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I have a dataset of students, with mock-final and final tests.

With hypotheses,

$H_0: \mu_{mock-final} = \mu_{final}$

$H_0: \mu_{mock-final} \ \neq \mu_{final}$

I started with 2-tailed t-test ttest_rel(scores.mock_final, scores.final) with significance level of $5\%$ and got, $t-stat, p-val = -5.503, 1.796 * 10^{-7}$

Since, $\ p-val << 0.05$, I reject my null hypothesis i.e., $\ \mu_{mock-final} \neq \mu_{final}$.

Now, I frame the hypothesis like this,

$H_0: \mu_{mock-final} > \mu_{final}$

$H_0: \mu_{mock-final} \ < \mu_{final}$

and again, performed t-test but this time with alternate = 'greater'

ttest_rel(scores.mock_final, scores.final, alternate = 'greater')

and got, $t-stat, p-val = -5.503, 0.99999991$

Now, what should I interpret from this?

Should I have used alternate = 'less' w.r.t my Alternate hypothesis?

Thanks in advance.

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    $\begingroup$ First ask this question - are you trying to see if the mock exam scores are different than the actual exam? $\endgroup$
    – Sean Roberson
    Commented Nov 5 at 3:05
  • $\begingroup$ @SeanRoberson Yes. To be specific, if mock test improved the final exam scores. $\endgroup$
    – commonSense
    Commented Nov 5 at 3:25
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    $\begingroup$ P-values can be interpreted in terms of the strength of evidence against the null hypothesis, but if you have an automatic rejection rule like you mention then you cannot use most of the evidential information for inference. See this open access chapter: link.springer.com/chapter/10.1007/164_2019_286 $\endgroup$
    – Michael Lew
    Commented Nov 6 at 19:48
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    $\begingroup$ For a one-sided p-value the values close to 1 indicate that the observed effect was in the opposite direction from that expected by the null hypothesis. Your final scores were, on average, greater than the mock scores. Plot the data as a graph before running the stats tests so that the test results don't distort your perception of what the data say. $\endgroup$
    – Michael Lew
    Commented Nov 6 at 19:51
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    $\begingroup$ You should have equal as well in one-sided alternative $H_a$ (not $H_0$). Some intuition here. $\endgroup$
    – dimitriy
    Commented Nov 6 at 20:43

1 Answer 1

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If you want to see if the real exam score is better than the mock, your alternative hypothesis is $H_A: \mu_{\text{mock}} < \mu_{\text{final}}$ so the alternate flag needs to be set to less.

Remember - the alternative hypothesis is the question you want answered!

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  • $\begingroup$ Okay. So, you mean to say we try to hypothesize in such a way that we surely reject the null hypothesis by getting p-value less than significance level, because that give strong evidence. Whereas the other part gives "not enough evidence", is my understanding correct? $\endgroup$
    – commonSense
    Commented Nov 5 at 3:56

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