"The greatest value of a picture is when it forces us to notice what we never expected to see.\" John Tukey 7.1 Overview So far, we have examined data obtained from one variable at a time (either categorical or quantitative) and learned how to describe the features and distribution of the variable using the appropriate visual displays and numerical measures. Now we will consider two variables simultaneously and explore the relationship between them using, as before, visual displays and numerical summaries. When graphing your variables, it is important that each graph provides clear and accurate summaries of the data that do not mislead. 7.2 Lesson Understand why we impose a causal model on our research question despite the fact that causation cannot be directly evaluated based on observational data. Assign roles to each of your variables. Which will play the role of explanatory variable and which will play the role of response variable? Learn to use the graphing decision ow chart to determine, based on variable types, the appropriate graph for visualizing each relationship. Consider what types of bivariate graphs will help you graphically visualize your research question. Understand how to interpret bivariate graphs. Note that in some cases, the bivariate association may differ for population subgroups. Graphing the subgroups by adding a third variable will help to visually determine if population subgroup differences may exist. What type is the response variable? / \\ Categorical Quantitative / \\ / \\ How many categories? What type is the explanatory variable? Only 2 More than 2 i/ A . . / \\ Categorical Quantitative l/ What type is the explanatory variable? Collapse V RESPONSE variable into 2 categories cl> Q i4 4 ' ' Bar Chart Categorical Quantitative \\i/ \\|/ What type is the explanatory variable? Bin/colapse c D c EXPLANATORY variable into categories V A Bar Chart Categorical Quantitative \\l/ c[>c Bar Chart Bin/collapse EXPLANATORY varidJIe into categories CDC Bar Chart N What type is the explanatory variable? /\\ Categorical ci>c Bar Chart Quantitative Bin/collapse EXPLANATORY varid>|e into categories cl>c Bar Chart \fD Question 1 1 pts Match each pairing of explanatory and response variables to their appropriate graph: [ Choose ] Categorical -> Categorical V Bar Chart Scatter Plot Categorical -> Quantitative [ Choose ] V Quantitative -> Categorical [ Choose ] V Quantitative -> Quantitative [ Choose ] V