 Some of the options that Jmovi gives you in working with data are really kind of surprising because they're not usually found in other statistical software, at least not in the standard installations. So if you're working in SPSS and you want to do a multivariate analysis of covariance, you might have trouble. You may not be included there in the base package or you may have to download additional things and other programs to make it work. But a sophisticated analysis like a mancova is available as part of the base package in Jmovi. That's an amazing thing. Now, Manova stands for multivariate analysis of covariance. And the multivariate part means you have more than one outcome variable and you're trying to model the group differences on all of those simultaneously. Plus, because there's the C in the middle, that means covariance and you could use a quantitative or continuous predictor. You don't have to because you can do either of the above with a mancova option in Jmovi. Let me show you how this works with the iris data again. All I'm going to do here is I'm going to see if there are group differences on all four of these variables. Now, I'm going to begin with the exploration, something I say that's always a good idea. So I'm going to come up here to exploration and go to descriptives. And what I'm going to do is I'm going to get these four quantitative or continuous variables. Put them here and I'm going to break it down by species split it by species. Now I actually am not concerned very much about the statistical table at the moment. So I'm just going to unclick all of this and close that up. What I do want is the plots and I'm going to do the density. That's the Leica histogram smooth. It's going to break it down by the three groups so we can see what sorts of differences there are between those groups and the data. I'm going to refer Jmovi to get there. But now what we have is the sepal length and we're looking at the three different species of iris flowers. We have a Satosa, Versicolor, and Virginica. And you can see that there are differences that things go up a little bit as we go from one species to another. The pattern switches around a little for sepal width where Satosa is the highest and the other two are really close. Pedal length, we have an enormous difference with Satosa way down here on the low end. And the other two are still distinguishable. And then pedal width, we actually have this nice separation between the three of them. And we can look at each of these separately. If we want to do four separate analysis of variance analysis, we could look at the group differences on each of these separately. The Minova or the Mancova allows us to do all of them at once. Although I'll let you know that sounds like it would be a big improvement, but it's often pretty hard to interpret the results because the math that goes into this gets much, much, much more sophisticated. But let's see what Jamovia can do to make this procedure at least a little more accessible. So I'm going to close this and I'm going to call to the ANOVA and come down to Mancova, which again stands for multivariate analysis of covariance. And when I click on that, the nice thing is it's not giving me all the possible options you could get because there would be a million. But the easy thing is what are the dependent or outcome variables? I'm actually going to pick all four of these flower measurements, put them over here, and then factors that says what defines the groups. That's this three species here. Now, if I wanted to use one of these measurements as a covariate, or if I had something else with covariate like the age of the plant or the height of the stem or something, I could put that in there too. I could do that because it doesn't change the output very much. And I just want to focus on what we have right here. The important thing is we really just have this one table that's kind of all that it's giving to us. In fact, we have the same analysis really done four different times when we come here to multivariate tests. The question that these four things are trying to tell us is, are there differences on these four variables simultaneously between the three different groups? And it turns out that all four versions of the math that goes into the multivariate analysis of variance or covariance, they're all giving us the same answer in this case. They're all saying that yeah, there's this huge difference. It's a highly significant difference. The p value you're looking for something less than five is much less than that. It also does univariate tests where it's looking at the variables separately. So we can look at sepal length. And this is the one factor of one way analysis of variance. And we can see, yeah, there are differences between the groups on all three of them. Now remember, with the analysis of variance, it doesn't mean that every group is different from every other one. If we come back up to here, for instance, you know, we can see that Satosa is different on sepal width, but VersaColor and Virginica are very similar to each other. And so there's a difference somewhere in the mix, even if not all three are different from each other. And that's what we get here. I'm just going to finish with one of the assumption checks. We can do the QQ plot of multivariate normality. Again, something that we're generally looking for, because a normal distribution or a bell curve is a good idea. And a multivariate normal distribution means that if you have one variable, that would be a bell curve. If you have two variables, it's doing it in an x and y dimension. And you're looking for sort of a smooth hill. And if it's three or four variables, then you get into, you know, higher dimensions and it's really hard to visualize. But if we just look at the quantiles, that is, that's what the QQ stands for is the quantiles. We have the chi squared quantiles across the bottom and the squared mahalinobus distance on the side, which is also a quantile. And the idea here is that if all the dots, those are our data points, fall on the diagonal line, then you have what is basically a multivariate normal distribution. We're really close to that. So I think we've met these assumptions. But really, the options that we're getting in genmobi here are pretty simple for what could be an extremely complex and sophisticated analysis. Basically, it is telling us that yes, you have a statistically significant manoeuvre. I could call it a mancova, but I didn't actually use a covariate this time around. And then it follows it up with univariate annovas for one factor at a time. And it's enough for us to be able to say, yes, there's something there. And if you have the theory that says what the differences should be, you might be able to tell that by looking at some of the univariate analyses as well. And so the nice thing again about genmobi is it makes this really sophisticated kind of question easy to answer. It gives you just enough information to get the yes-no that you're looking for if you're doing hypothesis-driven research. And that's going to be a very significant first step in understanding what's going on in your data.