It turns out that t-statistics can be computed a number of different ways on samples drawn in a number of different situations and still have the same relative frequency distribution. The relative frequency distribution of these t-statistics is the t-distribution. For each sample, the same statistic, called the t-statistic, which we will learn more about later, is calculated. The t-distribution can be formed by taking many samples (strictly, all possible samples) of the same size from a normal population. This chapter will discuss the normal distribution and then move on to a common sampling distribution, the t-distribution. If you ever took a class when you were “graded on a bell curve”, the instructor was fitting the class’s grades into a normal distribution-not a bad practice if the class is large and the tests are objective, since human performance in such situations is normally distributed. The normal distribution is the bell-shaped distribution that describes how so many natural, machine-made, or human performance outcomes are distributed. It is normal because many things have this same shape. The normal distribution is simply a distribution with a certain shape.
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