Sunday, July 3, 2011

On Statistics, Standardized Testing, and Big Heads

      So, I don't get to brag very much on this blog. Mostly, this is a cyber-scrapbook of my funny stories, with the occasional writing post. But today, I come to you full of enthusiasm (yes, I know I'm late--I worked twelve hours yesterday. UGGGGGHHHH) about AP SCORES!!!

Now, behold the awesome.
AP United States History-- 5
AP United States Government and Politics-- 5
AP English Language and Composition-- 5
AP Physics C: Mechanics-- 4

And just from last year, for fun:
AP Human Geography-- 5

     Now, for those of you who don't know, 5 is the best score possible--but I'll go into the scoring system in a minute. And before you judge me for getting a 4 on AP Physics (which is still real good), consider the fact that...I never took AP Physics, or Calculus, which you need for Physics. No, I took the test without taking the class, and would have made a 5 if not for the three open-ended questions asking for differential equations (which...I still don't know what those are.) And I am now, officially, an AP scholar--with distinction. And out of like six different boring college classes. So, ha!
     Over my years of exposure to standardized testing, it has become apparent to me that very few people understand the meaning of standardized scoring. That means children and adults alike (so high schoolers and authors, you can learn from this) Thus, I duly take it upon myself to explain to you the mysteries of standardized testing.

Consider the picture below. This is the average distribution of all test takers on any one test.
     In the middle, the peak represents the greatest number of one score, lets say at about 50%. To the left represents those that got higher than 50%, and the right represents those less than 50%. Notice that as the scores increase (or decrease) significantly, the number of those achieving those scores lessens dramatically. Now, for the fun stuff.
     If we compare the above graph to a standardized test, say AP Tests, we assign the median score the score of 3 (because the possible AP results range from 1 to 5, and 3 is in the middle of that) This makes the assumption that about 68% (no, I didn't just pick that number out of the air--check it out) of test takers got a 3 on the AP test. By simple math and the bell curve (shown above), we can see that 16% of testers got above a 3, and 16% got below a 3.
      Now, we apply statistical terms. A standard deviation is considered the "mean of the mean" so to speak (mean being average, not serial killer). Thus, one standard deviation increase/decrease from the average score is a significant decrease in the number of test takers achieving that score. One standard deviation accounts for 13.6%, and a second standard deviation decreases significantly--namely down to a mere 2.1%. Any more than that gets even smaller, but AP scores don't go that far.
      Thus, our graph becomes this (I used IQ tests because they're simple, and designed to show people how much better they are than everyone else):

      You might be wondering what my point in this blog post is. Well, I could lie and say that I wanted to educate you in the meaning of standardized testing scores. That's only partly it. Mostly, I just wanted to rub it in for everyone present (cyber speaking, of course) that I scored better than 95.44% of all AP testers.
      Let's take a moment to contemplate. WHOOOOOOOOOO-HOOOOOOOOOOOOO!
      Yes, I'm pretty happy. Yes, my head is probably three (or twelve) standard deviations from the normal head size. But no, I did not post this to make you jealous, or to any other way insult your intelligence or try to proclaim that I am better than you. I am just hugely excited.

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