Learn fundamental concepts in data analysis and statistical inference, focusing on one and two independent samples.

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From the course by Johns Hopkins University

Mathematical Biostatistics Boot Camp 2

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Learn fundamental concepts in data analysis and statistical inference, focusing on one and two independent samples.

From the lesson

Hypothesis Testing

In this module, you'll get an introduction to hypothesis testing, a core concept in statistics. We'll cover hypothesis testing for basic one and two group settings as well as power. After you've watched the videos and tried the homework, take a stab at the quiz.

- Brian Caffo, PhDProfessor, Biostatistics

Bloomberg School of Public Health

Hi, my name is Brian Caffo and this this Mathematical

Biostatistics Boot Camp 2, Lecture 2 on the subject of Power.

So in this lecture, we're going to talk about power, calculating power.

power, specifically for the T-test, and because the T-test involves

maybe a little bit of math that we don't want to

get into, we'll talk about how you can do it

using Monte Carlo, which is a standard way to estimate power.

So, as it's name would suggest, power is a good thing.

You want more power.

so power is the probability of rejecting

the null hypothesis when, in fact, it's false.

So the opposite of power, 1 minus power is the type two error rate.

and that's the probability of failing to reject a null hypothesis when it's false.

And we usually label that as beta. So, consider our

previous example involving the Respiratory Disturbance Index.

Here, we are testing whether or not mu was

30 versus the alternative, then mu is specifically greater

than 30.Then the power the power is exactly the

probability there are t statistics lies in the rejection region.

Recall that we calculated the rejection region was if the

normalized mean X bar minus 30,the value under the null hypothesis

divided by the standard error of the mean, s over square root n.

If that normalized mean was greater than a t quantile specifically, t1

minus alpha, n minus 1 quantile where alpha is the desired type one error rate.

So if the statistic is larger than that

t quantile, then we reject the null hypothesis.

So then the power is the probability that we reject the null hypothesis.

In other

words, the probability that our test statistic is larger than that quantile

but, instead of calculated under the null hypothesis that mu was 30, calculated

under the assumption of the alternative hypothesis that mu is specifically greater

than 30. So, in the even that

mu a approaches 30,

then this probability approaches alpha, the type one error rate.

but on the other hand, if it is not

specifically 30, if it's actually a power calculation, so the

mu is not 30 then this calculation depends on

the specific value of mu a that we plug in.

So, to do a power calculation, you actually

have to know the value under the null alternative

that you want to plug in and then you can perform the calculation.

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