Statistical Review

I was just reviewing my data about the Citadel and its performance. Wolff looked at my tablet, and laughed. There was something not quite pleasant about his laughter. In fact, it was quite pointed. So I looked at the page more closely.

In that document I saw these figures for 2009:

Table 3 above shows that our students’ grade average has increased over the previous year — 6.48% as compared to 6.47% in 2008 in spite of a larger cohort of candidates.

And so, like any conscientious researcher, I decided to see if this was significant.

First, I found an obvious and rather sloppy error. 6.48 and 6.47 were absolute averages, not percentages. The 6.48 was an average score from n=425 and the 6.47 was an average score from n=406.

Second, I found that this was not a significant increase. An increase of 0.01 over 425 students is +4.25 points — quite possibly the effect of just one student doing a lot better than his counterpart in the previous cohort.

Actually, let's suppose that every student did better by half a grade point (or 0.083 per subject) on average. Then you'd have an average score of 6.55 at least. That this did not happen tells me that the Citadel has reached a sort of plateau. It had a bad year in 2008, but 2007 and 2009 seem about the same.

Ah well. Time will tell. With a cohort of about 450 this year, we should see an average of 6.56 for a significant gain. I suspect this will not happen. I could be wrong.

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Note: Yes, I am aware that students with a full 42 subject points (over 6 subjects) can't do better than 7.00. However, one should hope that those doing badly will improve sufficiently to make up for lack of improvement at the top, since it is easier (percentage-wise) to improve a poor grade than a good one.