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.

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.

Probability of obtaining, by chance alone, an F value larger than the one calculated if in reality the variances are equal across all levels.

Records the degrees of freedom in the numerator of the 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 the Welch ANOVA. The numerator degrees of freedom in this situation is the number of levels used in calculations minus one.

Records the degrees of freedom in the denominator of the test. See Tests That the Variances Are Equal.

Probability of obtaining, by chance alone, an F value larger than the one calculated if in reality the means are equal across all levels. Observed significance probabilities of 0.05 or less are considered evidence of unequal means across the levels.