Ok, I have a group of about 320 students. I am particularly interested in 5 of them that form a group with a characteristic I'm interested in. I need to compare this group of 5's performance with the performance of the rest of the students to see if there is a significant difference.

Since I had such unequal groups, I thought a T-test would be most appropriate. I calculated the mean of the 315 students. I then selected only those 5 students I was interested in. Next, I did a simple T-test with the 5 students comparing them with the mean of the 315 students. The results were not significant (not really that surprising with only 4 degrees of freedom).

Then I tried it the other way (determined the mean of the 5 students, de-selected the 5 and performed a t-test comparing the 315 with the mean of the small group). This was WAS significant.

So which way is 'right?'

Is there a better way to do this?

Maybe I'm supposed to do a One Way ANOVA and just make sure there are equal variances?

Use the mean of the 315 as a "standard" or "known parameter" in a one-sample t-test, using the mean of the other 5 as your "sample."

Thanks, John M!