Other Special Designs - Randomized Block Designs

Sometimes, experiments with an N of 1 are designed deliberately in order to reduce the SS error, yielding a more sensitive ANOVA design. Specifically, the observations in the design can be arranged in blocks, in a manner that allows computation of an unconfounded main effect estimate of the blocking factor. The error term is then reduced by the SS due to the blocking factor. (The term randomized blocks was first used by Fisher, 1926.)

Example
Suppose we want to test the yield of different varieties of wheat under three types of fertilizer. We have four different fields available for our research, and decide to treat them as an additional blocking factor in the design. The design could be summarized as follows:
  Field (Block)
Fertilizer Variety I II III IV
1 A
  1. 2
  1. 1
  1. 1
  1. 3
 B
  1. 1
  1. 8
  1. 6
  1. 4
 C - - - -
 D - - - -
2 A - - - -
 B - - - -
 C - - - -
 D - - - -
3 A - - - -
 B - - - -
 C - - - -
 D - - - -

In this example, we are actually not interested in the effect of the blocking variable itself, that is, any significant differences between fields are of no theoretical interest to us. However, by estimating the SS due to the blocking factor (Field), we may be able to reduce the error variance, allowing for more sensitive tests for the effect of Fertilizer, Variety, and the interaction between the two. Also note that in this type of design you also decide to ignore any interactions of the blocking variable with the variables of interest.

Setting up the data file
The data file for this experiment is set up in the same way as you would set up the file from a regular full factorial between-groups experiment. The file should contain three grouping variables (Fertilizer, Variety, and Field) with codes that uniquely identify to which cell in the design each case belongs. The fourth variable in the file would be the dependent variable (Yield).
Specifying and analyzing the design
In GLM, specify the DESIGN (either via the GLM Analysis Syntax Editor dialog or the GLM Analysis Wizard Between Design - Custom Between Design tab) to include only the effects of interest.  For example, you could include in the model only the effects for Fertilizer, Variety, Field, and the interaction between Fertilizer and Variety. On the GLM Results - Quick tab, click the All effects button to review the ANOVA table for all effects.