Residual vs fitted plot

Homogeneity of variance plot

Histogram of residuals

Hello, I have a fairly big dataset containing 11000 data points. I am doing a ANOVA for my traits. But before that I have to make sure if the residuals are normally distributed or not. So, I did a linear modelling and plotted the residuals. What is your opinion on the residuals? Can I proceed with the ANOVA? I cannot perform the shapiro test as I have more than 5000 data points. I did a leveneTest and Anderson-Darling test of my residuals, but they are all highly significant. Moreover, I also did a lot of transformation like Box-Cox, log, square and cube root. In each cases the p-value is highly significant for residuals. Can you please suggest something?

Secondly, if I use a transformed data for ANOVA, do I need to use that transformed data for subsequent analyses like correlation, PCA etc.? or can I use non-transformed value for those analyses? I have some outliers which I must not delete. Please help. Regards Anik

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    $\begingroup$ Welcome to CV! I have marked this question a duplicate of Regression - How do I know if my residuals are normally distributed?. Btw, why are you interested in $p$-values if your sample size is that large? Almost any test will be significant. $\endgroup$ May 10, 2019 at 11:05
  • $\begingroup$ Well, I am just trying to be on the safe side. Because for doing an ANOVA, the assumptions should be met. Although I have no idea if the data is that large, then I should consider those or not. Also, I will do a GWAS with this data. And there the normality of residuals is an important issue. So, do you think I should not pay attention to the normality of residuals? $\endgroup$
    – Anik Dutta
    May 10, 2019 at 11:23
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    $\begingroup$ clearly your data are bounded between two values; they are obviously not normal. $\endgroup$
    – Glen_b
    May 10, 2019 at 12:09