1. Exploring Data Section 1.1 Analyzing Categorical Data

2. By the end of this lesson, you will… Display and analyze categorical data with a bar graph. Calculate and display the marginal distribution of a categorical variable from a two-way table. Calculate and display the conditional distribution of a categorical variable in a two-way table. Describe the association between two categorical variables by comparing appropriate conditional distributions.

3. Variables Categorical Divided by groups Quantitative Numerical values where you can find an average

4.  Exploratory Data Analysis:  Statistical practice of analyzing distributions of data through graphical displays and numerical summaries.  Allows us to identify patterns and departures from patterns in distributions.  Distribution:  Description of the values of the variables takes on and how often the variable takes on those values. Exploratory Data Analysis

6. How do we display Categorical data? The Bar Graph Things to remember: Make sure you label your axes and title your graph Scale your axes appropriately Each bar should correspond to the appropriate count. Leave room between bars & bars the same width. Do not use pictures

7. How do we display Categorical data? The Pie Graph: Things to remember: Must include all the categories that make up the whole Counts will be percentages. Emphasizes category to whole. Use computer software to create one.

8. Describing and Analyzing Categorical Data A two-way table of counts organizes data about two categorical variables measured for the same set of individuals. Two-way tables are often used to summarize large amounts of information by grouping outcomes into categories. Example: 200 adults shopping at a supermarket were asked about the highest level of education they had completed and whether or not they smoke cigarettes. Results are summarized in the table.

9. Conditional vs. Marginal Distributions A marginal distribution is the distribution of values of that variable among all individuals. Example: Marginal Distribution of Education ***Marginal distributions tell us nothing about the relationship between variables*** A conditional distribution a variable describes the values of that variable among individuals who have a specific value of another variable. Example: What is percent of smokers have completed 4 or more years of college? There are 2 sets of conditional distributions: one for the row variable and one for the column variable!!!

10. Describing and Analyzing Categorical Data Create a bar graph comparing education level among smokers and non-smokers. Things to remember: Make sure you label your axes and title your graph Scale your axes appropriately Each bar should correspond to the appropriate count. Leave room between bars.

11. Example: Side-by-Side Bar Graph Does there appear to be a relationship between smoking and education level? If knowing the value of one variable helps predict the value of the other variable, we referred to that as an association. Does knowing the education level of a shopper influence your prediction about the smoking habit?

12. Describing and Analyzing Categorical Data Do you think that milk consumption by young girls is independent of the survey year? You may wish to use a graphical display to support your answer. HINT: Think about what % of ALL GIRLS drank milk? Compare that % to each of the survey results…

13. Can you… Display and analyze categorical data with a bar graph? Calculate and display the marginal distribution of a categorical variable from a two-way table? Calculate and display the conditional distribution of a categorical variable in a two-way table? Describe the association between two categorical variables by comparing appropriate conditional distributions?