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I ran a paired T-test to determine the mean difference between pre and post intervention of one of the variables in my study. However the test was not run as the SPSS output showed "the correlation and t cannot be computed because the standard error of the difference is 0".

What should I do to get the p-value of the mean difference for that variable?

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Is the value of the paired difference exactly the same for every pair? That is what "the standard error of the difference is 0" seems to mean. – Macro Jun 24 '12 at 3:44
I think the difference between your two columns is a constant. Constant has no variability and thus no test can be done. – ttnphns Jun 24 '12 at 3:50
Of course a test can be done, @ttn: just not a t test! – whuber♦ Jun 24 '12 at 14:12
Please add some information on what kind of data you have... do you meet the assumptions of the t-test? – John Jun 24 '12 at 14:23
Sorry, @whuber, I meant "no t test..." or "the t-test can't..." – ttnphns Jun 24 '12 at 16:00
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When the standard error of the difference is 0 then you might go with a non-parameteric test. A sign test would be good. Rather than give you the probability on a t-distribution, it gives you the probability of that many successes (differences in the same direction). That would typically be a meaningful and useful kind of p-value to describe.

The variance of 0 means that all of the differences were the same. This can happen for a variety of reasons, for example, insensitive measurement, or genuinely extremely low variance of the effect. Perhaps you even rounded off the variability. It's very rare though, if you have data that follow the assumption of the t-test. Your data probably require a non-parametric test in the first place.

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Isn't the situation much, much simpler even than this? Is there any admissible test, parametric or not, that would reject a null hypothesis of equal means when every one of the differences equals zero? Whence, to answer the original question directly, why wouldn't the reply "your p-value is 100%" be adequate? – whuber♦ Jun 24 '12 at 16:16
But the sign test allows you to assume that there is some probability the difference could go the other way. It's not really a test of equal values but a test of equal probability of the value in a given direction. It's certainly possible it's much simpler. I'm all for saying there is no variability in the effect from what we've been given. However, it's also possible that a sign test is appropriate in the case. I was considering starting with an answer similar to what you say. But I was leaving that for someone else. – John Jun 24 '12 at 16:34
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@whuber - the differences aren't 0, they are all the same. Having said that, unless the sample size is very small, I have a hard time believing this isn't due to a data entry error of some sort, e.g., coding "Yes, this is a pre-intervention observation!" or "No, this isn't a pre-intervention observation!" instead of the variable itself. – jbowman Jun 24 '12 at 16:35
yes jbowman, that's a likely cause as well – John Jun 24 '12 at 16:35
@jb Good point! I had blithely assumed all the differences were zero (because almost any other constant value seems so unrealistic). +1. – whuber♦ Jun 24 '12 at 16:36

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