all 4 groups. How should i proceed? I have 14 such variables for which i need to test mean across all 4 groups. – NK2112 Jul 26 '17 at 10:32
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    This thread on robustness may help as well: https://stats.stackexchange.com/a/27723/27276 – hplieninger Jul 26 '17 at 10:36
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    @hplieninger If group is the only IV, then normality within groups is equivalent to normality of residuals. – Peter Flom Jul 26 '17 at 12:16
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    @PeterFlom Absolutely, I agree. I just realized too late that the OP was actually referring to that. – hplieninger Jul 26 '17 at 12:23
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    Well, i have tried checking normality of my dependent variable across all 4 groups using linear regression. But, regression consider the independent variable as a continuous (as i have coded it as 1,2,3 and 4) and giving me residual plot as a whole and not separate for each group. Does this makes any sense? or i am doing it terribally wrong? I am using SPSS version 20 for this.     – NK2112 Jul 27 '17 at 11:02
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    If you checked within groups, that's totally fine as @PeterFlom pointed out. If you want to check the residuals as a whole, you have (in SPSS) to do something like "General linear model" and specify group as a "fixed factor"; treating it as continous is wrong. – hplieninger Jul 27 '17 at 11:33

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The thread that @hplieninger suggested on robustness is certainly apropos. However, I suggest that you can avoid this problem by using a method that does not depend on normal residuals. Two such are robust regression and quantile regression.

Peter Flom
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