overview of the Shapiro Wilks W-Test
Shapiro and Wilk's W-test is a test for normality. The Shapiro Wilk test tests the null hypothesis that a sample follows a normal distribution.
The formula of the test statistic is:
where X is the studied sample, X⁡i is the ith smallest data in X, Xi is the ith data in X, ai are the coefficients to estimate straightness of the quantile-quantile plot.
The definitions of these coefficients are beyond the scope of this guide.
The null hypothesis that the sample follows a normal distribution is rejected if W is too small.
Pete wants to use a one sample t-test to test the mean of the average lifetime of light bulbs of a particular type, but he does not know if the observations are normally distributed. To test this, he applies Shapiro and Wilk's W-test to the sample of data.
His observed data:
Determine the null hypothesis:
Null hypothesis: The data is normally distributed
Collect the data:
Run the Shapiro Wilk w-Test:
Shapiro and Wilk's W-Test for Normality
Sample drawn from a population that follows a normal distribution
Sample drawn from population that does not follow a normal distribution
Sample Size: 20
Computed Statistic: .935508635130523
Computed p-value: .207505438819378
This statistical test does not provide enough evidence to conclude that the null hypothesis is false.
The Shapiro and Wilk's W-test returns a p-value = 0.207505. From this p-value, Pete concludes that the data can indeed be assumed to be normal and proceed with one sample t-test.
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