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I am running a ttest exercise, in which I have to compare the mean of two populations. Specifically,exercise is:

ttest age, by(labforce) ttest age, by(labforce) unequal

In both cases, I get p-values that do not reject the null for all three scenarios. What could be wrong? Should one of them at least be rejected at X significance level?

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    $\begingroup$ Welcome to across Validated! Why do you believe that you should reject the null hypotheses? $\endgroup$
    – Dave
    Jan 27, 2022 at 22:04
  • $\begingroup$ Thank you! I thought that if I do the t test and analyze the three scenarios (equal to 0, smaller, or bigger) at least in one of them the null should be rejected. Is that not correct? $\endgroup$
    – Ivana
    Jan 27, 2022 at 22:08
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    $\begingroup$ No. If the data are compatible with the null hypothesis, why would you want to reject it? (And if the true difference is 0, the null hypothesis is true for all three tests.) $\endgroup$
    – Christian Hennig
    Jan 27, 2022 at 23:13
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    $\begingroup$ As an aside, people in the LF are either working or actively looking for work. If your non-LF group has a lot of the young and the old, it's possible that the average for them matches the average for people in the LF, who tend to be in between in terms of age. So looking at the mean rather than bottom or top percentiles may obscure the differences. The higher SD in the non-LF group hints at that. $\endgroup$
    – dimitriy
    Jan 28, 2022 at 0:11

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No, there's no rule that says that one of the three null hypotheses must be rejected. To reject any of the hypotheses requires evidence. All your result means is that there is insufficient evidence to make any strong claims about differences based on the data.

Also, as Christian Hennig points out, the null hypotheses here are not exhaustive. A difference of exactly zero is consistent with rejecting all three of them.

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