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  • - [Instructor] What we're going to do in this video

  • is talk about hypothesis testing,

  • which is the heart of all of inferential statistics,

  • statistics that allow us to make inferences about the world.

  • So, to give us the gist of this,

  • let's start with a tangible example.

  • Let's say, hypothetically,

  • you run a website that has the mission

  • of giving everyone on the planet a free education,

  • and you wanna think about how you might change

  • the amount of time people spend on the site.

  • Ideally, you wanna increase the amount of time

  • people spend on the site

  • so there's more learning on the planet.

  • Well, currently the website has a white background like this

  • and the mean amount of time people spend

  • when you have a white background,

  • the mean amount of time when you have a white background

  • is 20 minutes.

  • And you or someone on your team,

  • maybe you read some type of study that says

  • people like to spend more time on yellow backgrounds.

  • I don't actually think that's true,

  • but let's just go with that for the sake of this video.

  • And so you have a hypothesis

  • that if you actually have a yellow background,

  • if you change your background to yellow,

  • that the mean amount of time that people spend

  • on a yellow background, on yellow,

  • is going to be different, is not going to be equal to

  • the mean amount of time people spend on a white background.

  • So, the question is how do you test this,

  • and how do you feel good about your inferences

  • that you make from your test?

  • And that is the heart of hypothesis testing.

  • And medical research, actually almost all research

  • involves some form of hypothesis testing.

  • So, how would you do this?

  • Well, the standard why to do this

  • is to set up a couple of hypothesis.

  • Hypotheses, I should say.

  • The first one is known as your null hypothesis,

  • and I often think about this as the skeptic's hypothesis.

  • Skeptics think that,

  • hey, it's hard to make a difference in this world,

  • or cynics feel like it's hard

  • to make a difference in the world

  • and so they always have this null hypothesis

  • that's saying, "Hey, you think you're making a difference,

  • "but you aren't."

  • So, the null hypothesis is that

  • the mean amount of time people spend on the yellow site,

  • or on a yellow site,

  • is going to be equal to the mean amount of time

  • that people spend on the current site

  • or the existing site or on a white site,

  • while the people who are thinking about,

  • "Hey, how do I make change?

  • "How do I make improvements in the world?"

  • they had some type of hypothesis

  • and we call that the alternative hypothesis.

  • And so the alternative hypothesis, A for alternative,

  • is that the mean time on the yellow site,

  • on the yellow site,

  • is actually different.

  • Is actually different.

  • It is not equal to the mean amount of time

  • on the white site.

  • So, how do we think about this

  • now that we set up these hypotheses?

  • Well, what we're going to do is

  • we are going to assume,

  • we assume the null hypothesis.

  • Then we build this yellow site

  • and then we take a sample

  • of the people using the yellow site,

  • and we say, "What is the probability

  • "of getting that sample mean,"

  • which is an approximation of the parameter of the true mean,

  • "what is the probability of getting that sample mean

  • "if we assume the null hypothesis?"

  • And if the probability of getting that sample mean

  • on the yellow site,

  • assuming the null hypothesis, is really low,

  • then we reject the null hypothesis,

  • which suggests the alternative.

  • On the other hand, if we get a sample mean

  • that seems pretty reasonable to get

  • if you assume the null hypothesis,

  • then we fail to reject the null hypothesis

  • and then that would not suggest the alternative.

  • Now, to make this a little bit more tangible,

  • and we'll go over this into a lot of videos,

  • if you assume the null hypothesis,

  • then there's a few things you can think about.

  • You can think about just the general distribution

  • of the amount of time people spend on the site.

  • It would look something like this.

  • We will, for this sake,

  • assume that it's a normal distribution,

  • and normal distributions are very important,

  • and/or things that are close to normal distributions,

  • for hypothesis testing.

  • But let's say that it's a normal distribution

  • of the amount of time people spend on the site

  • and so there is some mean.

  • We know that mean,

  • so the mean that people spend on that white site

  • is equal to 20 minutes.

  • And, remember, we're assuming the null hypothesis,

  • so we're assuming that this is also the amount of time

  • that people would spend on the yellow site.

  • We've assumed, assuming, the null hypothesis,

  • and you could view this as time or distribution

  • of time spent.

