This is a subpage to the Educational Disparities page. That page discusses misperceptions about changes in educational disparities over time arising from the failure to recognize the way standard measures of differences in outcome rates tend to be affected by the prevalence of an outcome. The same measurement issues discussed there regarding changes over time (and which are generally discussed on the Scanlan’s Rule page and various other pages of this site) apply as well to appraisals of the disparities by subject area.
Table 1 below is based on data in from a conference presentation titled “Closing the Gap on Educational Disparities” by Daria Paul Dana of University of Minnesota at Mankato. The presentation simply showed the proficiency rates by subject area for various demographic groups among Minnesota 10th graders in 2005 and did not attempt to quantify the differences. Table 1 set outs the white and black proficiency rates by subject along with the following measures of differences: (a) the ratio of the white proficiency rate to the black proficiency rate; (b) the ratio of the black rate of failure to achieve proficiency to the white rate or failing to achieve proficiency; (c) the absolute difference between proficiency rates; (d) the estimated effect size (which, as explained on the main Educational Disparities page and the Solutions sub-page of Measuring Health Disparities page is the difference between means, in terms of percentage of a standard deviation, derived from each pair of rates, as is the only plausible method of appraising the size of the difference between the situation of two groups reflected by a pair of outcome rates that is unaffected by the prevalence of the outcome). The subjects are ordered according to ascending white rate.
Table 1: White and Black Proficiency Rates by Subject with Measures of Differences (Minnesota 2005, Grade 10) [ref b3111a3]
Reading Complex Information
Identify Bias Point of View
Notice that, with minor exception, as proficiency increases, the relative difference in proficiency rates decreases and the relative difference in non-proficiency rates increases. Thus, those who rely on the former measure to appraise the size of educational disparities would commonly reach opposite conclusions about the comparative size of disparities from those who rely on the latter measure. Those who rely on absolute differences would find that the disparities differ little by subject. But, as with the conclusions based on either relative difference, such findings would lack a statistical foundation.
The only correct answer as to the size of disparities by subject matter reflected by outcome rates is that found in the EES column, and that of course can only be an estimate. The soundest appraisal of the comparative size of the differences would be based, not on outcome rates, but on mean test scores (with differences measured in terms of percentage of a standard deviation, something the EES attempt to approximate).
Table 2 presents a similar illustration based on the 2007 black and white proficiency rates in reading and mathematics in Table 1 of the Educational Disparities page. (Note that, because the white proficiency rate were the same for both subjects in 2006, one cannot make a point concerning the relationship of various measures with the prevalence of an outcome, as benchmarked by the white rate.) Table 2 shows the pattern whereby each of the three standard measures is in accord with the prevalence-related patterns. As shown by the EES, however, disparity is considerably larger for math than for reading.
Table 2: White and Black Proficiency Rates by Subject with Measures of Differences (from Table 1 of the Educational Disparities page) [ref b4327 b2]