# Standardize numbers for ranking ratios

I'm trying to rank some percentages. I have numerators and denominators for each ratio. To give a concrete example, consider ratio as total graduates / total students in a school.

But the issue is that total students vary over a long range (1000-20000). Smaller schools seem to have higher percentage of students graduating, but I want to standardize it, and not let the size of the school affect the ranking. Is there a way to do it?

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This is relatively simple to do mathematically. First, fit a regression line to the scatter plot of "total graduates" (y) vs. "total students" (x). You will probably see a downward sloping line if your assertion is correct (smaller schools graduate a higher %).

You can identify the slope and y-intercept for this line to convert it into an equation y = mx + b, and then do a little algebra to convert the equation into normalized form: "y / x = m + b / x"

Then, with all the ratios in your data , you should subtract this RHS:

normalized ratio = (total grads / total students) - (m + b / total students)

If the result is postive, then the ratio is above normal for that size (i.e. above the regression line) and if it is negative it is below the regression line. If you want all positive numbers, you can add a positive constant to move all results above zero.

This is how to do it mathematically, but I suggest that you consider whether it is wise, from a data analysis point of view, to normalize by school size. This depends on the purpose of your analysis and specifically how this ratio is being analyzed in relation to other data.

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