I received an email inquiry about a project that involved four repeat assessments on 10 different subjects. The question started out as, is my sample size 10 or is it 40?

My immediate response was to ask for more details, but to also point out that 4 repeated measurements on 10 subjects is not the same as 40 independent observations. There is almost always a positive correlation among these measurements and that implies a level of redundancy. You don’t get as much information as you would with 40 independent observations.

But it is not the same as a sample size of 10 either. The repeated measurements do add a level of precision, so you have more information than if you collected a single measurement on 10 subjects.

I then suggested that sometimes a design like this could be greatly simplified if you calculated a single summary statistic across the four measurements. For example, an average of the four measurements, a maximum value, or a difference between the first and last measurements might all be useful. At other times, however, such a summary would be overly simplistic and should be avoided.

It turns out that the data was categorical, so a change score or mean would be inappropriate. But the categories did have a natural ordering and selecting the maximum value was a good solution.

Repeated measurements lead to some of the most difficult problems with data management and with data analysis and the solutions are often very dependent on the context in which the repeated measurements were done.

You can find an earlier version of this page on my original website.