# Dropping data from people who have “perfect” scores

OK, so I have data from a class that had a preparatory self-test to see how prepared they were for the class, and the final results for the class. The preparatory self-test had a range from 0..13 and the final had a range from 0..100.

(don't mind the normal, none, distinction legend, that's just the class (Coursera) had a threshold for certificates at 50%, and you'd get a "with distinction" above 80%)

But, here, look at these two graphs:

(source: hex21.com)

(source: hex21.com)

The correlation coefficient for the full data set is r=0.29782 and if I remove the 13s from the preparatory self-test becomes r=0.294383, so I guess the correlation doesn't change all that much.

But, I guess my question was more sort of, is it valid/a good idea to remove the 13's from the preparatory test?

Here's what I was thinking: The final seems to be valid for the set of students being tested. But, you really can't distinguish between one student who got a 13 and another who got a 13, because they "maxed" out the test. (Like if you had a scale that measured up to 100 grams, and you put an elephant, a whale and a chicken on it, and declared them all to be "100 grams")

What should one do if the test is being maxed out by certain people? Is it better to leave it in, to remove it, or to do something else altogether with it?

Thanks!

• You can treat the 13s as censored results, adopting the view that they represent an interval from 13 on up achieved on some hypothetical test where the scores could go higher. (800s on the SAT work this way: it is scored internally to a higher range and censored at 800.) That suggests you use methods of censored regression. These methods include techniques of survival analysis. That gives you a very large set of practicable approaches you can research here. – whuber Dec 20 '13 at 17:05
• One can't help noticing the high-leverage outliers at the left. They contribute disproportionately to lowering the correlation coefficients. Such ridiculously low scores likely represent people who blatantly blew off the test. Because these scores can be recognized as anomalous in advance, if you intend to use these results for prediction, it would be valid to throw such scores out. – whuber Dec 20 '13 at 17:08
• @whuber I don't think a survival analysis would be appropriate here. Censoring is best used for time-to-event data modeling a binary outcome when the subject does not experience the outcome by a certain point, but no longer remains under observation. – AdamO Dec 20 '13 at 17:16
• @AdamO You might want to take that up with Dennis Helsel who advocates the survival analysis approach. Anyway, I don't follow your argument: one could plausibly view a test score as analogous to survival time and a "perfect" score as "survival" past a fixed threshold. The data will determine whether or not standard survival models apply to them. – whuber Dec 20 '13 at 18:22
• @AdamO This is not a truncated dataset, that's why. Removing the perfect scores would truncate it; including them censors it. – whuber Dec 20 '13 at 18:59