Welch and Brown-Forsythe one-way ANOVA
In an analysis of variance, it may happen that the variances can not be assumed to be equal. In this case, the F test of the ANOVA is not robust enough to be used.
XLSTAT offers two tests based on the F distribution but more robust than the classical F test.
These tests are:
- Welch Test or Welch ANOVA (Welch, 1951). The Welch test adjusts the denominator of the F ratio so it has the same expectation as the numerator when the null hypothesis is true, despite the heterogeneity of within-group variance. The p-value can be interpreted in the same manner as in the analysis of variance table.
- The Brown-Forsythe test or Brown-Forsythe F-ratio (1974). This test uses a different denominator for the formula of F in the ANOVA. Instead of dividing by the mean square of the error, the mean square is adjusted using the observed variances of each group. The p-value can be interpreted in the same manner as in the analysis of variance table.
These tests are only available with a one-way Analysis of Variance.
This analysis is available in the XLStat-Base addin for Microsoft Excel™