7. Parametric Hypothesis Testing

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MIT 18.650 Statistics for Applications, Fall 2016
Instructor: Philippe Rigollet

In this lecture, Prof. Rigollet talked about parametric hypothesis testing and discussed Cherry Blossom run and clinical trials as examples.

License: Creative Commons BY-NC-SA

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hypothesis testing actually starts at 52:13

yasmineguemouria

just great! This course is the best to clear up all the mess that is all around the testing hypothesis in various sources!

Gossamer

These lectures are amazing. For people like me working in related industry, I also recommend the book of "trustworthy online controlled experiments" as a companion book to these lectures (lectures 7-12) to gain a deeper understanding how these concepts are applied to real world product and business problems.

dehuiyang

About calculating the power of a test (1:13:00 ->), isn't the most conservative choice for theta 3.49? I mean, when the true theta equals 3.49, the power becomes 5 % (with 5 % significance level). This is because the sampling distributions of Xn_bar (standardized) under theta_0 (3.5) and theta_1 (3.49) are basically equal.

Using this logic, the power of a test would always be equal to the significance level. Obviously, there's a flaw in my logic, but where? Prof. Rigollet says that we should look at the worst possible case (1:13:28). In my humble opinion, the worst possible case is when the difference between theta_0 and theta_1 is miniscule.

EDIT:

Ok, so Prof. Rigollet basically answers my question in the next lecture (8. at 13.45 ->). If theta_1 is defined on a set Theta_1, then the power is the value where it is minimized within this set. What I didn't get at first, or got overly confused about, is that in real life I choose my theta_1 basically as my best guess. This way, in general it won't always be equal to the significance level. If I let theta_1 be such that it can be the 'next door neighbor' to my theta_0, then the power will be equal to the significance level.

iirolenkkari

Thank you for making this SO INTUITIVE. You rock.

agarwalarti

Absolutely well done and definitely keep it up!!! 👍👍👍👍👍

brainstormingsharing

17:46 He states "mean is at distance 1/sqrt(n) from the expectation" but I guess it should be 1/sqrt(n) x sigma:
edit: I guess it's the same question by SuperChrzascz

tempvariable

Shouldn't He have multiplied the 0.3 by sigma=sqrt[373] around 18:40 ?

SuperChrzaszcz

At 40:12 I don’t think he got the percentage of values between the sigmas of normal distribution right.
You have ~95% between +\- 2 (it’s actually +/-1.96)

gregoirealbizzati

At the end of the video, according to what the prof. said about the alpha=5% implied that there would be 5% of the innocents that would be guilty. I think that i kinda disagree with his statement since the hypothesis testing is about finding sufficient “evidences” to prove that the innocent is guilty. So, instead of sticking with his assumption, can we just say that we need at least 10 evidences to approve that the innocent is guilty?(actually it can be any number that the investigator would determine. I just made it up.

panurujsubanpong

that was some really badly cleaned blackboard at the 0:33

irenaolsanska

@17:30:00 he says we are 1/sqrt(n) away from the mean. How does the CLT say that? The CLT says sqrt(n)(theta-thetahat) converges in distribution to N(0, sigma^2), what part of that statement gives an indication that the distance of the estimated mean to true mean is approximately the inverse of the square root of the sample size? It looks like it says the distance is proportional to the square root of the sample size, not the inverse of the square root of the sample size.

Marteenez_