 One final variation of the analysis of variants that's available in Jmovi is what's called the freedom in test or a nonparametric analog to the repeated measures analysis of variants. The idea here is that you have several outcomes that you've measured for a group of people and you're looking for changes across those outcomes. I'm going to demonstrate how this works with the built-in example data from bugs where people who are rated on a number of demographic variables evaluate insects and how much they want to get rid of them, where those insects vary according to low and high disgust and low and high fright, and they rate it from a zero, meaning you don't want to get rid of it all, to a 10, want to get rid of it immediately. And we've done this analysis before with the standard repeated measures analysis of variants, but we can also do it with the ranked version, the freedom in test. And this is an advantage if you're worried about normality in your data. So most analyses like to have bell curves and normal distribution. If you don't have that, and we actually know that we have some nonnormality in this data, then a nonparametric test might be an appropriate and informative choice. But let's begin by looking at the distributions of these four variables. We've looked at them before, but I'm just going to come here to exploration and descriptives. And then I'm going to pick these four outcomes, low disgust, low fright, up through high disgust, high fright, I'll put those under variables. And I'm not so much concerned about these statistics as I want the plots that we can get for each of them. So I'm just going to hit density. And unfortunately, I can't get them stacked right next to each other, which would be most convenient. But we can still compare going up and down in the list to see what we have. An important question is, are they normal and around they on the same scale? Now, this first one, low disgust, low fright. It's, you know, not exactly normal, but it's not terribly different. We've got a pretty strongly skewed distribution with the low disgust, high fright, also strongly skewed with the high disgust, low fright, and then really skewed with the high disgust, high fright. And so this is a situation where using a nonparametric test based on ranks as opposed to a parametric test that also assumes things like normality, this might be a good option. So let's close this and come over to the analysis of variance and drop down to the last choice here. It's under nonparametric and is the repeated measures ANOVA, or the Friedman test is what it's also called. And I click on this and you know, there's not too many options here in the Jmovi dialogue, but there's enough to get what we need out of it. So what I need to do is I need to pick my measures that I'm looking at. And I simply pick all four of them, I click the first I do a shift click on the last and I move them all over. And in this situation, I'm not breaking them down into categories like disgust and fright like I did with the regular parametric analysis of variance. But I do this way. Now, I get this tiny little table, just three numbers that shows us that there is in fact a significant effect here. The first number here, the 55.8 is under the chi squared, that's the distribution that we use. And that's a capital chi, we have three degrees of freedom. And this deviates significantly from what we would expect at random. And so we do find a significant effect here. And if you want to, you can get pairwise comparisons, they're like the post hoc comparisons, the Bonfronier, the chiffet tests that we get with other procedures. And what we have here is a comparison of each set of variables here with the four variables, we have six possible comparisons. So low disgust low fright to low disgust high fright, that's statistically significant. And in fact, all of them are statistically significant one way or another. Let's get the descriptive statistics for these. This will be a very small table. And you can see some of that is similar to what we had. When we got this information up here, just arranged it differently. And then we can also get a descriptive plot, we can choose either means or medians. But since we've been talking about means, I'm going to leave it right there. It's just a little dot plot, it's not showing us a confidence interval, because that really works differently when you're talking about a ranked situation. And even though these are means, it still lets you know that all four of these are different from each other. And because of this paired comparisons using the Durban-Konover test, we can tell that all of these comparisons are significantly different from one another. And so that's a very quick run through of the Friedman test, which is a repeated measures analysis of variance analog for using non parametric or ranked data. And again, depending on how far your data deviate from normality, this may be a good choice for analyzing and finding the hidden meaning in your data.