``Analysis of Variance.'' A Statistical Test for heterogeneity of Means by analysis of group Variances. To apply the test, assume random sampling of a variate with equal Variances, independent errors, and a Normal Distribution. Let be the number of Replicates (sets of identical observations) within each of Factor Levels (treatment groups), and be the th observation within Factor Level . Also assume that the ANOVA is ``balanced'' by restricting to be the same for each Factor Level.

Now define the sum of square terms

(1) | |||

(2) | |||

(3) | |||

(4) | |||

(5) |

which are the total, treatment, and error sums of squares. Here, is the mean of observations within Factor Level , and is the ``group'' mean (i.e., mean of means). Compute the entries in the following table, obtaining the

(6) |

Category | SS | °Freedom | Mean Squared | F-Ratio |

Treatment | SSA | |||

Error | SSE | |||

Total | SST |

If the *P*-Value is small, reject the Null Hypothesis that all Means are the same for the
different groups.

© 1996-9

1999-05-25