Use this diagram to explain that subtracting a block effect from the values before using doing analysis of variance reduces the unexplained variability, and therefore the residual sum of squares.
Coloured vertical lines show the block means. Click Make all block means equal.
The resulting anova table has the correct explained and residual sum of squares but the residual degrees of freedom are too high.
Although the analysis is only approximate (since the residual df are wrong), explain that:
The F-ratio becomes large and the p-value becomes closer to zero when the block effects are removed.
Amino acid uptake by fish
Amino acid uptake varies considerably between fish. The intestines of each fish only give six perparations on which to do an experiment about how NaCN affects uptake of amino acid.
Comparing observers who watched grazing cattle in Uganda
Five observers simultaneously watched the same group of 10 cattle for 88 minutes in one afternoon. Each person reported the number of minutes that each animal was observed grazing.
The animals can be treated as blocks — we are mostly interested in differences between the observers in this study.