Reporting

It is generally more helpful to replace the individual standard errors for each factor level by a single value that represents the approximate standard error of the differences between pairs of means. The validity of doing so depends on the distribution of numbers of observations across the different levels of a parameter. There is some disparity in numbers of lambs across the four levels for genotype and the six levels for year in the previous table. Even with the variation in frequencies here, however, it is reasonable to calculate average standard errors. It is best to calculate the average standard error as the square root of the average of the sum of the squares of the individual standard errors. The average S.E.D. is then this figure multiplied by the square root of 2.

Thus, for genotype (see last GenStat output)

average standard error of difference (S.E.D) = square root [2(0.16² + 0.18² + 0.19² + 0.24²)/4] = 0.28

In general this can be considered to be a fairly satisfactory estimate provided there is no covariance between the different levels of the parameter. To get the exact average value one would, for genotype for instance, need to rerun the model three times, changing the reference level each time. One gets a series of standard errors of differences from the reference levels. By picking out the six values that correspond to the standard errors of the differences between the six different pairs of means, and calculating the average, one gets the correct average. In practice this is usually unnecessary.