# Statistics > Basic Statistics > Normality Test

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).

- To open the utility, select Statistics > Basic Statistics > Normality Test.
- Select the column containing the data values in the Input Variable drop-down menu.
- Select the significance level used in the Ryan-Joiner normality test.
- Select the Generate normal quantile plot check box if a normal quantile plot for the input data should be displayed.

- Enter the plot title in the Plot Title: text field.
- Enter labels for the x and y axis in the corresponding text fields.
- Select the Show regression line check box to show a best-fit line to the points on the plot.

- Click OK. The results of the Ryan-Joiner normality test will be displayed in the log window.