1. CATEGORICAL AND QUANTITATIVE VARIABLES TWO-WAY TABLES AP Statistics Chapter 1

2. Data Collection Data is never just numbers. There is context behind the data that is always important. Context is the: who, what, where, when, why, and how. Data is collected on individual cases with specific variables. Variables can be broken into two types CCategorical Variables QQuantitative Variables

3. Categorical Variables Categorical variables identify a category for each case. Data can be written as words, letters, or even numbers. Examples Subject; Department; Color; Yes/No; Class Rank

4. Quantitative Variables Quantitative variables record measurements or amounts of something Must have units. Examples Length; weight; volume; number of jelly beans; salary

5. Class Data Which Variables are Categorical? Which Variables are Quantitative?

6. Displaying Categorical Data Bar chart

7. Bar Chart A bar is given for each category of the variable along x–axis The y–axis can be the counts or frequency, or as a percent, relative frequency, without loss of basic shape.

8. Displaying Categorical Data Pie chart

9. Two Way Tables Used to compare observations for two different categorical variables Example – 200 adults at a supermarket were asked for their educational level and whether or not they smoked. High School 2 yr college 4+ yr college Smoker32513 Non-Smoker611772

10. Row totals and column totals give the marginal distributions. Relative frequencies are found by dividing each cell by the total. High School 2 yr college 4+ yr collegeTotals Smoker3251350 Non-Smoker611772150 Totals932285200 High School 2 yr college 4+ yr collegeTotals Smoker16%3%7%25% Non-Smoker31%9%36%75% Totals47%11%43%100%

11. Conditional Distributions show the distribution of one variable for individuals who satisfy the some condition on another variable. Example – the conditional distribution of smokers, conditional on education level What percent of shoppers with 4 or more years of college education were smokers? 13/85 = 15% High School 2 yr college 4+ yr collegeTotals Smoker34%23%15%25% Non-Smoker66%77%85%75% Totals100%

12. Conditional Distributions show the distribution of one variable for individuals who satisfy the some condition on another variable. Example – the conditional distribution of education level, conditional on smoker What percent of smokers had 4 or more years of college? 13/50 = 26% High School 2 yr college 4+ yr collegeTotals Smoker64%10%26%100% Non-Smoker41%11%48%100% Totals47%11%43%100%

13. Conditional Distributions help us determine is there is an association between two categorical variables might exist or if they are independent. If the distribution of one variable is the same for all categories of another, we say the variables are independent. Since the percentages for smoking are different for shoppers with high school education only are different, we conclude that some association between smoking and educational level achieved exists. High School 2 yr college 4+ yr collegeTotals Smoker64%10%26%100% Non-Smoker41%11%48%100% Totals47%11%43%100%