Making all block means equal

We showed earlier that it is poor to test for equal treatment means with an Analysis of Variance (anova) table that ignores the blocks. The extra variability in the response that is caused by differences between the blocks makes it far harder to detect treatment differences.

Adding or subtracting a value from each block to make all block means equal would get rid of the differences between the blocks. Although the resulting anova table is not completely correct for testing whether the treatment means are equal, its sums of squares are the basis for the test.

Amino acid uptake by fish

Grazing cattle in Uganda

The treatment and residual sums of squares shown above are the basis for testing whether the treatment means are all equal. However:

The analysis described on this page is not completely correct — the residual degrees of freedom are too high.

We will next describe the correct anova table for testing equal treatment means with randomised block data.