 Hi everyone, it's MJ and welcome back to hypothesis testing. What I want to do in this video is talk about the type of errors that we get while doing this type of testing. Once we've gone through this, it should help us to understand the hypothesis testing process a little better. There are two types of errors and I'm going to actually just write them out very quickly in the mathematical form. The first error is when we reject the hypothesis, so we reject the hypothesis, but the hypothesis is actually true and this is equal to something called alpha and it is known as the size of a test. So this is also, let's write this down, this is error number one. Error number two is the probability that we fail to reject the null hypothesis when in fact the null hypothesis is actually false. This is known as beta or the power of the test. If we had to draw this on a diagram, we would see the following. Let's say this is our null hypothesis that the population parameter is 0.05 and what we know is we've got our little distribution and we have, let's say, our upper and lower bounds and within this we're going to reject whatever is inside and we fail to reject everything that's inside and reject everything that is outside. Now what we're going to see is this is a probability distribution. There is a chance that we get our random sample and we calculate our estimator and it lies there and that the 0.5 is actually true. There is a chance that, it could be very small, it's very small, but there is a chance that this is our value and this is true, but we will reject it and say actually this isn't the case because we got this extreme value, so it is a mistake, it is an error and this is known as the alpha or the size of the test, but there's also a situation and I think this one's quite easy to understand. It's understanding that extreme events do sometimes happen and we reject it. The second error is a little bit more interesting. The second error is when our value lies within the critical region and so we're failing to reject the null hypothesis, but the problem is that the null hypothesis is actually false. Now how does that work? How does that work? Well remember, there could be another answer and I mean the answer could be that the population parameter is, let's say, its true value is 0.75 and it's just that 0.75 we had again an extreme event happening that it landed inside the critical region of our null test but it's actually not the situation. So this here is known as the power, so this thing here is our probability of us having a type 2 error and if we go back to the purple, I mean the pink, we see that this is the probability of us having a type 1 error and this is where we get into a little bit of a dilemma because whenever we try to minimize, if we try and minimize alpha, what we're going to end up doing is increasing or maximizing the beta and again as soon as we try to decrease beta, we are going to end up increasing alpha. So if we start making our confidence interval smaller, yes we will have less of the power happening but the pink will increase and vice versa and this is one of the things that you just need to get your head around with hypothesis testing and this is where stats and uncertainty and all these things creep in and people are getting uncomfortable with this but the fact is that we could be doing a test and we could be wrong, we could be wrong and that is what we just need to bear in mind that we can't say we accept H or the null hypothesis, we can only say that we fail to reject the null hypothesis and that's just to try to capture a little bit of the philosophical insight that we are dealing with uncertainty. So it's important to bear in mind these tests, what we see is we will design tests in such a way to minimize the power of a test and how we do that we normally set alpha equal to 0.5, we'll make that, that's normally the standard but we'll see this happening in examples and stuff as we go forward and we'll deal with some exam questions around this as well but I just wanted to give a very brief overview of the type of errors that we can come across in hypothesis testing but if you have any questions please don't hesitate to ask and I will definitely answer them. Thanks so much for watching, cheers.