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Ryan and Joiner (1976, [RYA1]) derived approximations to the distribution of this statistic using simulation, expressing the result in the form of fitted equations. The resulting test is very highly correlated with that of Shapiro and Wilk, so either test may be used and will produce very similar results. The Ryan-Joiner test is implemented in the Minitab software package but not widely elsewhere.

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Q: What is Ryan joiner test?
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