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2 different species (1 & 2). 17 variables (A-Q). N: number of meaurements. I needed to test for normality before performing ANOVA.

Using the software PAST this is the result: normality test

I highlighted in green the cells of values that would not support a normal distribution.

Given these results, how can I interpret the test? Can the relatively high number of measurements, at least in part, counterbalance the lack of normality that occurs for some variables?

After all, can I accept the result of ANOVA as plausible?

NB: I am not a statistician.

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    $\begingroup$ I think you need please to back up here and tell us more about the science before we can advise on the statistics. Wanting to apply ANOVA 17 times (see comment in reply to Peter's answer) implies that you are going to get a mass of results. What's the strategy for dealing with them? Also, phrasing the question in terms of "the result" or "the test" seems to contradict what you're telling us otherwise. Why different sample sizes? Does that mean problems with missing values? $\endgroup$
    – Nick Cox
    Aug 18, 2023 at 12:45

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You write:

I needed to test for normality before performing ANOVA.

No, you did not. ANOVA does not assume variables are normally distributed. It makes assumptions about the errors. Indeed, ANOVA is mostly made for categorical independent variables and they can't possibly be normal.

You should look at the normality of the residuals, but you should use plots (especially a quantile normal plot) to do so, not tests. Your table of results is a great illustration of one reason why you shouldn't use tests of normality: They disagree with each other. (Another reason is that the p value is conflated with the sample size).

Also, your sample size is too small for a model with 17 variables.

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    $\begingroup$ Picking up the last paragraph: The question is ambiguous to me. OP: Do you want to do ANOVA 17 times, or all your 17 variables different levels of one variable? $\endgroup$
    – Nick Cox
    Aug 18, 2023 at 12:24
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    $\begingroup$ @Nick Cox ANOVA 17 times $\endgroup$
    – dandelion
    Aug 18, 2023 at 12:28
  • $\begingroup$ @Peter Flom for residuals do you mean this plot? [![enter image description here][1]][1] [1]: i.stack.imgur.com/IXmHg.jpg Shapiro-Wilk. W: 0,9858 p(normal): 0,2044 Can I assume it is normal? $\endgroup$
    – dandelion
    Aug 18, 2023 at 12:38
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    $\begingroup$ That's a variation on what I meant, and it looks pretty normal to me. $\endgroup$
    – Peter Flom
    Aug 18, 2023 at 13:18

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