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Relations and Categorical Data. Target Goal: I can describe relationships among categorical data using two way tables. 1.1 cont. Hw: pg 24: 20, 21, 23, 26, 27 - 32. Now we will look at describing relationships between two or more categorical variables. Ex. Gender, race, occupation.

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## Relations and Categorical Data

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**Relations and Categorical Data**Target Goal: I can describe relationships among categorical data using two way tables. 1.1 cont. Hw: pg 24: 20, 21, 23, 26, 27 - 32**Now we will look at describing relationships between two or**more categorical variables. • Ex. Gender, race, occupation**To analyze categorical data, use counts or percentsof**individuals that fall into various categories.**Example : Education and Age**• Table presents Census Bureau data on the years of school completed by Americans at different ages.**Two Way Table: Describes Two Categorical Variables**• Row and column variable: least to most • Marginal distributions:totals that appear at the right and bottom margins for each individual variable. • Round off error: There is round off error depending on groupings.**Percents**• To describe relationships among categorical variables, calculate the appropriate percents from the counts given. • Percents:are often more informative than counts.**The percent of people 25 years of age or older that have at**least 4 years of college is:**Tip for deciding on what fraction gives the percent you**want: • Ask, “What group represents the totalthat I want a percent of?” • Can be tricky!**Exercise: Percents**• Give the marginal distribution of ageamong people 25 years or older in percents, starting from the counts in table 4.6. • Which totals do we use?**Find each one and the total:**• Age 25 to 34: 37,786/175,230 =21.6% • Age 35 to 54: • Age 55+: • Total = 100.1% due to rounding 46.5% 32.0%**Exercise: Using Percents to Make Bar Graph**• Using the counts in table 4.6, find the percent of people in each age group who did not complete high school.**Percent of people in each age group who did not complete**high school. 4,474/37,786 = 11.8% • age 25 to 34: • age 35 to 54: age 55+: 11.2% 25.4%**Draw a bar graph that compares these percents. State briefly**what the data show. (3 min) • Conclusion: • The percentage of people who did not finish high school is about the same for the 25 - 34 and the 35 – 54 age groups 11.8 and 11.2 % respectively. • But, the percentage almost doubles to 25.4% for the 55 and over age group.**Marginal distribution: compare each variable separately.**(Denominator is the grand total.) Conditional distribution: refers to only “people” who satisfy a certain condition (age 25-34). • Look only at column (or row). • Column (or row) total is the denominator.**Result: comparingconditional distributions of**“education” in different “age groups”describes the association between age and education. • Bar graphs to compare the education levels of three age groups. • Each graph compares the percents of three groups who fall in one of the four education levels.**Example, p. 13**• Two-Way Tables and Marginal Distributions Analyzing Categorical Data Examine the marginal distribution of chance of getting rich.**Example, p. 15**• Two-Way Tables and Conditional Distributions Analyzing Categorical Data Calculate the conditional distribution of opinion among males. Examine the relationship between gender and opinion.**You will be asked to express the Conditional Distribution**Describes the value of that variable among individuals who have a specific value of another variable.The conditional dist of ______________ among _____________. hw. 29) What percent of females thought they were going to be married in the next ten years.The conditional dist of _________________ among ___________________________.**Organizing a Statistical Problem**• As you learn more about statistics, you will be asked to solve more complex problems. • Here is a four-step process you can follow. Analyzing Categorical Data How to Organize a Statistical Problem: A Four-Step Process State: What’s the question that you’re trying to answer? Plan: How will you go about answering the question? What statistical techniques does this problem call for? Do: Make graphs and carry out needed calculations. Conclude: Give your practical conclusion in the setting of the real-world problem. See pg. 18 for an example. Hw question on 4 step process.**Looking Ahead…**In the next Section… • We’ll learn how to display quantitative data. • Dotplots • Stemplots • Histograms • We’ll also learn how to describe and compare distributions of quantitative data.

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