The R Book

Effect Sizes

In complicated designed experiments, it is easiest to summarize the effect sizes with the model.tables function. This takes the name of the fitted model object as its first argument, and you can specify whether you want the standard errors (as you typically would):

model.tables(model1, "means", se = TRUE)

Tables of means
Grand mean

3.851905

   Water

Water
 Tyne Wear
3.686 4.018

  Detergent

Detergent
BrandA  BrandB   BrandC   BrandD
 3.885   4.010    3.955    3.558

  Daphnia
Daphnia
Clone1   Clone2   Clone3
 2.840    4.577    4.139

Water:Detergent

      Detergent
Water  BrandA   BrandB   BrandC   BrandD
 Tyne   3.662    3.911    3.814    3.356
 Wear   4.108    4.109    4.095    3.760

Water:Daphnia

      Daphnia
Water  Clone1  Clone2  Clone3
 Tyne   2.868   3.806   4.383
 Wear   2.812   5.348   3.894

Detergent:Daphnia

Daphnia
Detergent  Clone1  Clone2  Clone3
   BrandA    2.73    3.919   5.003
   BrandB   2.929    4.403   4.698
   BrandC   3.071    4.773   4.019
   BrandD   2.627    5.214   2.834

Water:Detergent:Daphnia
, , Daphnia = Clone1

Detergent
Water   BrandA   BrandB   BrandC   BrandD
 Tyne    2.811    2.776    3.288    2.597
 Wear    2.653    3.082    2.855    2.656

, , Daphnia = Clone2

Detergent
Water  BrandA  BrandB  BrandC  BrandD
 Tyne   3.308   4.191   3.621   4.106
 Wear   4.530   4.615   5.925   6.322

, , Daphnia = Clone3

Detergent
Water   BrandA   BrandB   BrandC   BrandD
 Tyne    4.867    4.766    4.535    3.366
 Wear    5.140    4.630    3.504    2.303

Standard errors for differences of means
          Water   Detergent   Daphnia   Water:Detergent   Water:Daphnia
         0.1967      0.2782    0.2409            0.3934          0.3407
replic.      36          18        24                 9              12
         Detergent:Daphnia Water:Detergent:Daphnia
                    0.4818                  0.6814
replic.                  6                       3