Repeated measures ANOVA

Analysis of variance, or simply, ANOVA, is a type of parametric statistical test used to determine if there’s a significant difference between the means or averages of three or more groups. And significance is normally defined by a p-value of less than 0.05 or 5%.

Now when doing any parametric test, there are three key assumptions that we have to make about the population. First, the sample population must have been recruited randomly. Choosing names randomly ensures that the people included in the study will have similar characteristics to the target population. This is important because that ensures that the results of the test can be applied to the target population - meaning it has good external validity! The second assumption is that each individual in the sample was recruited independently from other individuals in the sample. In other words, no individuals influenced whether or not any other individual was included in the study. For example, if two friends decided to get their blood pressures measured on the same day, and they were both included in the study, these two individuals would not be independent of each other and the second assumption would not be met. Like random sampling, independent recruitment of individuals is important because it ensures that the sample population approximates the target population. The third assumption is that the sample size is large enough to approximate the target population, which usually means having more than 20 people. If it’s impossible to get a large sample size, then the sample population must follow a normal bell-shaped distribution for the characteristic being studied because that’s what we would expect to see in the target population.

Okay, now let’s say there’s a certain blood pressure medication, called Medication A, and you want to figure out if it helps lower systolic blood pressure after taking it for three months and after taking it for six months. So, you find 10 people and give each of them Medication A. Then, you measure each of their systolic blood pressures at time 1 - which is the time you initially gave them the medication - and then measure it again at time 2, let’s say 3 months later, and time 3, let’s say 6 months after they started taking the medication. You find out that the mean systolic blood pressure measurement at time 1 is 138; at time 2 it’s 132, and at time 3 it’s 130. Now, the next step is to figure out if 138, 132, and 130 are significantly different from one another, and you do that by performing an ANOVA test.

Specifically, we would use a repeated measures ANOVA test, because we’re looking at the same group of people at multiple time periods. In a repeated ANOVA test, time is the independent variable, and in this example, systolic blood pressure is the dependent variable. It might be tempting to think that medication type is the independent variable in this study, but this isn’t the case, since everyone in the study is taking the same medication type.