The Ryan-Joiner (RJ) test for Normality is very similar to the Shapiro-Wilk test, but the authors claim it is simpler to implement in software and to explain to users, since it is simply a version of the correlation between the sample data, yi, and the bith percentage point of the Normal distribution:
Since the mean of the b values is 0, we can simplify this expression (ignoring the shift of the y-values by their mean) to:
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.
[RYA1] Ryan T A, Joiner B L (1976) Normal Probability Plots and Tests for Normality," Technical Report, Statistics Department, The Pennsylvania State University. Available from: http://www.minitab.com/uploadedFiles/Shared_Resources/Documents/Articles/normal_probability_plots.pdf