Errors in Hypothesis Tests: Type I Error versus Type II Error

00:01 In this lesson, we will learn about the errors that can be made in hypothesis testing. In general, we can have two types of errors.

00:10 Type one error and type two error.

00:13 Sounds a bit boring, but this will be a fun lecture, I promise.

00:18 First we will define the problems, and then we will see some interesting examples.

00:24 Type one error is when you reject a true null hypothesis.

00:28 It is also called a false positive.

00:30 The probability of making this error is alpha.

00:33 The level of significance.

00:35 Since you, the researcher, choose the alpha, the responsibility for making this error lies solely on you.

00:43 Type two error is when you accept a false null hypothesis.

00:47 The probability of making this error is denoted by beta.

00:51 Beta depends mainly on sample size and magnitude of the effect.

00:55 So if your topic is difficult to test due to hard sampling or the effect you are looking for is almost negligible, it is more likely to make this type of error.

01:05 We should also mention that the probability of rejecting a false null hypothesis is equal to one minus beta.

01:12 This is the researchers goal to reject a false null hypothesis.

01:16 Therefore, one minus beta is called the power of the test.

01:21 Most often, researchers increase the power of a test by increasing the sample size.

01:28 This is a common table statisticians use to summarize the types of errors.

01:33 Now let's see an example that I heard from my professor back when I was studying statistics in university.

01:40 You are in love with this girl from the other class, but are unsure if she likes you.

01:46 The status quo in this situation is she doesn't like you back.

01:50 So h zero is, she doesn't like you back.

01:55 Generally there are four possibilities which can be summarized in the same table.

02:00 For you. The status quo is that she doesn't like you.

02:04 You are investigating what to do.

02:06 If you accept the null hypothesis, you accept the fact she doesn't like you.

02:10 Therefore, you do nothing.

02:14 If you reject null hypothesis, you reject the status quo.

02:18 You go to her and invite her out.

02:21 Okay. Great.

02:23 So far, so good.

02:25 Now the truth itself can be one of two options.

02:28 H zero is true or h zero is false.

02:33 So she doesn't like you back, or she does like you back, right? Ok What happens if you accept the null when it is true? You do nothing.

02:43 In reality, the girl doesn't like you back.

02:46 You save yourself the embarrassment.

02:48 And it's all good. Now, another possible situation is the following.

02:54 The null is not true.

02:55 So she actually likes you.

02:58 Your statistical test tells you to reject the null, and you go and invite her out.

03:04 Obviously that's favorable for everybody.

03:07 So it's all rainbows and butterflies.

03:10 That's all clear, I believe.

03:13 However, there are two errors you can make.

03:16 First, if she doesn't like you back, and you invite her out, you are making the type one error. You got a false positive.

03:24 What you do is go and invite her out.

03:26 She tells you she has a boyfriend that is much older, smarter and better at statistics than you and turns her back.

03:35 Okay. Now imagine she actually liked you, but you accepted the null and did nothing about it. In other words, you made a type two error.

03:44 You accepted a false null hypothesis and lost your chance.

03:48 You could have been made for each other, but she didn't even try.

03:53 Both of those cases are sad, but hypothesis testing is the way it is. You don't really want to make any of the two errors, but it happens sometimes.

04:02 You should be aware that statistics is very useful, but not perfect.

04:08 All right. That's all from our love slash life slash statistics lesson.

04:13 Thanks for watching.