I had two data samples; the first was constituted by 108 observations, the second was constituted by 88 observations. I used two Q-Q plots to check residuals normality. The Q-Q plots results were confirmed by the Shapiro Wilk test results. I read from statistical books that I could use other tests and there are differences among the tests. The Shapiro-Wilk test doesn't work well if several values in the data set are the same and works best for data sets with < 50, but can be used with larger data sets. The Kolmogorov -Smirnov is not sensitive to problems in the tails and for data sets > 50. Jarque -Bera test is a test for skewness and kurtosis, very effective. D’Agostino test is a powerful omnibus (skewness, kurtosis, centrality) test. W/S is simple but effective. Now, I have the following doubt: You would have examined in depth if you see that the results of a single test (in this case Shapiro-Wilk test) confirmed the graphical methods results? Are these differences among tests so important? What would you answer to those who ask you: "why did not you use other tests"? I am talking about assumption residuals normality distribution in regression. I would be very grateful to you if you could answer me.



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