 Probably the simplest data situation is trying to analyze just two possible outcomes. You can call that dichotomous data because it's split into two pieces. You can also call it binary. And in this case, we're going to look at the binomial test, which literally means two names. Think of it as heads or tails on or off, yes or no. And in this example, I'm going to use the state data. And I'm simply going to look at governor, because that's the only binary variable I have in here. And let's do this first, before we do a binomial test, let's get a little bit of descriptive statistics. I'm going to come over to exploration and go to descriptives. And all I need to do is get governor, put it over here into variables, it's going to tell me some things I don't really need to know. I might as well remove the statistics that really only work for quantitative or continuous variables. But what I do want is a frequency table. And what I do want is a bar plot. And when I get the two of those, it tells me what percentage I'm dealing with in terms of governors from state to state. We have 48 states represented because remember, this data only is for the lower 48 states of the United States. And we have 15 Democrat governors as of about a week ago, and 33 Republicans. And here's a bar chart that shows the difference. And so that's really easy to see it's about two to one. Now, in terms of binomial test, what we're doing is trying to tell whether our observed proportions differ significantly from some particular value. In a lot of inferential tests, it's really obvious that the null value is zero. Well, in the binomial test, you have a few choices. Now, let me close this and come over to frequencies. And the first thing we're going to look at is the two outcomes or binomial tests, it's under one sample proportion tests. If I click on that, it's actually a really simple dialogue box. All I need to do is pick the variable that I want, I'm going to use governor and move it over into this box, you can tell it's looking for something that is coded in Jmovi as either a nominal that is a categorical variable or ordinal. And right now, it's already done the test. And it has told me that these proportions are both significantly different from a null value of 50%. And I can get a confidence interval, which actually is a really nice idea in this particular case. And this lets me know that the percentage of Democrat governors has a 95% confidence interval that goes from 18.7% to 46.3%. And we have the flip side of that, or the Republican governors. Now, I'm going to close this for just a second, so I can open it up again. This one is done with a null value of 0.5 or 50% each. And maybe that's not the value that we want to use. You know, right now we have 68.8% Republican governors, let's say we want to compare it to maybe 10 years ago. And I don't know what the proportion of Republican and Democrat governors in the 48 contiguous states was 10 years ago. But let's just say, for instance, I'm going to do the confidence interval here. Let's say it was 60%. And we want to know whether there's been a change in the last 10 years. Then I can do this. And now it's going to compare these two numbers to 60%. And what we see here is it's a little different. Let me close this so we can see this. In the first case, because we're comparing to this 50% and each of these two values because they have to add up to 100% are equidistant from 50%, the p value is the same for the both of them. On the other hand, when we move the null value away from 50%, in this case to 0.6 or 60%, then the p values are very different. We find that the current observed proportion of Republican governors, which is 0.688, which is the same as 68.8%. That does not differ significantly from 60%. On the other hand, the number of Democrats does. And so we have this big difference, depending on how you set the null value. And it's going to depend what value you use. If it's something that really should be just as likely yes as no, then the default value of 0.5 is good. But if you're looking, for instance, at a game that has four players, then the default value of any one player winning is 0.25. And there can be other values depending on what you think is most likely to happen at random. But no matter how you do it, the proportion test is a very easy test to do in Jmovi. And it gives you the simplest kind of data, just a simple yes, no outcome. And it does both an inferential test with a probability value and a confidence interval.