Okay, in this video, I'm going to give you a very brief and very general introduction to a statistical technique called one way ANOVA. So here's an ova and ANOVA is actually an acronym. It stands for analysis of variance. And in this video, we're going to just briefly discuss two general topics. We're first going to ask the question, why do we need one-way analysis of variance? And then second, we're going to talk about the stages of analysis by using this approach. Okay? First, before we actually learn anything about one-way ANOVA, we should always understand why we would want to use it in the first place. Okay? In order to answer, in order to start delving to that question, we first need to know what one-way ANOVA actually does. What one-way ANOVA allows us to do is it allows us to simultaneously test for differences among the average values of two or more groups in an experiment. So for example, imagine that you had an experiment with three different groups or three different treatments. What a one-way ANOVA would allow you to do is to get a single p-value would allow you to know whether or not there are any differences among any of these groups in your experiment. Okay? Now at this point, you might be saying to yourself, well, I already know how to do a randomization test to compare differences between two groups. Or I already know how to do a t-test to compare differences between groups. If I already know how to compare two groups, why do I need to understand one way ANOVA? Well, let's, let's discuss that. Okay. Let's imagine that you're in this situation. Let's imagine you have an experiment where you actually have three treatments. And we'll say the treatments are called drug a, drug B, and drug C. And let's imagine you are a courageous student who's analyze these data using, say, two tests using three separate tests that each compared two of these mean values. So in the first test, the courageous students compared the mean value of drug age, the mean of drug B. And then they compared the mean of a versus C, and then the compared B versus C. And these are just the P-values. Okay, we're focusing on the p-values from this perspective and not the effect size in this video. Okay, so What's wrong with this approach? Well, we're going to talk about this from two different perspectives that are very related. First is I want you recall that if we're analyzing our data using a threshold P-value approach, in other words, where we compare a p-value that we obtained from our data. And we compare that p-value to a threshold value of 0.05. And if our p-value is smaller than that, then we say our results a significant. And if our p-value is larger than 0.05, then a statistically nonsignificant. Okay? I want you to recall that from that perspective. This perspective means that 120th of the time that we are analyzing data where the null hypothesis is true. In other words, 5. In this, using this perspective, 5% of the time when we're analyzing data with the truth is, there is no difference among our treatments than 5% of the time, we will get what's called a false positive or Type one error. And what this means is that just by random chance, 5% of the time we will get a p-value that is smaller than 0.05, even when there's nothing interesting going on in our data. And this leads us to conclude that there is something interesting going on in our data. Maybe I shouldn't use the term interesting. Because lack of evidence for effects can also be interesting. So I'll rephrase that and say 5% of the time. When we're analyzing data where the truth is that there's no difference among our treatments. We may get, we can get a p-value that would lead us to conclude that there are differences among our treatments. Okay? So again, we call that situation a false positive or a type one error. Now, this probability of 5% or one in 20, this should be ringing some alarm bells. Because what this perspective means is that the more tests we perform, the more opportunity there is to make this kind of mistake. Okay? And so performing multiple tests increases the chances of obtaining a false positive or a making a conclusion. That's a type one error. Okay? And this is why we need one way ANOVA. Because what we need is a method to analyze more than two groups simultaneously. So that on the level of the whole experiment, we're just getting one p-value. And by just getting one p-value, we ensure that our type one error rate remains at 5%. Okay, So that is the major benefit or one major benefit of using one-way ANOVA instead of a series of pairwise comparisons. Okay? Now, I want to set it was going to talk about this from two different perspectives. Just a little bit of recent history. First, in 2019, the American Statistical Association put its foot down and said that this perspective of comparing p-values against a threshold value, 0.05 or any threshold value is an unwise way to go about making conclusions from your experiments. And what they advocate instead is a series of things, but I'm just going to focus on the P-value perspective here. What they advocate instead with respect to p values, is to view P-values along a continuum of levels of evidence against the null hypothesis. So for example, in some other videos, I argue that a p-value of around 0.005. So you have an extra 0 in there. P-values of fat that are that small, say 0.005 or smaller, could be considered strong or substantial evidence to reject your null hypothesis. I also suggested a p-value of around 0.05. So p-value around this thresholds that often is used a p-value, but that magnitude might be considered moderate evidence to reject the null hypothesis. Whereas p-values it even larger like 0.1 or 0.2 or larger than that, those would be considered weak evidence to reject the null hypothesis. Okay? So this perspective of looking at P-values along a continuum is a more appropriate way to, to make conclusions. But these arguments that I'm making about why it's important to use a one way ANOVA as opposed to a series of pairwise tests, like a series of t-tests, for example, those arguments still hold from this continuous or continue with p-values perspective. Because under this perspective, we can just recognize that the more tests that we perform, the more opportunity there is for us to get a small p-value generally, regardless of whether or not we're comparing that p-value to 0.05. And so as you perform more tests, and we increase the opportunity to get a small p-value just by random chance. Then performing multiple tests still opens up the possibility or still increases the possibility of our obtaining false positive or Type 1 errors. Okay, so even from this more modern perspective, we still want to minimize the number of tests that we perform to reduce our chances of making these types of errors. And so still, one way ANOVA is a great way to go. Okay, so that was our first message from this video. That's one of the main reasons why we like to use why and when. One way ANOVA to analyze experiments or we have more than two groups. The second thing I'd like to clarify in this video is a stages of analysis. Because analysis of variance as a complete analysis involves two general stages. The first stage of an analysis of variance involves this process of obtaining one single p-value, which allows us to test for there being, allows us to get evidence for whether or not we should reject our general null, null hypothesis. That there might be differences among any of the groups we're comparing. Okay? In other words, the first stage of analysis of variance and gives us 1 p value that allows us to test whether or not there are any differences that might occur between any of the groups in our experiment. Okay? Critically, this p-value that we get from this first stage does not tell us anything about which of those treatments might differ. So back to this experiment where we had three groups. If we perform a one-way analysis of variance upon an experiment with these three groups. And we got a p-value that was convincingly small to tell us we had reason to reject the null hypothesis. And that would tell us that we have good reason to believe that somewhere in our experiment, there were differences among our various groups. But this first stage does not tell us which groups likely differ from which. That question is usually one that we wants to answer. We're usually interested to know in specifically which groups are different from which. And to answer that question, we need to go on to a second stage of analysis using something called post hoc tests. And with one-way ANOVA, we often use what's called a Tukey's test. And in the second stage, in that stage, we can make comparisons among our various treatments to get better insight about the evidence for differences among each of our specific groups. Okay? So a full analysis using one-way ANOVA involves both of these stages. The first stage allows us to get evidence for whether or not there's or so. It gives us insight as to whether or not there's any evidence overall for differences among any groups. And the second stage allows us to better understand which groups likely differ from one another. If this first stage tells us that there's reason to believe that there are differences among groups. And that's that I wanted to tell you in this video. We talked about why we wants to use one-way ANOVA in the first place as opposed to using a series of pairwise tests like a series of t-tests. And then I'm clarify that a one-way nova actually involves two stages of the analysis. Okay. We'll stop the video there. I hope it's been helpful and I'll say, thank you very much.