This section applies only when the means are computed from independent samples. The formulas are more complicated when the two means are not independent. Let's say that a researcher has come up with a drug that improves memory. Consider two hypothetical populations: the performance of people on a memory test if they had taken the drug and the performance of people if they had not. Assume that the mean (μ) and the variance () of the distribution of people taking the drug are 50 and 25 respectively and that the mean (μ) and the variance () of the distribution of people not taking the drug are 40 and 24 respectively. It follows that the drug, on average, improves performance on the memory test by 10 points. This 10-point improvement is for the whole population. Now consider the sampling distribution of the difference between means. This distribution can be understood by thinking of the following sampling plan: