Using Median Splits to Motivate Learning

Abstract

I know the mean is 14.0 and the standard deviation is 2.4, but what does it tell me? Such a comment reveals the need for concrete reference points. A few statistics (e.g., skewness) can be compared with known distributions, and a stan? dardized sample can be compared with normal percentiles. But the median split offers a simple way to make a univariate statistics assignment both more meaningful and more interesting. The idea is to divide the sample on Y into two subgroups based on values of another variable X suspected of being causally related to Y. Students are then asked to compare central tendency, dispersion, and shape for these two subgroups. For example, to investigate whether infant mortality rates [Hammond Almanac, 1982, p. 271] are related to per capita income [U.S. Bureau of the Census, Statistical Abstract of the U.S., 1982-1983, p. 429] we divide the fifty states into two equal groups, those above and those below the median income. Then, we split infant mortality rates into two groups corresponding to the low-income and high-income states and prepare simple summary statistics for the two groups. We present our descriptive statistics side-by-side, as shown in Table 1, rounding heavily so the presentation is effective [A. S. C. Ehrenberg, The problem of numeracy, American Statistician 35 (1981) 67-71].