In most of my previous statistics tutorials, the techniques we have looked at have involved independent groups designs (where the groups being compared are made up of different people). However, we do have another option when designing experiments: subjecting the same people to different conditions. It's not difficult to imagine the benefits of this. Even on a practical level, it means we do not have to recruit as many participants. Statistically though, it also has the advantage of probably reducing the amount of error in our study. That is to say, we remove all the noise that is associated with the fact that people are different and that may affect the way they respond to our manipulation. Fabulous as they sound, they do have some shortcomings. All of the analysis techniques we've covered so far implicitly assume that observations have been randomly selected from the populations they represent. This cannot be true of repeated measures. There is dependency in the data by virtue of the fact that some people may do better on all the tasks in general than others. Therefore, we need specific procedures that can take this into account. In this video, I describe and demonstrate one such test - the one way repeated measures ANOVA.
Just like any analysis, we start off by looking at descriptive statistics to get a sense of what's going on in our date. We than have to restructure our data in a way that you may not be used to. In software packages like SPSS, each row in the dataset represents one participants and the columns represent their scores on different variables. This is called the wide format of data. In order to conduct this particular analysis, we need our data in the long format. This is where each row represents a single score on a single condition (so it participate has more than one row). Fortunately, R has packages that we can use to move between the two formats. After giving an example of how to do that, I go on to do the actual analysis. As part of this, we address the assumption of sphericity. Essentially, this says that, if we have to concede our data were not independent, then at least we need to know that level of dependency is the same across all conditions. Once we found a significant effect on the main analysis, we go on to find out which groups differ using post-hoc tests