Power and the within-subjects design. In an article applying models that use rep

Question

Power and the within-subjects design. In an article applying models that use repeated measures, thomas and zumbo (2012) identified that the within subjects ANOVA “ Can have ….. High power (p.42). As also identified in this chapter for the one-way within-subjects ANOVA, state the three rules for identifying when the within-subjects design is likely to be a more powerful test than a between-subjects design. Power and the within-subjects design. In an article applying models that use repeated measures, thomas and zumbo (2012) identified that the within subjects ANOVA “ Can have ….. High power (p.42). As also identified in this chapter for the one-way within-subjects ANOVA, state the three rules for identifying when the within-subjects design is likely to be a more powerful test than a between-subjects design.

Explanation / Answer

A within-subjects design is an experiment in which the same group of subjects serves in more than one treatment. Note that I’m using the word "treatment" to refer to levels of the independent variable, rather than "group". It’s probably always better to use the word "treatment", as opposed to group. The term "group" can be very misleading when you are using a within-subjects design because the same "group" of people is often in more than one treatment. As an example of a within-subjects design, let’s say that we are interested in the effect of different types of exercise on memory. We decide to use two treatments, aerobic exercise and anaerobic exercise. In the aerobic condition we will have participants run in place for five minutes, after which they will take a memory test. In the anaerobic condition we will have them lift weights for five minutes, after which they will take a different memory test of equivalent difficulty. Since we are using a within-subjects design we have all participants begin by running in place and taking the test, after which we have the same group of people lift weights and then take the test. We compare the memory test scores in order to answer the question as to what type of exercise aids memory the most.

Strengths

There are two fundamental advantages of the within subjects design: a) power and b) reduction in error variance associated with individual differences. A fundamental inferential statistics principle is that, as the number of subjects increases, statistical power increases, and the probability of beta error decreases (the probability of not finding an effect when one "truly" exists). This is why it is always better to have more subjects, and why, if you look at a significance table, such as the t-table, as the number of subjects increases the t value necessary for statistical significance decreases. The reason this is so relevant to the within subjects design is that, by using a within-subjects design you have in effect increased the number of "subjects" relative to a between subjects design. For example, in the exercise experiment, since you have the same subjects in both groups, you will have twice as many "subjects" as you would have had if you would have used a between-subjects design. If ten students sign up for the experiment, and you use a between-subjects design, with equal size groups, you will have five subjects in the aerobic condition and 5 in the anaerobic condition. However, if you use a within-subjects design you will in effect have 10 subjects in both conditions. Just as with the term "groups" vs. "treatments", instead of using the term "subjects" it’s better to speak of "observations", since the term subjects is misleading in the within-subjects design when the same person may effectively be more than one "subject".

The reduction in error variance is due to the fact that much of the error variance in a between-subjects’ design is due to the fact that, even though you randomly assigned subjects to groups, the two groups may differ with regard to important individual difference factors that effect the dependent variable. With within-subjects designs, the conditions are always exactly equivalent with respect to individual difference variables since the participants are the same in the different conditions. So, in our exercise example above, any factor that may effect performance on the dependent variable (memory) such as sleep the night before, intelligence, or memory skill, will be exactly the same for the two conditions, because they are the exact same group of people in the two conditions.

The important point is that this small but consistent difference can be detected in the face of large overall differences among the subjects. Indeed, the difference between conditions is very small relative to the differences among subjects. It is because the conditions can be compared within each of the subjects that allows the small difference to be apparent. Differences between subjects are taken into account and are therefore not error.

Removing variance due to differences between subjects from the error variance greatly increases the power of significance tests. Therefore, within-subjects designs are almost always more powerful than between-subject designs. Since power is such an important consideration in the design of experiments, within-subject designs are generally preferable to between-subject designs.

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