🎓 💄 Topic comparing --- Improve content #200
Description
What
Dumping some feedback I got from a statistician colleague.
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In your example of the drug trial, I would qualify the recovery time, although an observation, as a random variable too, as it is a property or characteristic of interest that you want to understand. -
In your drug trial example, you have “the drug group recovered, on average, 1.6 faster”; I assume you are missing “days” in that statement. -
Typo: “… there were only 50 observations fro[m] each group” -
When talking about why assuming no real difference, you could (as I do) talk about the alternative idea of always assuming a difference or always assuming there is an association, i.e. does it make sense to assume that there is always an association between any two variables (e.g. some exposure and a disease) or that we should assume there is no association until we find sufficient evidence?
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For simplicity, maybe consider:
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Null hypothesis#2: If the drug has no impact, then we would expect that the average recovery to be no different than the placebo. -
Null hypothesis
#3: Therefore, the difference in the average recovery times between the two randomly assigned groups would be an example of a result we got by random chance.
since this gives the same message. -
Interpreting Results: Although not super important, I would qualify what “the same or better”, i.e. recovery time better than or equal to 1.6 days. -
nterpreting Results: Missing a 0, it should be 0.000205 or 0.0205% or one in 50,000 chance. -
T-tests and MU test: It may be worth noting that permutation tests are nonparametric, which is why both the t-test and MU test can be applied.
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The only “issue” I really see is a bit pedantic. Testing a difference or association is a two-sided test but your example is a one-sided lower test. So, since your alternative is mu_drug < mu_placbeo, then this works but since a two-sided test is mu_drug != mu_drug, and therefore could be either mu_drug < mu_placebo or mu_drug > mu_placebo, we need to “double” that probability to get our p-value. Not sure how you want to address this or if it is worth it, but a new section on what is the alternative and how it will impact the p-value calculation may be needed.