The most elementary statistical test is the paired samples t-test with just two pairs. Here the data set to be analysed consists of two numbers (the two paired differences), and the statistical test examines whether the population mean is zero. This test can be derived in a surprisingly fast and intuitive manner by plotting one number against the other on a piece of graph paper, then joining th...

We consider the situation in two sample testing when one variance is assumed to be known while the other variance is considered unknown. This situation arises, for example, when one is interested in comparing a standard treatment with a new treatment. Although this situation occurs relatively infrequently, our example discusses the important tool of moment matching and makes the classic two sam...

Researchers occasionally have to work with an extremely small sample size, defined herein as N ≤ 5. Some methodologists have cautioned against using the t-test when the sample size is extremely small, whereas others have suggested that using the t-test is feasible in such a case. The present simulation study estimated the Type I error rate and statistical power of the oneand two-sample ttests f...