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was 9, so he made 9 of 15 threes and this is the distribution under the null hypothesis, so how extreme was his test statistic that we got? Well, we discovered that it wasn't extreme enough, so the hypothesis test said to reject the null hypothesis if the test statistic is in the top 5% of the distribution and in fact we found that he was not in the top 5% of the distribution. distribution, what the p value does is it takes our test statistic and it actually calculates that region so it says our test statistic is in the top 30 point 4 percent of the 0.304 distribution, so it's actually measuring which part of the distribution is at or above our test statistic, in other words it is measuring how extreme our sample is, so if our p value is very small the more extreme our sample must have been and therefore , we are more likely to reject the null hypothesis and if the p-value is large, we are less likely to reject the null hypothesis, so if it is closer to one, it is this one. this was 0.3, so we had a fairly large pink area.

Here we are less likely to reject the null hypothesis and that is exactly what happened in our case. We do not reject our null hypothesis. Now, the last point I could make and it's something you probably have. We may have already figured it out, but if this p-value falls below 0.05, it implies that our test statistic must be in the rejection region. Let me repeat that if the p value is less than point O five, it means that our test statistic, wherever we are, must be in the rejection region, so the rejection region was built, that yellow bit let's go back, that yellow bit was constructed so that there is five percent highlighted, five percent of the entire distribution that has been highlighted, so if our p-value is less than five percent or less less than 0.05, if the pink bit was less than 0.05, we know we must be somewhere in that rejection region, our test statistic must be in the rejection region, so what that implies is that if the p-value is less than the level of significance of your hypothesis In a test you are going to reject the null hypothesis, so it is a very quick way to evaluate if we are going to reject our null hypothesis correctly.

So, when you do a hypothesis test, let's recap whatever you're looking for evidence for goes on your alternative hypothesis and then if you do the test and your p value is very, very small, that provides evidence for that alternative hypothesis, it provides enough evidence for us to reject the null hypothesis, so that's it for the theoretical component. of this video, stop the clock, I lasted less than 30 minutes. I don't believe it. I think it's been a few minutes, but I'm not even going to stop the video here because I thought I'd give you a little extra section.

It has to do with p-values ​​because they have been in the news for the last few years I would say, and not necessarily in a good way, people have been throwing a lot of shade at scientific research lately and it is somewhat justified because of this thing called P-hacking, so if you've had enough of the theoretical component of

statistics

today, well, I'll tell you that's it, we're done, but let's take a look at P-hacking to see how a bad thing works. use of p values. can invalidate scientific research, so let's talk about what P hacking is all about and it might start with the same old boring probability density function we saw before.

Now, as we've seen in hypothesis testing, we start with the null hypothesis that there is no effect and then we take a sample and we want to see a sample that is extreme enough that we can reject that null hypothesis, so we'll build this rejection region, which is this yellow shaded region up here. My choice of colors may not have been the best, but I hope you As we can see, it is shaded yellow, so if our sample is in this region here, we can reject the null hypothesis and by doing so we would say that there is a significant effect and all of a sudden that's great, we can publish our paper to show that well this is exactly the case if we have a sample that is in our rejection region, in other words a sample that is extreme enough for us to reject the null hypothesis, it does not mean that the null hypothesis is false, it is still possible So we just get an odd sample, the whole purpose of a p-value is to say, well, how likely are we to get this sample statistic if the null hypothesis is true and if the p-value is low enough, we say oh, that's it. starting to be too low, but at the same time, as long as that p- with non-zero values, there is an outside possibility, but it turns out that you get a strange sample where, in fact, there was no effect to put it in basketball terms, just say that since Leonard was a 50% 3-point shooter, it's still possible for him to score. 14 or 15 of 15 three-pointers, very unlikely if his true three-point percentage was 50%, but possible, so how does this relate to good and bad research?

Well, in good research what you do is you theorize some kind of effect and maybe that could be that red wine causes cancer, let's say as a correct example, then we collect our data and we test just that effect that red wine causes cancer and If we find that the p value of this test is less than 0.05, we can conclude something. solid evidence of the effect of red wine on cancer and that's all well and good and that's good research, that process of theorizing some effect, then collecting data and testing that exact effect is how one does good research, now it's They do bad research this way and unfortunately I'm going to suggest this be done all the time if you collect your data first with just the general idea of ​​seeing what causes cancer, so let's collect a lot of data from people who have cancer, a Lots of lifestyle data.

Also, if they smoke, if they drink wine, all these kinds of things, we'll test all these different effects, we'll try red wine, we'll try smoking, we'll try exercise, we'll test exposure two main pathways all these kinds of things and then we'll review all those effects and we will find those where P is less than 0.05, but let's say there were four where we tested red wine on cancer and then we will publish our results and say yes, red wine causes cancer because the p value is lower to 0.5. This is called pee hacking and is potentially widespread in research and is quite problematic now it's not necessarily obvious why this is so much worse than our good research. here on the left, but as I said before, when we conclude strong evidence of some effect, we are basically saying that there is a very, very low probability that this happened by chance.

What happens when you try 10 different things? If you try 10 different things. it becomes more likely that one of them, by chance, is quite extreme in their sampling. Well, let's go even further if we test 20 different things, we actually expect 1 of those 20 things to have a p-value less than 0.05, ie. Actually, what does the p value mean if there is a 5% chance that the effect we saw was simply due to the randomness of the sampling process that if we test 20 things, 5% of 20 is 1, it is likely that one of those 20 things show that strength of effect, so that's where the hacking comes in, we try all these different things and we just find the one that seems significant and then we can pretend that that was what we were looking for all along. and it's actually a big deal anyway that hopefully it put into practice some of the things you can learn in

statistics

and of course I've treated things in a very superficial way but that was the point of this video, but look.

If you like this, I have more in-depth discussions, one where I go into the actual formula and math of it all, you can check it all out at Zed Statistics com, but if you're interested, you can like, subscribe, and do that. all those things you have to do, but yeah, I hope you enjoyed them