Frequency Tables
- Normality Tab
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.
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 (e.g., see 1992);
if there are more than 5,000 observations,
this test cannot be performed.