Check model assumptions

Before we continue with the analysis, it is important to check model assumptions, because if assumptions are not met, then the conclusions from our analysis will not be valid.

Recall that the assumptions for ?_ij were independence and identical distribution (iid), with ?_ij  ~N(0, σ^2 ), and we use the observed residuals to check the assumptions.

Checking model assumptions:

Independence: we cannot check this using the data, independence is assured by the randomization process.

Normality: residuals should follow a normal distribution (not data itself!).

We can use a quantile-quantile plot or QQ plot for short (Normal plot and Half-Normal plot in the GenStat output).


The plot shows the residuals versus expected values given a Normal distribution. If both correspond well, dots should be on a diagonal as the ones shown in the plot are.

Equal variance: the variation should be the same for different treatment levels.

We can plot residuals versus fitted values (Fitted-value plot in GenStat).

Dispersion around 0 (red line in the plot) should be approximately the same along the x axis as roughly is the case in the example shown.