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How to Curve With a Bell Curve

Curving on a bell curve -- or, more formally, curving to fit a normal distribution -- means taking a set of scores on a test and attempting to make their distribution close to a bell shaped curve. This can often only be approximated unless you have a large number of scores (say, over 100). The feasibility of doing this also depends on the distribution of the original scores. If half the scores are 80 and half are 70, there is no way to curve the scores to anything like a bell shaped curve. In essence, you need a lot of scores, and they need to vary. One way of doing this is the Box Cox transformation.

Instructions

    • 1

      Gather your original data. Call each score a Y_i, where i ranges from 1 to the number of scores that you have.

    • 2

      For each score, calculate (yi^L-1)/L, where L is a parameter that can be varied. Start with L = 2. If a student got a score of 20, this would be (20^2-1)/20 = (400-1)/20 = 19.95. Do this for each score.

    • 3

      Graph the data and see if it is close to normal.

    • 4

      Repeat steps 2 and 3 for other choices of L. You can try with L = -2, -1.5, -1, -0.5, 0, 0.5, 1.0 and 1.5. When L = 0 instead of (yi^L-1)/L, use log(Yi).

    • 5

      Use whichever transformation is closest to a bell curve.

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