Basic Analysis and Graphing - SAS

Chapter 5 Performing Oneway Analysis 157
Unequal Variances
Tests That the Variances Are Equal Report
The Tests That the Variances Are Equal report shows the differences between group means to the grand
mean and to the median, and gives a summary of testing procedures.
If the equal variances test reveals that the group variances are significantly different, use Welch’s test instead
of the regular ANOVA test. The Welch statistic is based on the usual ANOVA F test. However, the means are
weighted by the reciprocal of the group mean variances (Welch 1951; Brown and Forsythe 1974b; Asiribo,
Osebekwin, and Gurland 1990). If there are only two levels, the Welch ANOVA is equivalent to an unequal
variance t-test.
Table 5.18 Description of the Tests That the Variances Are Equal Report
Level
Count
Std Dev
MeanAbsDif to Mean
MeanAbsDif to Median
Test
F Ratio
DFNum
DFDen
p-Value
Lists the factor levels occurring in the data.
Records the frequencies of each level.
Records the standard deviations of the response for each factor level. The
standard deviations are equal to the means of the O’Brien variable. If a level
occurs only once in the data, no standard deviation is calculated.
Records the mean absolute difference of the response and group mean. The
mean absolute differences are equal to the group means of the Levene
variable.
Records the absolute difference of the response and group median. The
mean absolute differences are equal to the group means of the
Brown-Forsythe variable.
Lists the names of the tests performed.
Records a calculated F statistic for each test.
See “Statistical Details for the Tests That the Variances Are Equal Report” on
page 181.
Records the degrees of freedom in the numerator for each test. If a factor has
k levels, the numerator has k - 1 degrees of freedom. Levels occurring only
once in the data are not used in calculating test statistics for O’Brien,
Brown-Forsythe, or Levene. The numerator degrees of freedom in this
situation is the number of levels used in calculations minus one.
Records the degrees of freedom used in the denominator for each test. For
O’Brien, Brown-Forsythe, and Levene, a degree of freedom is subtracted for
each factor level used in calculating the test statistic. One more degree of
freedom is subtracted for the overall mean. If a factor has k levels, the
denominator degrees of freedom is n - k -1.
Probability of obtaining, by chance alone, an F value larger than the one
calculated if in reality the variances are equal across all levels.