SAT curves confidence intervals for the curious soul

Test Preparation SAT Preparation
1

<p>So I decided to take a look at eriktheread’s extremely useful document and see if I could make some confidence intervals, just for the heck of it. Looking at the math curves by month, this is what I got for the two-sided 95% confidence intervals for October, May, and June for a 53 raw score:</p>

<p>October:
n=7
Sx=10.69
avg=781
(771.54, 791.32)</p>

<p>January:
n=6
Sx=12.11
avg=783.33
(770.62,796.04)</p>

<p>May:
n=6
Sx=8.94
avg=790
(780.61,799.39)</p>

<p>Sorry that I didn’t do my assumptions.</p>

<p>Given the amount of data that was available, I’d warn against drawing any conclusions. Yes, the May average is the highest. But I would hardly call the difference significant given that there is so little data and the fact that the intervals largely overlap each other. These are just confidence intervals for what a raw of 53 in math would be; I’m not really sure how to take the entire curves into account for comparison. If anyone can think of a statistically sound way of doing a serious comparison between months and curves or has more data to present, I’d love to help. Also, please point out if I made any serious errors with this. This was really just for fun; I’m not trying to “prove” anything.</p>

<p>Anyone up for some hypothesis testing?</p>

2

<p>Please excuse a plebe like me, but what do these stats mean in English?</p>

3

<p>This is straight off of AP stats. The range in parentheses is the range that the curve is 95% certain to be in for a given month based on past data. So for May, we are 95% confident that the SAT math score for -1 will be between 780.61 and 799.39. But the limited amount of data makes this test pretty inaccurate.</p>

<p>I’m debating doing a chi squared test of independence to see if there’s significant evidence that the score is independent of the month xD</p>

4

<p>Problem with chi square is that, unfortunately, the data isn’t in counts. Still a work in progress.</p>

5

<p>What were the actual scaled scores for a raw score of 53 in October and January?</p>