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

About KCS

Kovach Computing Services (KCS) was founded in 1993 by Dr. Warren Kovach. The company specializes in the development and marketing of inexpensive and easy-to-use statistical software for scientists, as well as in data analysis consulting.

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