Introduction to Type I and Type II errors (video) | Khan Academy

Video transcript

– [ Instructor ] What we’re gon na do in this video is talk about type I errors and Type II errors and this is in the context of meaning testing. thus fair as a short bite of review, in order to do a significance test, we beginning come up with a null and an option hypothesis. And we ‘ll do this on some population in question. This will say some hypotheses about a truthful parameter for this population. And the nothing hypothesis tends to be kind of what was always assumed or the condition quo while the option hypothesis, hey, there ‘s news here, there ‘s something alternative here. And to test it, and we ‘re truly testing the null hypothesis. We ‘re gon na decide whether we want to reject or fail to reject the nothing hypothesis, we take a sample distribution. We take a sample distribution from this population. Using that sample distribution, we calculate a statistic, we calculate a statistic, that ‘s trying to estimate the parameter in interrogate. And then using that statistic, we try to come up with the probability of getting that statistic, the probability of getting that statistic that we just calculated from that sample of a certain size, given if we were to assume that our nothing hypothesis, if our null hypothesis is true. And if this probability, which is frequently known as a p-value, is below some threshold that we set ahead of clock time which is known as the meaning degree, then we reject the null hypothesis. Let me write this down. so this good over here, this is our p-value. This should all be review, we introduced it in other videos. We have seen on other videos if our p-value is less than our significance floor, then we reject our null hypothesis, and if our p-value is greater than or equal to our significance flat, alpha, then we fail to reject, fail to reject our nothing guess. And when we reject our nothing hypothesis, some people will say that might suggest the alternative hypothesis. And the reason why this makes sense is if the probability of getting the statistic from a sample of a certain size, if we assume that the nothing hypothesis is dependable is sanely abject if it ‘s below a doorsill, possibly this threshold is 5 %, if the probability of that happening was less than 5 %, then hey, possibly it’s fair to reject it. But we might be wrong in either of these scenarios and that ‘s where these errors come into play. Let ‘s make a grid to make this clear. So there ‘s the world, let me put reality up here, so the reality is there ‘s two possible scenarios in reality, one is the nothing guess is on-key and the early is that the nothing hypothesis is delusive, and then based on our significance examination, there ‘s two things that we might do, we might reject the null hypothesis, or we might fail to reject the nothing hypothesis. And indeed let ‘s put a little power system here to think about the different combinations, the different scenarios here. so in a scenario where the null hypothesis is true, but we reject it, that feels like an mistake. We should n’t reject something that is truthful and that indeed is a type I error. type I error. You should n’t reject the null hypothesis if it was true. And you can even figure out what is the probability of getting a type I error. Well that ‘s gon na be your meaning level because if your null hypothesis is genuine, let ‘s say that your significance tied is 5 %, well 5 % of the prison term, evening if your null hypothesis is truthful, you ‘re going to get a statistic that ‘s going to make you reject the null guess. So one way to think about the probability of a Type I error is your significance level. now, if your nothing hypothesis is true and you failed to reject it, well that ‘s effective. This we can write this as, this is a adjust decision. The effective matter just happened to happen this clock. now, if your nothing hypothesis is false and you reject it, that ‘s besides good. That is the compensate conclusion. But if your null guess is delusive and you failed to reject it, well then that is a Type II error. That is a Type II error. now with this context, in the following few videos, we will actually do some examples where we try to identify, one, whether an mistake is occurring and whether that error is a type I or a Type II.

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