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1/4/2023 0 Comments Shapiro wilk test![]() In conclusion, in this tutorial, we have seen how to test two samples for normality using Shapiro-Wilk and Jarque-Bera tests. This gap is confirmed by the normality tests (see below) which allow us to assert with no hesitation that we need to reject the hypothesis that the sample might be normally distributed. Contrary to what we have observed for the first sample, we notice here on the Q-Q plot that there are two strong deviations indicating that the distribution is most probably not normal. The following results are for the second sample. We notice that with the Shapiro-Wilk test, the risk of being wrong when rejecting the null assumption is smaller than with the Jarque-Bera test. The Shapiro-Wilk and Jarque-Bera confirm that we cannot reject the normality assumption for the sample. We can see here that the empiric cdf is very close to the bisecting line. In the other cases some deviations from the bisecting line should be observed. In the case of a sample following a normal distribution, we should observe an alignment with the first bisecting line. The Q-Q plot allows us to compare the cumulative distribution function (cdf) of the sample (abscissa) to the cumulative distribution function of the normal distribution with the same mean and standard deviation (ordinates). The first result displayed is the Q-Q plot for the first sample. The results are first displayed for the first sample and then for the second sample. Interpreting the results of a Shapiro-Wilk and other normality tests The computations begin once you have clicked on the OK button, and the results are displayed on a new sheet. The Q-Q plot option is activated to allow us to visually check the normality of the samples. Select the two samples in the Data field. Once you've clicked on the button, the dialog box appears. Select the XLSTAT / Describing data / Normality tests, or click on the corresponding button of the Describing data menu. 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