Shapiro-Wilk Test
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Tap a term to see what it means, or .
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Example: the weights of eleven men, in pounds, from Shapiro and Wilk's original paper. Do the data look like they come from a normal? Change the values to test your own.
Step by step
What each term means
- Statistic W
- From 0 to 1. Near 1, the sorted data line up with what a normal sample would give; lower values point to departure from normality.
- Combination of the Sorted Values
- x₍ᵢ₎ is the i-th smallest value. The weights aᵢ come from the expected quantiles of a normal sample of the same size: the numerator is a standard deviation estimate that only holds if the data are normal.
- Sum of Squares
- The usual variation, which estimates the standard deviation without assuming anything. W compares the two estimates.
When to use it, assumptions and alternatives: the Shapiro-Wilk test in the statistical tests catalog.