Public vs. Private School Performance--2005 Season Only
The debate has raged since the beginning of the Ohio high school football playoff system (perhaps before):
I recently read a thread in a jjhuddle forum discussing this topic and one poster suggested that private schools be boosted up one division for playoff purposes. This didn't seem like an unreasonable suggestion, but it did strike me as somewhat arbitrary. Shouldn't we attempt to quantify the advantage a school obtains over public schools before we determine what solution is appropriate?
Football affords us a great opportunity to do some quantitative analysis. The OHSAA has developed a system (the computer point rankings) that purports to assign a numeric score in order to roughly identify the best teams in the state. My thought was that if we used these computer rankings in tandem with enrollment figures for schools we could see if non-public schools outperform public schools on a per student basis. As importantly, we could measure how much of an outperformance there was (if any).
We must keep in mind that even if outperformance is proven, it is not likely that it is all caused merely because of the distinction between public and non-public. It would be extremely difficult to isolate the true advantage a private school may have just by virtue of being private. Perhaps some consensus could be reached that would assign a certain percentage of the overperformance to an "unfair advantage." By measuring the magnitude of the advantage, a multiplier could be assigned to non-public schools in order to achieve parity between them and public schools. This could also be expanded to calculate the difference between open enrollment and non-open enrollment schools to see if any correction is warranted in that regard.
(Note: Although I believe the data tend to indicate that non-publics do have a discernable advantage over publics, I am not sure that it is wise to attempt to correct for this difference. The reasons for and against such an implementation have been debated ad nauseum; I offer this objective analysis only to shed some light on an often emotionally-driven debate. However, if you would like to know my thoughts on the matter "pre-study" click here. I provide this information for the purpose of disclosing any biases I may have.)
The links below use only the results from the 2005 season. Click here for a more statistically significant analysis using the past six seasons.
Click here for the summarized results.
Another technique to see if any difference exists between public and private schools is to look at the data graphically. I have constructed six scatterplots (one of each division) demonstrating the different relationships between enrollment and points per student and the differences between public and private schools.
Click here to see the graphs.
A much more powerful statistical technique is regression analysis. A regression attempts to predict one independent variable based on other variable(s). I have run regressions on each of the divisions. My predictive variables are enrollment and public/private. By doing this, it can be demonstrated whether there is a significant relationship between these variables and the independent variable, points per student. If there is a significant relationship, the importance of that relationship can be quantified.
Click here to see regression results.
There is almost certainly a geographic function to the ability for a parochial school to gain an advantage over public schools.
Click here to see a discussion of geographic factors.
Your Help Needed!!! Please click here to provide information that would help with a geographic study involving the "enrollment pools" of parochial schools.
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