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4.1 Homogeneity of variance4.1 Homogeneity of variance 53It is assumed that the variance is homogeneous, that is, the size of the random variationis similar over all the units. Homogeneity of variance can easily be assessed by plottingthe residuals (estimates of the random error) against the fitted values: if the variance ishomogeneous, the residuals should lie within a uniform band as in Figure 4.1 below.Figure 4.1 Figure 4.2It is quite common, especially with count data, to find that the variation of the residualsincreases as the value of the response increases, as in Figure 4.2. In this case, the standarderrors of differences between treatments will be over-estimated for differences betweentreatments with low means, and under-estimated for differences between larger means,causing incorrect conclusions to be drawn. If a plot of residuals against fitted valuesindicates non-homogeneity of variances, a transformation of the data should beconsidered, as we show in Section 4.5.One situation where unequal variances can occur, but where a transformation may nothelp, is when analyses are performed on data collected in different years or at differentlocations. It is then important to check that the variances within the years (or at eachlocation) are homogeneous. Otherwise a weighted analysis will be required, with the datafrom each year being weighted by the reciprocal of the variance at that year. (This can bedone automatically by using the Multiple Experiments / Meta Analysis (REML) menu,although we do not cover that here.)