I am healthcare professional with minimal knowledge on statistics.

I am comparing 2 anti-hypertensives for their efficacy in lowering blood pressure, Drug A is the current standard treatment and Drug B is a new drug which was expected to be more effective in lowering blood pressure.

Therefore, my null hypothesis will be there is no difference between efficacy of Drug A and Drug B in lowering BP. Alternative hypothesis will be drug B is more effective than Drug A in lowering blood pressure.

I know I have to use Kolmogorov-Smirnov Test to test for normality before using t-test or Mann-Whitney to test for significance.

The question here is, from what i understand is that the p-value should be halved for t-test or Mann-Whitney as my hypothesis is one-tailed, but how about p-value for Kolmogorov-Smirnov? Do we keep with p<0.05 or halved it to p<0.025? (I think i supposed to run one-sample KS test using blood pressure to test for normality)

Thanks, if can please explain in layman terms as I do not have statistical background.


marked as duplicate by Alexis, kjetil b halvorsen, Peter Flom Jan 6 at 10:50

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Unless there is another version, the one-sample Kolmogorov–Smirnov test is about testing whether or not a sample is compatible with a certain distribution $F$ or with a family of distributions $F_\theta$ (the null). The alternative is that the distribution or family of distributions is not behind the sample. As such there is no side, no larger or smaller distribution.

  • $\begingroup$ thanks for the answer, just to double confirm, for testing of normality, we are actually comparing whether the sample is compatible with the normality distribution, so in this case the p-value won't be affected by our hypothesis, is my understanding correct? $\endgroup$ – Cheah Jan 5 at 13:50
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    $\begingroup$ Is an update to your assertion in order? Does it make sense to perform a one-tailed Kolmogorov-Smirnov test? $\endgroup$ – Alexis Jan 5 at 17:25
  • $\begingroup$ @Alexis: thank you, an interesting one-sided version, but which requires a setting where an ordering of two cdfs over the entire real line is meaningful, setting that seems quite different from the present case. $\endgroup$ – Xi'an Jan 5 at 17:34
  • $\begingroup$ Possibly... my area of epidemiology is not in the clinical realm, but a noninferiority test (what I suspect Cheah is asking about) assuming average causal effect is ordered over enough of the distribution to make meaningful inferences seems plausible? $\endgroup$ – Alexis Jan 5 at 17:38
  • $\begingroup$ I have not a clue about the context and no competence in this area of application. My point is much simpler: testing $F=F_0$ vs $F\ne F_0$ is quite different from testing $F=F_0$ vs $F\le F_0$. $\endgroup$ – Xi'an Jan 6 at 8:10

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