![]() ![]() 05, we fail to reject the null hypothesis. The following code shows how to perform a Shapiro-Wilk test on this sample of 100 data values to determine if it came from a normal distribution: from scipy.stats import shapiro #generate dataset of 100 random values that follow a standard normal distribution Suppose we have the following sample data: from numpy.random import seed Example 1: Shapiro-Wilk Test on Normally Distributed Data This tutorial shows a couple examples of how to use this function in practice. If the p-value is below a certain significance level, then we have sufficient evidence to say that the sample data does not come from a normal distribution. This function returns a test statistic and a corresponding p-value. To perform a Shapiro-Wilk test in Python we can use the () function, which takes on the following syntax: It is used to determine whether or not a sample comes from a normal distribution. If the test statistic W is smaller than the critical threshold (see table below) the assumption of a normal distribution has to be rejected.The Shapiro-Wilk test is a test of normality. Calculate the test statistic W = b 2/S 2.The parameters a n-i+1 depend on the sample size and have to be taken from a table published by Shapiro and Wilk a) if n is even, then b is calculated using mit k = n/2:ī) if n is odd, b is calculated by using k=(n-1)/2, the median must not be included.The sample of size n (x 1,x 2.x n) has to be sorted in increasing order, the resulting sorted sample will be designated by y 1,y 2.y n (y 1 ![]() In order to calculate the statistic W one has to perform the following procedure: If the quotient is significantly lower than 1.0 then the null hypothesis (of having a normal distribution) should be rejected. Both estimated values should approximately equal in the case of a normal distribution and thus should result in a quotient of close to 1.0. The basis idea behind the Shapiro-Wilk test is to estimate the variance of the sample in two ways: (1) the regression line in the QQ-Plot allows to estimate the variance, and (2) the variance of the sample can also be regarded as an estimator of the population variance. In contrast to other comparison tests the Shapiro-Wilk test is only applicable to check for normality. The Shapiro-Wilk test is a test for normal distribution exhibiting high power, leading to good results even with a small number of observations. ![]()
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