So now let's test for moderation within the context of our final inferential test, the correlation coefficient. You might remember this scatter plot in correlation based on the Gapminder data between rate of urban dwellers in each country and the internet use rate. We found that this was a significant association with the correlation of 0.61. But might this relationship, this correlation between urban rate and internet use rate differ based on countries with different income levels? To explore this question, we've created a third variable called income group which is categorical. For this new variable, the income per person variable, which is quantitative, was categorized as a high income country given a value of 3, a moderate income country given a value of 2, and a low income country given a value of 1. The adjustments we make with the correlation coefficient are very similar to the adjustments we made to our ANOVA syntax and our chi square syntax when testing moderation. We begin by creating the third variable, a new categorical variable, called income group. We sort the data by this new categorical third variable. Next, we run the correlation between urban rate and internet use. And then we include a bystatement, telling SAS to calculate the correlation coefficient for each income group. When we examine the correlation coefficients between urban rate and internet use rate for each of the income groups, we find the following. For the low income group, the correlation between urban rate and internet use rate is 0.11 and the p-value is not significant. For the moderate income countries, the association between internet use rate and urban rate is 0.329 with a significant p-value at 0.0014. And finally, among high income countries, the correlation coefficient is 0.089, again with a large p-value, suggesting that the association between urban rate and internet use rate is not significant for high income countries. When we map these findings onto the associated scatter plots for each income group, we're able to better visualize the significant and non-significant relationships. Estimating the line of best fit within each scatter plot shows the positive association between urban rate and internet use rate among the moderate income countries and almost no relationship between those two variables in both the low income and high income countries. Asking questions about statistical interactions can be an interesting way to explore your data and your associations of interest. This is not difficult to do using the skills you've acquired this far. There are more advanced topics that we can cover here such as multivariate techniques that can be very powerful. But even without these techniques, we can still use bivariate inferential tools of ANOVA, Chi Square and correlation to describe our sample, make inferences about the larger population, and really begin to understand what relationships these associations hold, under what conditions, or at what levels of our third variable. Now that we've found associations, can we assume that association applies causation? We'll answer that question soon.