It does this by ordering and standardizing the sample ( standardizing refers to converting the data to a distribution with mean μ = 0 and standard deviation σ = 1). That is, it examines how close the sample data fit to a normal distribution. The Shapiro–Wilk test is essentially a goodness-of-fit test. If Calc W > Tab W, then we do not reject the null hypothesis. ■Ĭompare the test statistic with a critical value: The critical W values for a Shapiro–Wilk test are shown in Table A.7 in the Appendix. Finally, the test statistic is computed as Calc W = b 2 ( n − 1 ) s 2, where s is the sample standard deviation. Next, we calculate b = a 1 ( x ( n ) − x ( 1 ) ) + a 2 ( x ( n − 1 ) − x ( 2 ) ) …, where a 1, a 2, … are the coefficients from Table A.6 (see Appendix). ■Ĭompute a test statistic: We do this by first ranking the sample values in increasing order – we denote these ranked data by ( x ( 1 ) x ( 2 ) … x ( n − 1 ) x ( n )), where n is the sample size. We can choose any degree of confidence, but common choices are 95% and 99%. ■įorm null and alternative hypotheses and choose a degree of confidence: For the Shapiro–Wilk test, the null hypothesis is that the sample comes from a normal distribution, and the alternative hypothesis is that it does not. The Shapiro–Wilk test is a hypothesis test, and so we will follow the checklist for hypothesis testing that we first introduced in Section 5.2.
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