Significance of individual scores on t test

Don

New Member
#1
Hi folks, I have a question.
How do I determine the significance of individual scores from
dependent t test results?
I did a t test with a group (8 students) before and after
experimental treatment.
The pretest-posttest scores were as follows:
-----------------------------------------
Student / Test 1 / Test 2
A / 23 / 27
B / 19.5 / 30
C / 18 / 22
D / 21 / 23.5
E / 29.5 / 35.5
F / 32.5 / 33
G / 13 / 15
H / 28 / 32.5

--------------------------------------------------
The mean test score improvement was 4.25, and standard deviation
was 2.8394.
The t score was -3.96 (df = 7) and the p values were:
P - one-tailed = 0.0027305
P - two-tailed = 0.005461b
Thus, there was statistically significant improvement for the group.
Though all students improved to some degree, how do I determine
which ones made statistically significant improvement?
Thanks a million,
Don
 
#2
In general, statistics make a claim about a parameter of a distribution. In your case above, you have made the claim that the true mean of the distribution of the difference in scores before and after treatment is greater than 0. The p-value indicates the confidence with which you believe this to be true. You would now like to make a claim about a single individual for which there is no analogy. For example, one could make a claim about the true mean of the distribution of the difference in scores before and after treatment for a particular student, but you would need multiple observations. In only this case could you say that a student had made a significant improvement.

If you intend to reward those who improved more, then perhaps you could select those who did better than the mean(average) improvement.

~Matt