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Block Design
Sir Ronald Fisher, the father of modern experimental design, extolled the advantages of block designs in his classic book, The Design of Experiments. He observed that block designs enable researchers to reduce error variation and thereby obtain more powerful tests of false null hypotheses. In the behavioral sciences, a significant source of error variation is the nuisance variable of individual differences. This nuisance variable can be isolated by assigning participants or experimental units to blocks so that at the beginning of an experiment, the participants within a block are more homogeneous with respect to the dependent variable than are participants in different blocks. Three procedures are used to form homogeneous blocks.
- Match participants on a variable that is correlated with the dependent variable. Each block consists of a set of matched participants.
- Observe each participant under all or a portion of the treatment levels or treatment combinations. Each block consists of a single participant who is observed two or more times. Depending on the nature of the treatment, a period of time between treatment level administrations may be necessary in order for the effects of one treatment level to dissipate before the participant is observed under other levels.
- Use identical twins or litter mates. Each block consists of participants who have identical or similar genetic characteristics.
Block designs also can be used to isolate other nuisance variables, such as the effects of administering treatments at different times of day, on different days of the week, or in different testing facilities. The salient features of the five most often used block designs are described next.
Block Designs with One Treatment
Dependent Samples t-Statistic Design
The simplest block design is the randomization and analysis plan that is used with a t statistic for dependent samples. Consider an experiment to compare two ways of memorizing Spanish vocabulary. The dependent variable is the number of trials required to learn the vocabulary list to the criterion of three correct recitations. The null and alternative hypotheses for the experiment are, respectively,
and
where μ1 and μ2 denote the population means for the two memorization approaches. It is reasonable to believe that IQ is negatively correlated with the number of trials required to memorize Spanish vocabulary. To isolate this nuisance variable, n blocks of participants can be formed so that the two participants in each block have similar IQs. A simple way to form blocks of matched participants is to rank the participants in terms of IQ. The participants ranked 1 and 2 are assigned to Block 1, those ranked 3 and 4 are assigned to Block 2, and so on. Suppose that 20 participants have volunteered for the memorization experiment. In this case, n = 10 blocks of dependent samples can be formed. The two participants in each block are randomly assigned to the memorization approaches. The layout for the experiment is shown in Figure 1.
The null hypothesis is tested using a t statistic for dependent samples. If the researcher's hunch is correct—that IQ is correlated with the number of trials to learn—the design should result in a more powerful test of a false null hypothesis than would a t-statistic design for independent samples. The increased power results from isolating the nuisance variable of IQ so that it does not appear in the estimates of the error effects.
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