I was wondering, how many assumptions of normal distribution must be violated to conduct a non-parametric test?
In my opinion, in my dataset, only one assumption has been violated which is p<0.05.
I think the first Q-Q plot looks ok but I am not sure. Also, I don't understand what the other Q-Q plot is for, and which one should I consider.

Therefore, I included an SPSS output so that someone more knowledgeable could give me a second opinion on this.

Please help!

testing for normality 1.jpg testing for normality 2.jpg testing for normality 3.jpg testing for normality 4.jpg


TS Contributor
Normality of the dependent variable is not an assumption for ANOVA.

The distribution within the ANOVA cells may be of interest, or simply the
distribution of the prediction errors from your model (the residuals).

But if the total sample size is large enough (n > 30 or so), that
normally-distributed-errors assumption is no longer necessary.

By the way, statistical tests of significance are nearly useless for such
analyses. They test whether the sample data deviate so much from the
null hypothesis ("the data are sampled from an exactely normally
distributed population, YES or NO?"), that it may be rejected. If sample
size is small (= low statistical power), the Null hypothesis can only be
rejected if there are vast deviations in the sample. If sample size is large,
even negligible deviations become "significant" (i.e. the Null hypothesis of
EXACT normality in the population is rejected).

With kind regards