# Violation of assumptions for a one Way ANOVA analysis

I am trying to do a one way ANOVA and having some difficulty proceeding it. Among all the assumptions, I am stuck with these two: normality and equal variance. My questions are,

1. My independent variable has 4 categories. The normality assumption is satisfied for two of the 4 categories. I read that ANOVA is quite robust so a small violation of normality is not a big deal. How can I decide that the violation is acceptable?

2. If homogeneity of variances is violated, it is suggested to do a Welch's F test. I assume I can only do that if the normality assumption is satisfied. Is that correct?

Looking forward to any suggestions! .

• Since ANOVA is regression, some of these questions have answers at stats.stackexchange.com/questions/32600. It's unclear what a "significant outlier assumption" might be--one hopes there are no outliers and that check is a big part of normality testing in the first place. Might I suggest you therefore focus on the third and fourth questions alone?
– whuber
Commented Mar 24, 2017 at 21:04
• You should probably break this into separate questions / threads. You should also probably search the site, a lot of this may be available already. Lastly, very few people will know what SPSS does or why. That question (2) you should ask the SPSS tech support, not us. Commented Mar 24, 2017 at 21:05
• @gung I searched. Specifically, I would like to know how far the violation of normality is acceptable. Doing some normality test like Kolmogorov-Smirnov or Shapiro-Wilk test produce non-normality (based on p-value) for some categories but a rough look at the histogram seems okay. Commented Mar 24, 2017 at 21:15
• If your histogram looks ok then it probably is. If your sample size is large then statistical tests will always produce a significant value. If it looks normal to you then I wouldn't worry Commented Mar 25, 2017 at 3:50
• @ConorNeilson thanks. One thing just crossed over my head. If my sample size is over 30 in each group, can I assume normality? Commented Mar 27, 2017 at 14:45