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I have a two-sample t-test where the t-statistic is equal to the critical t-value (at three decimal points) at a p-value of 0.05. does this mean i reject the null hypothesis or the opposite? thank you so much!

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  • $\begingroup$ Also see here for another duplicate. $\endgroup$ – Glen_b Apr 15 '14 at 4:51
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The traditional tests says that the probability has to be less than 0.05, so this is not statistically significant.

However, this shows up the problem of being forced to make a dichotomous yes/no decision for statistical significance. Are you really going to make a decision one way or the other when your answer could be changed by one person (or whatever you're measuring) moving by 1 point.

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    $\begingroup$ This answer is not quite correct, I am sorry. The critical region strictly speaking includes the critical value itself. If the test statistic is continuous and p were "exactly" 0.05, that should be rejected for a 5% test (though the probability of this is 0). If the test statistic is discrete, then you would generally choose an achievable significance level (and typically, one smaller than the desired type I error rate, but this is not a rule) -- but once you choose the achievable significance - say 0.0467, for example - then the case at that boundary is in the rejection region). ...ctd $\endgroup$ – Glen_b Apr 15 '14 at 3:52
  • $\begingroup$ ctd ... If - as occasionally happens - you get a discrete test that can achieve the exact desired significance (0.05 say), then you definitely reject when p=0.05, or you aren't doing a 5% test! Please see the discussion at the indicated duplicate. $\endgroup$ – Glen_b Apr 15 '14 at 3:56
  • $\begingroup$ This case: wilcox.test(c(1,4,5),c(2,3,6:12),alt="less") is an example of exactly 5% being achieved with a discrete test statistic (in this case for a one tailed test). In that case, you must reject the null for a test with a 5% type I error rate. [I find it helps to state the rejection rule and the implied type I error rate for the rejection rule you give.] $\endgroup$ – Glen_b Apr 15 '14 at 4:46

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