Agility Ratings and Ground Meat: Introducing Mann-Whitney Differences

Abstract

This is an Elementary Statistics course for undergraduates majoring in social sciences, business and related subjects, not mathematics. The amount of mathematics studied by most students in the course is limited, and so is their enthusiasm for mathematics. Under these circumstances but really in all introductions to statistics it seems appropriate to introduce the concepts of confidence interval estimation and hypothesis testing first by use of methods free of distributional assumptions, advanced probability theory or computational involvement. Accordingly, the course has begun with the definition of a sample median and the other order statistics (no computation) and the use of sample order statistics as confidence limits for a population median. Confidence probabilities could be calculated by very simple algebraic reasoning in some cases or estimated by doing a little experimental sampling. Subsequently, we always look up the probability, or the interval for a desired probability, in a table. Thus a student is able to estimate a population median by a confidence interval without going through much of a hassle. After this, the identical method is applied to samples of differences in matched pairs or before-andafter studies to estimate how much difference a treatment makes or to inquire whether it makes any difference. Hypothesis testing thus drops out as a corollary: Reject the null hypothesis if the hypothetical difference of population medians (e.g. 0) is not in the confidence interval. The comparison of two independent samples with respect to location is then introduced as follows: