Question about the hypothesized mean in a t-test

[Amanda Ode]

Dear all in Statalist,

I want to perform a t-test for a hypothesized mean of, for instance, +/-2. Is there way to do that without needing to perform the test for the positive and then for the negative value?

The following code is an example of what I am doing to test the hypothesis. I need combine the last two commands somehow to make Stata compare the obtained mean to the given limits (+/-2) instead of one value (2).

gen T3_Diff = T3_X - T3_Y
ttest T3_Diff == 2     
ttest T3_Diff == -2

I hope I'm clear enough.

[Nick Cox]

The idea that a difference should be less than 2 in absolute value doesn't correspond to any test that the mean difference is 2.

Is this really a significance test problem at all? Suppose you work out the fraction of absolute differences greater than 2, or its complement. Does that tell you what you need?.

[Rich Goldstein]

I don't understand what your situation is - do you have one variable and want to test whether the mean of that is +/-2 or do you have two unpaired variables and one to test whether the difference in means is +/-2 or do you have two paired variables (e.g., pre- and post-) ...?

[Amanda Ode]

In our studies, the mean difference for paired samples should lie, let's say, between +/-2. My colleagues seem to have problems interpreting the results as when they get a difference of -3 the obtained p value is >0.05 when comparing it to the hypothesized value of 2. I just wanted to make it easier for them to see the results for the span of -2 to 2 instead of just one value (2). My colleagues should obviously be more observant.

[Nick Cox]

In a test of the difference between two means you are testing a hypothesis that the difference is a certain value, most usually but not necessarily 0.

What you want sounds quite different, but it's hard to say what it is.

As said, any idea that the difference should be between 2 and -2 does not mean that the mean difference is 2, or even that the mean absolute difference is 2.

I'd back up here and tell us more about where 2 comes from. It sounds as if there is a measurement procedure and you're repeating measurements and there is some rule of thumb, say "we expect repeated measurements to differ by no more than 2 [unstated units]". So, that is false whenever it is not true.

I don't see that you have answered my question in #2

[Amanda Ode]

Thank you Nick for your explanation. Apparently, I haven't been clear enough and I really apologize for that. As this is not a significance test problem and it is all about a function in Stata, I will get back to Statalist when I need more help on this issue.