Desc – Shapiro-Wilk Test

On this webpage, we describe in detail the Shapiro-Wilk option of the Real Statistics Descriptive Statistics and Normality data analysis tool. We use the example data shown in Figure 3 of the Descriptive Statistics and Normality Tool, repeated in Figure 1 below.

Figure 1 – Example data

Shapiro-Wilk option

When the Shapiro-Wilk option is chosen on the dialog box in Figure 2 of Descriptive Statistics and Normality Tool on the data in Figure 1, the output in Figure 2 is displayed. Note that in addition to obtaining the results of the Shapiro-Wilk test for normality on each of the three data sets in Figure 1, this option also displays the results of the d’Agostino-Pearson test for normality.

Figure 2 – Shapiro-Wilk and d’Agostino-Pearson Tests

We see from Figure 2, that both tests indicate that the data in X likely comes from a normally distributed population, while data in Z is unlikely to come from a normally distributed population. The two tests give different results for data set Y. Note that the presence of outliers may account for a non-normal result.

Details

The formulas used to calculate the values for data set X in Figure 2 are shown in Figure 3.

Figure 3 – Formula details

If you change any of the values in Figure 1, the values output in Figure 2 will change accordingly. You can also change the alpha value in row 7 or 14 and the conclusions in rows 8 and 15 will change accordingly.

If you add additional elements to the data sets in Figure 3, these will not be considered. If you replace any of the numeric values with a blank or non-numeric value, then this element will no longer figure into the calculation of the various statistics displayed in Figure 2.

See Shapiro-Wilk Expanded Test and d’Agostino-Pearson Test for more information about these tests and the worksheet formulas used in Figure 2.