1. Comparitive Graphs

2. Two Way Table Describes two categorical variables.
One variable is shown in the rows and the other is in the columns.

3. Example of Two Way Table
Young adults by gender & chance of getting rich
Gender
Opinion
Female
Male
Total
Almost no chance 96 98
194
Some chance but probably not
426
286
712
A chance
696
720
1416
A godd chance
663
758
1421
Almost certain
486
597
1083
2367
2459
4826

4. 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

5. 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.

6. Percentages Often are more informative
Used when comparing groups of different sizes.

7. Young adults by gender & chance of getting rich
Find the percent of young adults who they there is a good chance they will be rich.
Young adults by gender & chance of getting rich
Gender
Opinion
Female
Male
Total
Almost no chance 96 98
194
Some chance but probably not
426
286
712
A chance
696
720
1416
A godd chance
663
758
1421
Almost certain
486
597
1083
2367
2459
4826

8. Young adults by gender & chance of getting rich
Find the marginal distribution (in %) of opinions. Make a graph to display the marginal distribution.
Young adults by gender & chance of getting rich
Gender
Opinion
Female
Male
Total
Almost no chance 96 98
194
Some chance but probably not
426
286
712
A chance
696
720
1416
A godd chance
663
758
1421
Almost certain
486
597
1083
2367
2459
4826

9. Response
Percent
Almost no chance
4.0%
Some chance but probably not
14.8%
A chance
29.3%
A good chance
29.4%
Almost certain
22.4%

10. Young adults by gender & chance of getting rich
Find the marginal distribution (in %) of gender. Make a graph to display the marginal distribution.
Young adults by gender & chance of getting rich
Gender
Opinion
Female
Male
Total
Almost no chance 96 98
194
Some chance but probably not
426
286
712
A chance
696
720
1416
A godd chance
663
758
1421
Almost certain
486
597
1083
2367
2459
4826

11. Response
Percent
Male
51%
Female
49%

12. 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

13. Conditional Distribution of young women and men and their opinion.
Young adults by gender & chance of getting rich
Gender
Opinion
Female
Male
Almost no chance 96 98
Some chance but probably not
426
286
A chance
696
720
A godd chance
663
758
Almost certain
486
597
Total
2367
2459

14. Segmented Bar Graph Response Women Men Almost no chance 4.1% 4%
Some chance but probably not
18.0%
11.6%
A chance
29.4%
29.3%
A good chance
28%
30.8%
Almost certain
20.5%
24.3%

15. 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.

16. 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.

17. 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?”

18. 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.
Response
Women
Men
Almost no chance
4.1% 4%
Some chance but probably not
18.0%
11.6%
A chance
29.4%
29.3%
A good chance
28%
30.8%
Almost certain
20.5%
24.3%

19. 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!

20. Side-by Side Comparative Bar Graph
Response
Women
Men
Almost no chance
4.1% 4%
Some chance but probably not
18.0%
11.6%
A chance
29.4%
29.3%
A good chance
28%
30.8%
Almost certain
20.5%
24.3%

21. 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.

22. 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.

23. 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.

24. Accident victims are sometimes taken by helicopter from the accident scene to a hospital. Helicopters save taim. Do they also save lives?
Helicopter
Road
Victim Died 64
260
Victim survived
136
840
Total
200
1100
32% of helicopter patients died, but only 24% of the others did. This seems discouraging!

25. Helicopter is sent mostly to serious accidents.
Helicopter
Road
Died 48 60
Survived 52 40
Total
100
Less Serious Accident
Helicopter
Road
Died 16
200
Survived 84
800
Total
100
1000

26. Titanic Disaster

27. Homework
Page 24
(19, 21, 23, 24, 25, 27-32, 33, 35, 36)