QPM Lab 9: Contingency Tables and Bivariate Displays in R

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1 QPM Lab 9: Contingency Tables and Bivariate Displays in R Department of Political Science Washington University, St. Louis November 3-4, 2016 QPM Lab 9: Contingency Tables and Bivariate Displays in R 1

2 Goals for Today Today s lab will introduce you to the different types of bivariate data displays: Discrete by Discrete (Contingency Tables) Discrete by Continuous Continuous by Continuous It will also attempt to get at bivariate regressions. QPM Lab 9: Contingency Tables and Bivariate Displays in R 2

3 Why Useful? It is very common that a question relies on a discussion of the relationship between two variables. What type of variables? Age and Vote Intentions Party Ideology and Party Desire to Form Coalitions Income groups and Spending on Alcohol QPM Lab 9: Contingency Tables and Bivariate Displays in R 3

4 Discrete by Discrete Data Display Assume the two variables of interest are both countably discrete. To examine the relationship between these variables, we will use contingency tables. A contingency table is used to plot membership by groups. Democrat Republican Male Female How can we interpret this table? QPM Lab 9: Contingency Tables and Bivariate Displays in R 4

5 Contingency Tables The same contingency table with row percentages. Does it make more sense to percentagize by sex or vote in the previous table? General rule: percentagize by the independent/ explanatory variable. Below we do it by gender (i.e. by row). Democrat Republican Male 39.1% 60.9% Female 66.1% 33.9% Note that the percentages add up to 100 on each row, not over each column. QPM Lab 9: Contingency Tables and Bivariate Displays in R 5

6 Contingency Tables in R Everything below is IMPORTANT for handout: Recall: Contingency tables take factors. Convert otherwise! Frequency: freq.tab <- with(data, table(factor1, factor2)) Percentage: with(data, round(prop.table(freq.tab)*100, 2)) What is the appropriate test? Chi-squared: chisq.test(freq.tab) QPM Lab 9: Contingency Tables and Bivariate Displays in R 6

7 Discrete by Continuous Displays When we have one discrete variable and one continuous Rely on some of the methods that we have used previously! Options: boxplots for each group; histograms for each group; plot the distribution of observations for each group. QPM Lab 9: Contingency Tables and Bivariate Displays in R 7

8 Discrete by Continuous Displays Ideology by age group in Brazil Ideology and more Age categories QPM Lab 9: Contingency Tables and Bivariate Displays in R 8

9 Generic R code for the boxplot boxplot(y x, data = dataset, xlab = "Informative X label", ylab = "Informative Y label", main = "Informative Title", col = c(col1, col2,...)) QPM Lab 9: Contingency Tables and Bivariate Displays in R 9

10 Discrete by Continuous Displays Age distribution for Mexico and Brazil Frequency Age QPM Lab 9: Contingency Tables and Bivariate Displays in R 10

11 Generic R code for the histogram hist(x, data = dataset, breaks = c(num1, num2,...), freq = TRUE, xlab = "Informative X label", ylab = "Informative Y label", main = "Informative Title", col = "color") QPM Lab 9: Contingency Tables and Bivariate Displays in R 11

12 Continuous by Continuous Displays If we want to examine the relationship between two continuous variables graphically, we will utilize a scatterplot. Income by Age Income by Ideology (21-point scale) Note: when ordered categories are plenty enough, consider them as continuous QPM Lab 9: Contingency Tables and Bivariate Displays in R 12

13 Continuous by Continuous Displays Scatterplot Example Miles Per Gallon Car Weight QPM Lab 9: Contingency Tables and Bivariate Displays in R 13

14 Generic R code for the scatterplot plot(x, y, data = dataset, main = Informative Title", xlab = Informative X label", ylab = Informative Y label", pch = 19) Note: Change for different types Add regression line (y x) abline(lm(y x), data=dataset, col = color") QPM Lab 9: Contingency Tables and Bivariate Displays in R 14

15 What do scatterplots tell us? Scatterplots allow us to assess the direction and strength of a relationship between 2 variables. 3 types of relationships: Positive: As x increases, y also increases. Negative: As x increases, y decreases. No relationship: There is no relationship between the variables. Careful with nominal variables: Directions do not apply! We can only say whether or not a relationship exists. QPM Lab 9: Contingency Tables and Bivariate Displays in R 15

16 Caution: Scatterplots in R In R, we can only make scatterplots with numeric variables! Check whether the variable is numeric: R code: str(datasetname$variableofinterest) R code: is.numeric(datasetname$variableofinterest) If your variable is not numeric in structure but convertible to be numeric, for instance Numbers as factor levels Numbers as characters, within quotation marks Convert it to a numeric variable (only if it makes sense): R code: datasetname$newvariable <- as.numeric(datasetname$variableofinterest) QPM Lab 9: Contingency Tables and Bivariate Displays in R 16