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I'm doing a pre-test and post-test comparison of sexual health knowledge using paired sample t-test.So I measure participants knowledge before camp and after a camp. My t test showed pre and post test are significantly different but it does not meet the assumption of correlation. My pre-test and post-test are not correlated, r = 0.081, almost could be considered zero correlation. Could anyone help to explain or interpret?

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    $\begingroup$ I don't quite see what you need explained. Plainly means can be different whether or not the paired values are correlated. Can you clarify what the problem is that needs explaining? $\endgroup$ – Glen_b Oct 7 '16 at 10:28
  • $\begingroup$ Hi Glen As this is a repeated measure t test, since the participants were doing the same test, theoretically speaking, their pre and post test should be correlated, shouldn't they? $\endgroup$ – Shirley Oct 7 '16 at 15:18
  • $\begingroup$ You'd expect so, but it's possible to see small correlations for one reason or another. The issue here is not whether the correlation was lower than what you expected, but rather how that relates to whether the difference was significant. The power benefit of the paired test is somewhat lower (compared to one done in a similar situation but with larger pair-correlation) but how does that lead to such surprise at significance that there's something to explain? I feel like there's an underlying premise that is not explicit, which may be better to clear up. $\endgroup$ – Glen_b Oct 7 '16 at 22:56
  • $\begingroup$ It's something that I have never encountered so far and hence I felt it may be due to EV or NV that occurred in the research process. $\endgroup$ – Shirley Oct 8 '16 at 16:45
  • $\begingroup$ Sorry, I'm not sure what you mean by "EV or NV" ... (EV might be extraneous variables I guess). However, it might be worth expanding the abbreviations and adding to the end of your question. I'll likely delete many of these comments soon. $\endgroup$ – Glen_b Oct 8 '16 at 21:44
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It is odd that pretest and posttest results are not correlated (see below), but it has nothing to do with whether they are different and there is no assumption that two variables have to be correlated to do a statistical test of the difference.

You are doing a paired t-test. This test, in particular, does not assume that the pre and post values are correlated.

However, if they are not correlated, then an independent samples t-test would give very similar results to a paired t-test.

I would be concerned at the lack of correlation - not because of worries about the t-test but because of worries about the reliability of the sexual health knowledge test. I'd examine the data carefully to try to figure out this odd result. Did all the people get similar scores on either the pre or post test?

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  • $\begingroup$ Thank you Peter for helping me understand. Now I know it's not an assumption. But it is still weird that pre and post test are not correlated because if they were same participants doing the same test, theoretically speaking it should be correlated. Could you help me understand why you said "because of worries about the reliability of the sexual health knowledge test"? Does that mean, the lack of correlation could be due to the reliability of test? Answering your question: Yes they either got similar scores or improved 3 or 4 points in post test. $\endgroup$ – Shirley Oct 7 '16 at 15:12
  • $\begingroup$ Yes, if the test was not reliable, that would affect the correlation. What I meant though was whether everyone got the same scores on the pretest OR the posttest. This could happen if the test was too easy or too hard. $\endgroup$ – Peter Flom Oct 7 '16 at 20:30

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