![]() ![]() ![]() The probability of getting a p < 0.05 depends on the size of your sampleĪ large enough sample size will make the Shapiro-Wilk test detect the smallest deviation from normality, in this case the p-value will be < 0.05 even if the variable is, in fact, normally distributed. “ The distribution of the variable was determined using the Shapiro-Wilk test“.Ģ.“ Normality of the data was confirmed by a Shapiro-Wilk test“.“ The normality assumption was verified using the Shapiro-Wilk test“.“ The Shapiro-Wilk test indicates that the variable has a normal distribution“.So be aware of incorrect interpretations like the following: This is why in the example above, where we reported a Shapiro-Wilk test with a p > 0.05, we used the words: “the Shapiro-Wilk test did not show evidence of non-normality“. A p > 0.05 does not prove the alternative hypothesis:Ī Shapiro-Wilk test with a p > 0.05 does not mean that the variable is normally distributed, it only means that you cannot reject the null hypothesis which states that the variable is normally distributed. Important notes for reporting a Shapiro-Wilk test 1. Based on this outcome, a non-parametric test was used, and the median with the interquartile range were used to summarize the variable X. So a Shapiro-Wilk test was performed and showed that the distribution of X departed significantly from normality (W = 0.96, p-value < 0.01). Since we had a small sample size, determining the distribution of the variable X was important for choosing an appropriate statistical method. Here are 2 examples: Example 1: Reporting a Shapiro-Wilk test with p ≤ 0.05 The consequences/interpretation of these results.The results of the test: the value of the test statistic W and the p-value associated with it.When reporting the Shapiro-Wilk test, the following should be mentioned: the variable MAY BE normally distributed). If p > 0.05: then the null hypothesis cannot be rejected (i.e.the variable is NOT normally distributed). If p ≤ 0.05: then the null hypothesis can be rejected (i.e.The null hypothesis (H 0) states that the variable is normally distributed, and the alternative hypothesis (H 1) states that the variable is NOT normally distributed. The Shapiro-Wilk test is a statistical test used to check if a continuous variable follows a normal distribution. ![]()
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