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I'm not that familiar with statistics, especially not with T-tests, however I need to apply a T-test for my dataset. My dataset is basically an observation of productivity over several weeks, where week 1 and 2 are considered as phase 1 and week 3 as phase 2. I'm comparing if there's a productivity increase between phase 1 and phase 2.

Now, the one-sided T-test rejects the Null hypothesis (with 90%), where the two sided does not reject the Null hypothesis (between 80% and 90%).

Could someone explain to me, what this behavior means and which result I should focus more on?

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Let say the significance level $ \alpha $ is 0.05

For a one tailed t-test, the hypothesis is rejected when the test statistic > the 95% quantile (or less than 5% quantile depends on your alternative). While for a two tailed t-test, the hypothesis is rejected when test statistic > the 97.5% qunatile or < 2.5 quantile.

In both case, the type one error is 5% , but when your test statistic lies between 95% and 97.5% quantile, then you will see rejetion for one-tailed test but not two-tailed test.

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  • $\begingroup$ Mmh okay, so does that mean the dataset is somewhat statistically significant? Or how do I need to interpret this result? $\endgroup$
    – Scorpia
    Jun 23 at 11:41
  • $\begingroup$ @Scorpia The best practise for hypothesis testing is you formulate your hypothesis before looking at the dataset. You could formulate your hypothesis in this way: If you want to test whether the productivity changes but you are not sure whether it would increase or decrease, then you should use a 2 tail test. In constrats, if you guess there should be an increase, you should use 1 tail test. $\endgroup$
    – Bayesian
    Jun 24 at 1:49

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