1
$\begingroup$

I am trying to identify the outliers from a group for a research article. I wanted to know if there was a formal statistical method of doing so. Here is an example of the data:

There are 500 students in a class who submit an unequal, but large number of assignments. All of these assignments are graded on a 0-100% scale. One student's submissions are better than everyone else's (student mean = 85%; class mean = 50%).

ANOVA analysis reveals that there is an outlier, but to my understanding, cannot identify the outlier. Post-hoc Tukey tests will show me pairwise differences between the students, but I am interested in separating the outlier student vs the rest of the class.

Some one also suggested that I run multiple t-tests where I compare a selected student's mean score with everyone else's mean score, and do this in a loop so that every student was compared to the rest of the class. However, I'm not sure if this is valid, especially with respect to alpha slippage.

Please note: the scenario described above is for the purposes of explaining my question only. The true dataset has over 35,000 samples. Thanks!

Improve this question
$\endgroup$
6
  • 1
    $\begingroup$ There are many threads here on outliers: did you read some before posting? What makes you say that ANOVA "reveals" an outlier? A sample of 10 is rather small to do anything here. Perhaps you just have an underlying skewed distribution and your sample makes you think you have an outlier. What's the real problem scientifically? If you distrust the 85% mean that's more a matter of substantive investigation. Otherwise, just see whether you get similar results with any method less sensitive to extreme values. $\endgroup$
    – Nick Cox
    Commented Dec 17, 2015 at 13:19
  • $\begingroup$ Check this: en.wikipedia.org/wiki/Studentized_residual $\endgroup$
    – Repmat
    Commented Dec 17, 2015 at 13:42
  • $\begingroup$ Hi Nick, I did read the threads that I could find on this question. It was there that we got the inspiration for the multiple t-tests, and I wanted to know if that was a valid approach. The actual dataset is more like 35,000 values. $\endgroup$
    – drdeezy
    Commented Dec 18, 2015 at 16:34
  • $\begingroup$ Is your sample size really n=10? $\endgroup$
    – user603
    Commented Dec 20, 2015 at 23:57
  • $\begingroup$ No, our sample size is ~35,000. I just used 10 for the purposes of the example. I'll edit the sample size so it does not cause further confusion. $\endgroup$
    – drdeezy
    Commented Dec 21, 2015 at 2:41

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.