Statistical Composition

It is very easy to make mistakes with statistics.  Averages can often produce the wrong impression.  For example, consider a situation where there are two schools ( 1 and 2 )and two groups of people ( X and Y ).

School 1 has 10 students from group X and 100 students from group Y.

Of those, 5 students from group X graduate and 80 students from group Y graduate.

School 2 has 100 students from group X and 10 students from group Y.

Of those, 70 students from group X graduate and all 10 students from group Y graduate.

It should be pretty obvious that, no matter who you are, you should go to School 2.  Group X has a graduation rate of 50% in school 1 and 70% in school 2.  Group Y has a graduation rate of 80% in school 1 and 100% in school 2.  School 2 is simply better for everyone.

But if you just look at the overall numbers, school 2 has 80 people graduate and school 1 has 85 people graduate, with the same number of students. School 1 looks better, even though it is actually worse.

This kind of thing cause all kinds of problems when people throw around statistics on things like schooling and health care.  For example, you may have heard that schools in Wisconsin, with their collective bargaining for teachers, are better.

Here is the truth:

The NAEP is an annual standardized test given to 4th and 8th graders around the country to measure proficiency in math, science, and reading. Participation is fairly universal; if you've had a 4th or 8th grader in the last few years, you're probably familiar with it. Results are compiled on the NAEP website, broken down by grade, state, subject and ethnicity.
So how does brokeass, dumbass, redneck Texas stack up against progressive unionized Wisconsin?
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2009 8th Grade Math
White students: Texas 301, Wisconsin 294 (national 294)
Black students: Texas 272, Wisconsin 254 (national 260)
Hispanic students: Texas 277, Wisconsin 268 (national 260)
...(more test score lists)
...
To recap: white students in Texas perform better than white students in Wisconsin, black students in Texas perform better than black students in Wisconsin, Hispanic students in Texas perform better than Hispanic students in Wisconsin.
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the gap between white students and minority students in Texas was much less than the gap between white and minority students in Wisconsin. In other words, students are better off in Texas schools than in Wisconsin schools - especially minority students.
Conclusion: instead of chanting slogans in Madison, maybe it's time for Wisconsin teachers to take refresher lessons from their non-union counterparts in the Lone Star State.