Frequency Tables - Normality Tab
Procedure
- Select the Normality tab of the Frequency Tables dialog box to access options to test the normality of the selected variables. Options for generating probability plots are available on the Descr. tab. When any of the check boxes on this tab are selected, after the frequency tables for the selected variable have been produced (via the Summary button), additional spreadsheets will be created with the requested tests of normality (one spreadsheet per test).
- To display these tests only, click the Tests for normality button.
Result
Tests for normality
Click the Tests for normality button to produce the results spreadsheets with the requested tests of normality (see below) for the selected Variables.
Kolmogorov-Smirnov test, mean/std. dev known
Select the Kolmogorov-Smirnov test, mean/std. dev known check box to compute the Kolmogorov-Smirnov one-sample test of normality when the Tests for normality button is clicked.
Specifically, if the Kolmogorov-Smirnov D statistic is significant, the hypothesis that the respective distribution is normal should be rejected. The probability values that will be reported are based on those tabulated by Massey (1951); those probability values are valid when the mean and standard deviation of the normal distribution are known a priori and not estimated from the data. However, usually those parameters are computed from the actual data. In that case, the test for normality involves a complex conditional hypothesis ("how likely is it to obtain a D statistic of this magnitude or greater, contingent upon the mean and standard deviation computed from the data"), and the Lilliefors probabilities should be interpreted (Lilliefors, 1967). Note that, in recent years, the Shapiro-Wilk's W test (see below) has become the preferred test of normality because of its good power properties as compared to a wide range of alternative tests (Shapiro, Wilk, & Chen, 1968).
Lilliefors test, mean/std. dv unknown
Select the Lilliefors test, mean/std. dv unknown check box to compute the Kolmogorov-Smirnov one-sample D statistic and report the Lilliefors probabilities (see previous paragraph; see also Lilliefors, 1967) when the Tests for normality button is clicked.
Shapiro-Wilk's W test
Select the Shapiro-Wilk's W test check box to compute the Shapiro-Wilk's W test of normality when the Tests for normality button is clicked.
If the W statistic is significant, the hypothesis that the respective distribution is normal should be rejected. The Shapiro-Wilk's W test is the preferred test of normality because of its good power properties as compared to a wide range of alternative tests (Shapiro, Wilk, & Chen, 1968). The algorithm implemented in Statistica employs an extension to the test described in Royston (1992), which enables it to be applied to samples with up to 5,000 observations ( see 1992); if there are more than 5,000 observations, this test cannot be performed.