The normality test utility performs the Ryan-Joiner normality test and creates a normal quantile plot for a set of sample data values. The Ryan-Joiner normality test computes a correlation coefficient and critical value used to test the claim that a population is normally distributed. The null hypothesis of the test is that the population is normal. The test statistic is the correlation coefficient r:
where x and y are the ordered observations and their normal scores, respectively. The normal scores for the ordered observations are the inverse cumulative normal probabilities for (i+1)/(n+1), where n is the sample size and i=0...n-1.
The critical values for significance level α = 0.10, 0.05, and 0.01 are approximated as follows:
If the test statistic r is less than the critical value, reject the null hypothesis that the population is normal; otherwise, fail to reject the null hypothesis.
This utility allows the user to specify a column containing the sample data values. The user can select the significance level used for the Ryan-Joiner normality test. It also provides the option of generating a normal quantile plot (along with the options of having a plot title, axis labels, a regression line, and whether the data values should be used as x or y coordinates).