Ophthalmic statistics note 1: unit of analysis

Abstract

A senior colleague has conducted a study and asks me to analyse their data. They give me an excel spreadsheet containing 80 observations of intraocular pressure (IOP)—40 of which were made after using drug A and 40 of which were made after using drug B (see table 1). View this table: Table 1 80 observations of IOP My colleague asks me to find out whether drug A or drug B is better in terms of reducing IOP. I think back to my medical school training and recall something called a t test, which I believe may be relevant. Using the internet I discover that there is indeed a t test and that the t test can be used to compare the means of two groups. I apply the test and feedback the results (including a two-tailed p value of 0.0024) to my colleague (see online supplementary appendix 1, figure S1 for results of analysis). The paper is written and submitted. After some time, it is returned with several comments made by reviewers. One of these questions is whether I have assessed the assumptions made by a t test. I must admit to not being entirely clear what this sentence means. Using the internet once more, I learn that the p value I quoted to my colleague has been calculated using statistical theory, but that if this p value is to be regarded as robust or valid, my data must adhere to some rules (or assumptions). Assumption 1 of the t test is that my data follow approximate normality. I draw a histogram of my IOP observations and see that it looks roughly symmetric, which reassures me somewhat as evidently rough normality can be assumed with an approximate symmetric histogram (see figure 1). Figure 1 Histogram of 80 observations of intraocular pressure (overall and by drug …