Date: Thu, 23 Oct 2003 02:02:33 +0100 John Whittington "SAS(r) Discussion" John Whittington Re: chi square analysis to identify the outliers To: Karriere Sucher text/plain; charset="us-ascii"; format=flowed

At 11:41 22/10/03 -0700, Karriere Sucher wrote:

>I have a sample of math exam scores for 10 students. They are 8, 25, 35, >41, 50, 75, 75, 79, 92, 99. How to use SAS to conduct a chi square >analysis to find out whether the student with the score 99 and the student >with the scroe 8 are two outliers. My second question is I calculated the >mean to be 57.9 and the standard deviation is 30.4. Then 95% CI will >roughly be the range of -3 ~ 119 (mean plus / minus two standard >deviations). But in reality the scroe can only be in the range of 0 ~ 100. >How to interpret the negative score and the score that is greater than 100.

Having read both this and your subsequent message, I really don't think it makes sense to try to use a statistical approach such as you are suggesting in order to determine which students (if any) should receive prizes and which should receive penalties. If you had 1000 students, then it might be more appropriate, but with only 10, statistical approaches are not really going to help you.

Under any circumstances, the definition of 'an outlier' is essentially arbitrary, but it's difficult to see what arbitrary definition would help you here.

As Peter has suggested, my advice would be to forget statistics and just rely upon your eyes. If you do that, you would surely conclude that the person who got 99 (out of 100) deserves a prize (if (s)he doesn't, then who ever would?!) - and possibly/probably ALSO the person who got 92 (quite a long way above the next closest mark). As for whether or not the person who scored 8 deserves a 'penalty', your guess is as good as mine; (s)he certainly got a very low score compared with everyone else, but that's really all that we (or statistical methods) can say.

Of course, you might decide that if more than one person got over 90, then no-one was sufficiently 'remarkable' to deserve a prize - in which case the figures you give would result in no prizes being awarded!

Kind Regards,

John

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