In a SPSS for pair sample t-test, how do we interpret (r)? For example, we have the data of same individuals on two time points (stress time 1 and Stress time 2) and the value of (r) is significant. so how do we interpret the significant and non significant r values?
I'm not sure I understand your question. You interpret it the same way you would any other Pearson correlation--i.e., it is a measure of the direction and strength of the linear association between the time 1 and time 2 stress scores.
The reason SPSS shows it in the output for the paired t-test is that paired scores are expected to be (positively) correlated; and the covariance between the paired scores enters into the formula for the standard error of the difference between the means. (The covariance is similar to correlation, but is in raw score units rather than standard score units.) You can find more info online. E.g.,
http://onlinestatbook.com/2/tests_of_means/correlated.html
I'm not sure I understand your question. You interpret it the same way you would any other Pearson correlation--i.e., it is a measure of the direction and strength of the linear association between the time 1 and time 2 stress scores.
The reason SPSS shows it in the output for the paired t-test is that paired scores are expected to be (positively) correlated; and the covariance between the paired scores enters into the formula for the standard error of the difference between the means. (The covariance is similar to correlation, but is in raw score units rather than standard score units.) You can find more info online. E.g.,
http://onlinestatbook.com/2/tests_of_means/correlated.html
Correlation means the two variables are strengths each other either positively or negatively, so when you have a significant correlation between stress 1 and stress 2 for the same person , it means that each of the two stress situations are enforcing each other for this person.
when you say pair sample are you referring to the same person measured at time 1 and time 2? or pairs as in matched groups i.e. separate individuals? They come with different set of assumptions and interpretations...The handbook that accompanies SPSS has the small medium and large significance levels for r. Very useful book by Allen and Bennett.
I agree with the colleagues above. I'd just add that if you're interested in comparing Stress 1 and Stress 2 you would report only the values for the t-test (and not the values for the correlation). This would answer a question of the type "Is condition 1 more stressful than condition 2?". I recommend the book David Field "Discovering Statistics using SPSS" which does an excellent job in presenting clear-cut guidance at different levels of depth (undergraduates, postgraduates, researchers).
Thanks every body.@ Bruce Weaver is it possible that there is non significant relationship between the same variables (e.g., how we interpret the non-significant relationship between stress T1 and Stress T2
Well, given that p-values are related to sample size (i.e., the larger the sample size, the smaller the p-value, all other things being equal), sure, you could have a situation where the correlation between the two paired scores is not statistically significant. But if you are comparing the two means, you still need to take that correlation into account by using a paired t-test.
Naeem,
"how we interpret the non-significant relationship between stress T1 and Stress T2?"
Imagine T1 is a variable that measures something BEFORE an intervention (or treatment) and T2 a variable that measures the same thing AFTER an intervention (or treatment).
With an example : let T1 and T2 be white cell counts in people with cancer and let the treatment be some anti-cancer medicine.
Imagine the treatment works for half of the sample, so for these people T2 value will be higher that T1 value, and that the treatment hurts the other people, so for those people T2 value will be lower that T1 value.
In that case you may well get a nonsignificant relation between T1 and T2.
Now, on the contrary, if the medicine does some good to all people, without exception, the T2 score of each patient will be greater that the T1 score for the same patient, so that T1 and T2 scores will be correlated. You may think of this latter example in the following way :
T2 = T1 + effect of being that very patient + effect of the medicine + error
Seeing things this way you see that:
*T2 depends on T1;
*T2 depends on being a particular person;
*T2 depends on the medicine (the medicine makes T2 higher than T1)
*T2 "depends on" error: there is always some measurement error
Hth,
SCM
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