Testing for equal treatment means

If there is no baseline treatment, analysis should start with a single hypothesis test for whether all treatment means are equal. The standard multi-group analysis of variance test for equal means in a completely randomised experiment (ignoring the blocks) should not be used for experiments with blocks.

Ignoring the existence of blocks makes it much harder to detect differences between treatments.

Example

Five different observers each watched the same group of 10 cattle and reported how long each animal spent grazing.

Wrong analysis

Ignoring the fact that the same animals were observed by all five observers, the data would be analysed with the anova table below. From the large p-value, we would conclude that there were no differences between the observers.

Correct analysis

Much of the variability in the data is due to differences between the animals (blocks), and an analysis that ignores this is much less sensitive to differences between the observers. We will not explain the correct test for blocked data until later in this section, but it gives a p-value that is interpreted in the same way as the p-value above. It is shown below and shows that there are almost certainly differences between the observers.