Match test structure to the data

Independent-sample tests compare separate groups; paired tests analyse within-pair differences, such as before and after observations on the same students. A paired t statistic is mean difference divided by its standard error: t=(mean(d)-d0)/(sd/√n), df=n-1. The differences should be independent across pairs and approximately normal for small-sample exact t inference. Do not test paired data as though all readings were independent.