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Comparitive Graphs. Two Way Table. Describes two categorical variables. One variable is shown in the rows and the other is in the columns. Example of Two Way Table. Reading a Two-Way Table. Look at the distribution of each variable separately.
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Two Way Table • Describes two categorical variables. • One variable is shown in the rows and the other is in the columns.
Reading a Two-Way Table • Look at the distribution of each variable separately. • The totals on the right are strictly the values for the distribution of opinions about becoming rich for all. • The totals at the bottom are for gender
Marginal Distribution • The marginal distribution of one of the categorical variables in a two-way table of counts is the distribution of values of that variable among all individuals described by the table. • It’s the distribution of each category alone.
Percentages • Often are more informative • Used when comparing groups of different sizes.
Find the percent of young adults who they there is a good chance they will be rich.
Find the marginal distribution (in %) of opinions. Make a graph to display the marginal distribution.
Find the marginal distribution (in %) of gender. Make a graph to display the marginal distribution.
Conditional Distribution • It describes the values of that variable among individuals who have a specific value of another variable. • To describe the relationship between the two categorical variables
Conditional Distribution of young women and men and their opinion.
Did we look at the right conditional distribution? • Our goal was to analyze the relationship between gender and opinion about chances of becoming rich for these young adults.
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.
State • What is the relationship between gender and responses to the question “What do you think are the chances you will have much more than a middle-class income at age 30?”
Plan • We suspect that gender might influence a young adult’s opinion about the chance of getting rich. So we’ll compare the conditional distributions of response for men alone and for women alone.
Do • We’ll make a side-by side bar graph to compare the opinions of males and females. • I could have used a segmented as well!
Conclude • Based on the sample data, men seem somewhat more optimistic about their future income than women. Men were less likely to say that they have “some chance but probably no” than women (11.6% vs 18.0%). Men were more likely to say that they have a “good chance” (30.8% vs 28.0%) aor alre “almost certain” (24.3% vs 20.5%) to have much more than a middle-class income by age 30 than women were.
Association • We say there is an association between two variables if specific values of one variable tend to occur in common with specific values of the other. • Be careful though….even a strong association between two categorical variables can be influenced by other variables lurking in the background.
Simpson’s Paradox • An association between two variables that holds for each individual value of a thrid variable can be changed or even reversed when the data for all values of the third variable are combined. This reversal is called Simpson’s paradox.
Accident victims are sometimes taken by helicopter from the accident scene to a hospital. Helicopters save taim. Do they also save lives? 32% of helicopter patients died, but only 24% of the others did. This seems discouraging!
Homework • Page 24 • (19, 21, 23, 24, 25, 27-32, 33, 35, 36)
