In paired sample t-test, is it possible that the correlation between two same variables (for example, Stress time 1 and Stress time 2) is not significant. What could be the possible reasons for not significant correlation? As data is collected at two time points, with the gap of 6 months.
There are many reasons why a correlation is non-significant. The main ones are:
- The population correlation, rho, is actually zero, and not finding a significant correlation is "correct"
- The power is too low, because the sample size is too small. You just don't have enough data to have "significant evidence" to claim that rho is not zero.
- The power is too low because the population correlation is very close to zero (e.g. 0.02). You need a *huge* sample in order to have a decent probability of claiming a significant effect.
The context of your question is lacking, but there are many instances in which a six months gap is such a long time, that the correlation between the two time points is indeed very small.
Depending on how you measured stress (which I assume is the measure you're referencing) it may be that the construct is somewhat volatile and there'd be no expectation of the same measure being correlated at a 6-month interval.
For example, if the recall period of the question was one week (i.e. what was your stress level in the past week?) its entirely possible that someone's stress level today has no correlation with their stress level 6 months from today.
Since you mention the paired t-test and correlation together, are you really doing both? If your goal is to look for similarities between the two time points and such similarities actually exist, then you would have a "non-significant" t-test result because the t-test is looking for differences. To look for similarities, you should calculate the mean difference and its confidence interval, hoping to find that the mean difference is zero and the confidence interval is narrow around zero. If you really are calculating a correlation, I agree with what Stefan and Casper said.
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