Imagine you're given the task of evaluating the abilities of the individuals in a group -- perhaps in sharp-shooting -- and award ratings like A or F. You might plan a series of challenges of increasing difficulty. What should you do if these turn out to be much harder than you planned -- so that while you expected a mean success rate of 60%, it was actually 20%? An obvious solution is to multiply all scores by 3 to bring up the average. But it turns out that this (and any other linear correctio...

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