Fundamental to statistical analyses is the comparison of means of one variable from two or more populations. Population samples may be constructed (i.e., experimental and control groups), or they may be natural groupings (i.e., students at a particular grade in different years). If the populations are similar, the mean comparisons are straightforward; if not, the question arises as to whether the mean differences are due to differences in the variable or differences in the populations. Partitioning analysis is a way of distinguishing between these differences.

This paper is a demonstration of how partitioning analysis can be used to help separate changes in reading and mathematical proficiency from changes in school populations over assessment years. NAEP reading and mathematics trend data were readily available from published NAEP reports. Subgroup means were published separately for White, Black, Hispanic, and “Other” students. We selected 13-year-old students from four assessment years as sufficient for this demonstration.

Partitioning analysis separates the difference between two means into three parts: proficiency effect, population effect, and joint effect. The proficiency effect is the change in means attributable to changes in student ability, the population effect is the part attributable to population changes, and the joint effect is the part attributable to the way that the population and proficiency work together. Partitioning analysis makes it simple to compute a well-known statistic, the standardized mean, which estimates what the mean would have been if the percentages of the various subgroups had remained the same.