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I am quite an amateur in statistics. I have data where I would like to test if I can perform parametric or non-parametric testing depending on if the data is normally distributed or not. The data has one dependent variable "time to fatigue" that I wish to study and two grouping factors: "length" and "velocity".

The grouping factor "length" has 3 levels: 15, 30, and 100. The grouping factor "velocity" has 2 levels: 35 and 45.

In each level, there are 10 values of the dependent variable i.e., "time to fatigue".

Now if I wish to answer the question of whether "length" and "velocity" and "length: velocity" affect the "time to fatigue", I can perform a 2-way ANOVA.

However, I must make sure if I can perform parametric 2-way ANOVA or not.

My question now is on which data I must check the normality assumption.

Should I check if the 10 values of "time to fatigue" for each level are normally distributed? OR Should I check if the "time to fatigue" within each grouping factor is normally distributed? OR Should I check if the "time to fatigue" (taking all time to fatigue values at once) are normally distributed? What is the right approach? And what would it signify if one or two out of the above three options are normally distributed?

Thank you

Muhammad Usama Ashraf
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  • Have you seen this Q&A https://stats.stackexchange.com/questions/2492/is-normality-testing-essentially-useless – mdewey Aug 21 '22 at 14:03
  • Thanks for sharing. I did go through it. To me, the problem is not about what normality is and how well it should be treated. I am more concerned with an answer about the methodological approach to testing normality in a given data. – Muhammad Usama Ashraf Aug 21 '22 at 14:42
  • If you are really concerned about normality then you need to test the residuals from the fitted model. – mdewey Aug 21 '22 at 14:52

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