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In a nutshell: I have performed two t-tests (A und B, each two-samples/paired). Both found significant differences. Can I tell, whether the difference observed in comparison A is significantly larger then the difference observed in comparison B?

Background

I'd like to test a hypothesis á la "Measure D is more similar to measure E than to measure F".

Previously, hypotheses were tested, whether the three measures yield different results. Therefore, t-tests D/E and D/F have already been presented.

Now, to test the hypothesis stated above, I'd like to run a test on the t-statistics derived from the previous t-tests.

I know that there is a test to compare correlation coefficients (e.g., http://vassarstats.net/rdiff.html), but I do not understand the idea behind sufficiently to make a transfer to t-statistics...

And...

If there is a more elegant way thana t-test to test measures for differences - or to test if one difference is larger than another - please let me know, as well. Thanks!

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    $\begingroup$ Are there any data common to the two t-tests? If so, you will need to account for the lack of independence between these tests. That suggests you edit this post to include information about the nature of the data and how they are inter-related. $\endgroup$
    – whuber
    May 26, 2015 at 22:31

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I think you'd need to provide more scientific context about exactly what you are comparing, and what questions you want to answer, in order to get a definitive answer. But I think it is likely that your data could be entered into a two-way ANOVA program, and the interaction P value is what you are looking for.

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