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Monday, April 9, 2007

### 116

I have new respect for the MPRE.  This is slightly lower than Alan predicted.  All the NCBE tells you in the "How to Interpret Your Scaled Score" is that the high is 150, the low is 50, and the mean is 100.  I don't know what the standard deviation is.  I am in the midst of rationalizing why I didn't get a 150.

[Jeff Lipshaw]

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I always try the "I was just too smart for the exam" rationalization. Works for me in all situations, but in this case it has some truth. Certainly one can be way too ethical for the exam. This score, as you know, is fine and should be quite a relief. In any event, it is barely below the realistic and very good score I ultimately predicted, and congratulations for another life hoop you have flung through. Boston bound!

Posted by: Childress | Apr 9, 2007 1:38:41 PM

Jeff, the MPRE usually has a std dev of 15. So with a 116, you are approximately at the 83rd or 84 percentile. Congratulations. (If you got a 130, you would have been in the top 2 percent.) bh.

Posted by: William Henderson | Apr 9, 2007 2:44:11 PM

Hmm. My recollection is that on a standard or normal distribution, one standard deviation puts you at about 68%; two at 95.5%; and three at something above 98%. On the other hand, say, Stanford-Binet IQ testing, where I recall the standard deviation to be 16, having an IQ of 116 puts you at the 68%ile, 132 at 95.5%ile, and 148 at the 98+%ile. But there is no upper limit as with the MPRE scaled score.

Posted by: Jeff Lipshaw | Apr 10, 2007 7:07:05 AM

Jeff, In a normal distribution ~65% will be within one std dev of the mean (the mean and median should be nearly identical). So if the mean is 100, ~65% of all test-takers will get between an 85 and a 115. ~95% will get between a 70 and a 130. Hence, a 115 is ~ 1 std. dev *above* the mean (65/2 = 32.5; 50th% + 32.5 = 82.5 percentile; add another point or two for a 116 = ~83rd or 84th percentile). bh.

Posted by: William Henderson | Apr 10, 2007 3:34:02 PM

Got it. We are on the same page. The difference between one tail and two.

In industry, say when you machine a part, there is a mean specification and then a tolerance with an upper and lower limit, hence we are looking at both tails. The idea of Six Sigma is that you want six standard deviations on each side of the mean to fit within the tolerance. So you don't have to look at one tail and then add 50%. At one sigma, you are at 65-68% within the tolerance, at two sigma, 95%, and so on, until at six sigma you only have three parts per million outside the tolerance limits.

Posted by: Jeff Lipshaw | Apr 11, 2007 4:43:38 AM