Ranking based on delta from mean

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Ranking based on delta from mean
Message posted by Casey Kester on March 10, 2000 at 12:00 AM (ET)

I'm starting a high school database that will include statistics for sports such as batting average. I want to determine the mean for the population that entered a batting average. I then want to determine how far away the entry for a given student is from the mean. I then want to assign a ranking value to that student for that category, sum the ranking values for that student for the other categories he's entered, and arrive at an overall ranking level.

I can do all this using the database. My question whether I can defend this when questioned by coaches and students? Can I assign points to a student based on how far from the mean they are, sum those points, and then rank the students based on their point totals and have the ranking be considered valid?

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Re: Ranking based on delta from mean
Message posted by Jack Tomsky on March 10, 2000 at 12:00 AM (ET)

You can define a statistic any way you want. The only issue arises is if you claim that your statistic has some particular probability distribution, such as a normal. There are other techniques, such as principal component analysis, which takes into account the correlations among the different categories. It gives you the linear combination(s) which maximize the variance between students relative to the variance within students.

Jack

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