  • Now, one of the things we're going to talk about

  • in future videos is if you have this distribution,

  • you can actually come up with another distribution

  • of the means of samples you might get.

  • So, there's something else called the sampling distribution,

  • and I know it's very confusing at first.

  • Sampling distribution of the sample

  • of the sample mean,

  • and it'll be for a given sample size,

  • for sample size, sample size.

  • Let's say this is sample size 1,000.

  • I'm just making things up.

  • I could've said N,

  • but I'm just gonna make this a little bit more tangible.

  • Well, we're going to get statistical methods

  • for how you can think about this distribution

  • assuming this distribution we have on the left.

  • And it turns out this distribution

  • is going to look like the one on the left,

  • but it's going to be narrower around that mean.

  • It's going to look something like this.

  • And, actually, the larger your sample sizes are going to be,

  • the narrower it's going to get.

  • Now, remember, this isn't just the distribution

  • of the amount of time people spend on the site.

  • This is the distribution that if I were to take a sample

  • of the amount of time people spend on the site

  • and calculate the means,

  • this is the distribution of those sample means I might get.

  • Now, the center of this distribution is still

  • our mean for white which is equal to the mean for yellow.

  • Remember, we're assuming the null hypothesis.

  • The mean for yellow.

  • But each of these points,

  • for example, if I think about this,

  • this is amount of time that someone might spend

  • and you can see that there's a low probability about it.

  • This over here, this would be a sample mean you might get

  • for a time that you sampled 1,000 people

  • and you calculated the mean,

  • and you see that there's a low probability for it.

  • So, then what you would do is,

  • if you were able to statistically generate these things

  • assuming the null hypothesis,

  • and don't worry too much,

  • we'll find out the techniques for doing this

  • and the assumptions we need to make for doing this,

  • what we do is then take a sample of 1,000.

  • So, you take your sample of 1,000,

  • so sample 1,000,

  • and then from that you are able to calculate a sample mean.

  • You are able to calculate that.

  • And let's say you get a sample mean of 30 minutes.

  • And let's say, actually, that that is right over here,

  • that this is 30 minutes right over here.

  • The center was 20 minutes.

  • The next thing, what you do is you say,

  • "What's the probability of getting a result

  • "at least that extreme assuming the null hypothesis?"

  • And that high probability on these curves,

  • it would be this right tail here

  • and it would be the left tail

  • that is equally far on the left side,

  • so it'd be like that.

  • And what you do is you look.

  • You look at this probability,

  • which would be these yellow areas there,

  • and then we think about the probability

  • of getting a result at least as extreme as 30 minutes.

  • So, probability of getting,

  • getting a sample mean at least

  • as extreme

  • as the sample mean equaling 30 minutes,

  • assuming, assuming

  • your null hypothesis,

  • and that's exactly what those yellow areas are all about.

  • And you compare that to some pre-specified threshold.

  • So, that threshold is oftentimes 5%.

  • Sometimes it's 1%.

  • But if this probability is less than or equal to,

  • if it's less than or equal to your threshold,

  • and the threshold is oftentimes denoted

  • by the Greek letter alpha,

  • well, we say, "Hey, that was a very low probability

  • "of getting a result at least this extreme

  • "if we assume the null hypothesis,"

  • and so that will allow us to reject,

  • reject the null hypothesis,

  • which would suggest, suggest the alternative.

  • Notice we haven't proven the alternative.

  • We also haven't proven the the null hypothesis

  • is for sure false.

  • We've just said if we assume the null hypothesis,

  • there's a very low probability of getting a result

  • at least as extreme as what we just got,

  • so we will reject the null.

  • Now, if it's the other way around,

  • if the probability of getting a sample mean

  • at least as extreme as this is still reasonable,

  • if it's greater than your pre-specified threshold,

  • then you fail to reject the null.

  • You fail to reject

  • your null hypothesis.

  • So, I'll leave you there.

  • In future videos,

  • we'll go into much more depth into all of this,

  • but this is to give you a sense of how hypothesis testing

  • allows science or all of us in the world

  • to start making inferences that we can feel good about.

- [Instructor] What we're going to do in this video

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假設檢驗的理念 (Idea behind hypothesis testing)

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    林宜悉 發佈於 2021 年 01 月 14 日
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