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Qualifier: I am not a statistician. I have 4 data sets and want to determine whether the 4 regression coefficients obtained are statistically significantly different. I compared each pair of coefficients separately (6 hypotheses) with t-tests and found no significant difference (t values ~1 for 6 d.f.). Does this support my null hypothesis (there is no significant difference in the coefficients) or do I need to make a correction because I am comparing multiple hypotheses. That is, if I made a correction would it only make the level of significance even lower?

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    $\begingroup$ If the form of the regression is the same for all 4 data sets, you could have more power to detect differences in regression coefficients among data sets by analyzing all your data together in a single regression, including an indicator variable for the data set, and seeing if there is a significant interaction between the data-set variable and the variable(s) whose regression coefficient(s) you are examining. Editing your question to provide more details about your study might help. $\endgroup$ – EdM Jan 4 '17 at 15:53
  • $\begingroup$ Another advantage of the suggestion made by @EdM is that you get a single, more powerful test. $\endgroup$ – mdewey Jan 4 '17 at 16:23
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Answering briefly on this.

Using a P-value in Null Hypothesis Significance Testing (NHST) does not allow you to draw conclusions about your null hypothesis, just that you cannot reject it at the observed data. This is a common misconception. See e.g. Nickerson, R. S. (2000). Null hypothesis significance testing: A review of an old and continuing controversy. Psychological Methods, 5, 241-301.

Instead, you could calculate confidence intervals to get an idea about the population estimate, see for example Abserson 2002 - or use Bayesian statistics, but that is another chapter.

You are right that your P-values will be even higher when correction for multiple comparisons is performed.

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  • $\begingroup$ I think you mean a high P-value. If the P-value is sufficiently low common practice is to to reject the null hypothesis. $\endgroup$ – Michael R. Chernick Jan 4 '17 at 20:22
  • $\begingroup$ Thanks for the addition, I was looking for a better way to say this. Incorporated an edit! $\endgroup$ – David Jan 4 '17 at 21:05

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