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# Non-zero null hypotheses for t-tests

In the t-test module, I do not see where a user can specify a non-zero null hypothesis (i.e., specifying a hypothesized mu of a non-zero value). For a pre-post study, I might be interested in testing whether the difference is at least 5 or more. All alternate hypothesis selections seem to imply a null hypothesis of 0. Is there a possible workaround or an approach to this problem that I am missing? Many thanks in advance!

John

• edited November 4

For a two-group t test, I would subtract 5 from each value in the group with the higher mean (call it Group 2), and then do a one-sided t test t assess whether the mean of the transformed Group 2 data is significantly greater than the mean of the Group 1 data?

For a paired-samples t test, I would take the same approach but subtract 5 from each value in the *condition* with the higher mean.

However, I've just noticed that JASP includes an "Equivalence t tests" module. So far, I'm able to get the exact same results with the module as I did using the method I described above.

R

• An even simpler approach: For the t test, opt to view the 95% confidence interval for the difference between the two means. Reject the null hypothesis if the interval includes 5 or -5.

R

• I meant to write . . . Reject the null hypothesis if the interval EXcludes 5 or -5.

R

• Hi John,

The paired-samples t-test compares whether the differences between two repeated samples are statistically significantly different to zero or not (zero means no difference; thus, this is the null hypothesis). Therefore, there's no way (or at least not to the best of my knowledge) to state another number than zero in the null hypothesis for this test. However, you can make a similar analysis using the pre-post differences and the one-sample t-test. You first need to calculate the difference for each participant (or case); you can do it in JASP. Next, select the "One Sample T-Test" in the "T-Tests" tab. Move the calculated differences right to the variables box, the t-test is selected by default, and you can choose what's the hypothetical population mean for the differences in the "Test value" box (zero by default, but you can modify it as desired, in this case, 5 to match your request). See the attached picture.

I hope it helps.

Best,

Alejandro.