Generally a stat book is divided into two parts: Hypothesis Testing and Estimator Theory. Given data points, in hypothesis testing, we choose between null $H_0$ and alternate hypothesis $H_1$ for certain entity (for eg mean). My opinion is that why can't I choose an estimator from data and directly evaluate it. This way I will get the same answer? (Infact it will save me the trouble of even guessing the $H_0$ and $H_1$.
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What do you mean by "directly evaluate it"? Suppose you conduct a clinical trial and find that the response rate to Drug A is 50% and the response rate to Drug B is 60%. How do you determine if those represent truly different response rates or statistical noise? – Nuclear Hoagie Aug 25 '21 at 20:04
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This is a naive comment for a deep topic, but note the existence of nonparametric tests that cannot be related to the estimation of any parameter. – Miguel Aug 25 '21 at 20:19
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@NuclearHoagie My approach to your question would be to learn a model (for eg estimate the probability density using various available non-parametric techniques) using data from Drug A, and then use this model to predict the response of people taking Drug B. If the difference between prediction and actual data of Drug B is less (say accuracy is >99%), then they are similar, else they are not. Let me know if i am missing something in my argument. – Manish Kumar Singh Aug 25 '21 at 20:54
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@ManishKumarSingh It sounds like you're just doing a hypothesis test in a non-rigorous manner. You calculate some statistics from the data, and if those statistics exceed a pre-defined threshold, you are confident enough to say there is a real difference in the underlying populations. That's basically a hypothesis test, except you no longer have a proper statistical interpretation of the result since you're operating outside of a probabilistic framework. – Nuclear Hoagie Aug 25 '21 at 21:15