 If you're working with experimental data, then the analysis of variance or ANOVA or ANOVA is going to be a very common method of analyzing your data. What it lets you do is compare the means of more than two conditions, or it lets you compare the means of more than two factors, each of which may have two or more conditions. To demonstrate how this works in Jmovi, I'm going to use the tooth growth data set that you can get as one of these sample data sets. And what it shows is three things. It shows two manipulated variables, which are SUP for the vitamin C supplement. It either uses vitamin C or orange juice. And the dosage, which is 500, 1,000, or 2,000 milligrams, I assume. And how it affects the length of tooth growth in guinea pigs. The idea here is that vitamin C is good for tooth growth. And so let's take a look at how these variables, these two factors, each affect the length of tooth growth along with their interaction between the two. To do this, we come up here to the ANOVA or ANOVA menu. And we're going to use this standard ANOVA dialog. So I'm going to open that one up. And the dependent variable is the outcome, the thing that you're trying to predict or model, and that's len for length. And then the fixed factors are the two categorical or nominal variables that you use to predict the length. And I'm going to shift click both of these and put them over here. And what we get is the basic ANOVA table right here on the right. And what it shows us is the main effect for each of the variables. So SUP, and we have a sum of squares, a degrees of freedom, mean squares. The second to last column is the F value. And that's the test statistic. And then right next to it is the P value that's used for hypothesis testing. And if that number's less than 05, it's considered statistically significant. And it turns out that in this case, the main effect for supplement is statistically significant, the main effect for dose is significant. And the interaction of SUP and dose is also statistically significant. Now, there are several things that we can do here. But one of the most important is going to be to get a measure of effect size. And the most common measure of that for the analysis of variance is eta squared. It's a Greek letter, it kind of looks like a lowercase n. Because we have more than one factor, we want to use the partial eta squared. So we click on that and we simply get a new column in our table off to the right. And eta squared can be read sort of like a proportion of variance explained. And it goes from 0 to 1 where 0 is 0%, 1 is 100%. And what you see here, for instance, is that SUP has an eta squared of 224. So that means that can account for 22% of the variance in the length of the tooth growth. Dosage accounts for 77%, that's a huge amount. And the interaction still accounts for 13%. And this is the most basic version of the analysis of variance that could be useful to you. But I do want to show you some of the options that Jamobi gives you very quickly. One is, if you want to specifically control the model, and for instance, the kinds of interactions, then you can set those here. Now we only have two factors and one possible interaction. So this is limited. But if we had, say for instance, four factors, then there would be a lot of possible interactions and you could choose which ones you wanted directly, as well as the type of sum of squares that you're going to calculate. There are assumption checks. So for instance, the analysis of variance assumes that you have essentially the same amount of variability within each group. We can check that with a homogeneity test. It uses the Levine test. And you actually want a p value that is greater than 05 because you don't want them to be significantly different from each other. So we're good here. And you can do the QQ plot of residuals. That stands for quantile-quantile plot, whereas comparing it against a normal distribution. The idea here is you're looking at the leftovers from your prediction. You want them to be both symmetrical or spread out approximately the same across groups and you want them to be maybe normally distributed. If it were a perfect normal distribution, they would all fall on this diagonal line. It isn't massively far off, so we're probably pretty good. Often in an experimental design, you have specific contrasts or comparisons you want to make between particular conditions. And you can set those up here if you want. And you can also do them within each condition. Now, this is going to make the most sense if you're doing something that shows growth across different levels. You have a lot of different choices here. I'm not going to use those, but those are available if you want them. Post-hoc tests are a common approach if you have factors with more than two variables. One of ours does. It's the dose. There are three different levels on that one. So I'm going to choose both dose and the supplement by the dose. And you can pick what kind of correction you want. The Tukey for John Tukey's test is the default one. It's the one that I prefer. And so I'm going to scroll down here a little bit. And you get a really big table. But what you can see here, for instance, is that all three supplement levels differ from each other. And you can scroll down here and see which ones compare against each other. But an easier way to look at this is going to be with the estimated marginal means. And you do this by clicking these factors and putting them over here. And it's going to produce a chart down here. And so there's the graph. And we see that orange juice is associated with more tooth growth than vitamin C. We can do a similar one for dose. We'll put add new term and put dose down there. And we'll get another one that shows the effect of the dosage. And again, ignoring the difference between the two supplements. So here we come down and we see that, well, what do you know? More dosage means more tooth growth. But the interesting one is the interaction. Now, it's not obvious how to do that in Jmovi. I'm going to say give me a new term here. But what I need to do is I need to select both of these at once. So I'm going to shift click to get both of them and then slide those over and it adds both. And then I'm going to get an interaction chart. And since we had a statistically significant interaction in our table, this is going to be important. And you can see here that the supplement, well, orange juice is more effective than vitamin C at the low dose, at the medium dose, but they're the same at the high dose. And that is a great graphical representation of the effect of the dosage and also the best single summary of the effects of these two factors, both separately and combined within our data, which is the point of doing the factorial analysis of variants.