Type 1 errors

I want to do a quick video on something that you're likely to see in a statistics class, and that's the notion of a Type 1 Error. And all this error means is that you've rejected-- this is the error of rejecting-- let me do this in a different color-- rejecting the null hypothesis even though it is true. So for example, in actually all of the hypothesis testing examples we've seen, we start assuming that the null hypothesis is true. We always assume that the null hypothesis is true. And given that the null hypothesis is true, we say OK, if the null hypothesis is true then the mean is usually going to be equal to some value. So we create some distribution. Assuming that the null hypothesis is true, it normally has some mean value right over there. Then we have some statistic and we're seeing if the null hypothesis is true, what is the probability of getting that statistic, or getting a result that extreme or more extreme then that statistic. So let's say that the statistic gives us some value over here, and we say gee, you know what, there's only, I don't know, there might be a 1% chance, there's only a 1% probability of getting a result that extreme or greater. And then if that's low enough of a threshold for us, we will reject the null hypothesis. So in this case we will-- so actually let's think of it this way. Let's say that 1% is our threshold. We say look, we're going to assume that the null hypothesis is true. There's some threshold that if we get a value any more extreme than that value, there's less than a 1% chance of that happening. So let's say we're looking at sample means. We get a sample mean that is way out here. We say, well, there's less than a 1% chance of that happening given that the null hypothesis is true. So we are going to reject the null hypothesis. So we will reject the null hypothesis. Now what does that mean though? Let's say that this area, the probability of getting a result like that or that much more extreme is just this area right here. So let's say that's 0.5%, or maybe I can write it this way. Let's say it's 0.5%. And because it's so unlikely to get a statistic like that assuming that the null hypothesis is true, we decide to reject the null hypothesis. Or another way to view it is there's a 0.5% chance that we have made a Type 1 Error in rejecting the null hypothesis. Because if the null hypothesis is true there's a 0.5% chance that this could still happen. So in rejecting it we would make a mistake. There's a 0.5% chance we've made a Type 1 Error. I just want to clear that up. Hopefully that clarified it for you. It's sometimes a little bit confusing. But we're going to use what we learned in this video and the previous video to now tackle an actual example.