1. Warm-up An investigator wants to study the effectiveness of two surgical procedures to correct near-sightedness: Procedure A uses cuts from a scalpel and procedure B uses a laser. The data to be collected are the degrees of improvement in vision after the procedure is performed. Design an experiment for this.

2. Comparitive Graphs

3. Section 1.1 Creating and Interpreting Comparative Graphs After this section, you should be able to… CONSTRUCT and INTERPRET Comparative bar graphs CONSTRUCT and INTERPRET Segmented bar graphs CONSTRUCT and INTERPRET Two Way Tables CALCULATE & INTERPRET marginal and conditional distributions ORGANIZE statistical problems Learning Objectives

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

5. Example of Two Way Table Young adults by gender & chance of getting rich Gender OpinionFemaleMaleTotal Almost no chance9698194 Some chance but probably not426286712 A 50-50 chance6967201416 A godd chance6637581421 Almost certain4865971083 Total236724594826

6. 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

7. 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.

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

9. 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 OpinionFemaleMaleTotal Almost no chance9698194 Some chance but probably not426286712 A 50-50 chance6967201416 A godd chance6637581421 Almost certain4865971083 Total236724594826

10. Find the marginal distribution (in %) of opinions. Make a graph to display the marginal distribution. Young adults by gender & chance of getting rich Gender OpinionFemaleMaleTotal Almost no chance9698194 Some chance but probably not426286712 A 50-50 chance6967201416 A godd chance6637581421 Almost certain4865971083 Total236724594826

11. ResponsePercent Almost no chance4.0% Some chance but probably not14.8% A 50-50 chance29.3% A good chance29.4% Almost certain22.4%

12. Find the marginal distribution (in %) of gender. Make a graph to display the marginal distribution. Young adults by gender & chance of getting rich Gender OpinionFemaleMaleTotal Almost no chance9698194 Some chance but probably not426286712 A 50-50 chance6967201416 A godd chance6637581421 Almost certain4865971083 Total236724594826

13. ResponsePercent Male51% Female49%

14. 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

15. Conditional Distribution of young women and men and their opinion. Young adults by gender & chance of getting rich Gender OpinionFemaleMale Almost no chance9698 Some chance but probably not426286 A 50-50 chance696720 A godd chance663758 Almost certain486597 Total23672459

16. Side-by-Side Bar Graph ResponseWomenMen Almost no chance4.1%4% Some chance but probably not18.0%11.6% A 50-50 chance29.4%29.3% A good chance28%30.8% Almost certain20.5%24.3%

17. Segmented Bar Graph ResponseWomenMen Almost no chance4.1%4% Some chance but probably not18.0%11.6% A 50-50 chance29.4%29.3% A good chance28%30.8% Almost certain20.5%24.3%

18. 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. Hint: Does gender influence opinion or opinion influence gender? Since gender influences opinion, then we want to consider the conditional distribution of opinion for each gender.

19. 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.

20. 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?”

21. 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. ResponseWomenMen Almost no chance4.1%4% Some chance but probably not18.0%11.6% A 50-50 chance29.4%29.3% A good chance28%30.8% Almost certain20.5%24.3%

22. 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!

23. Side-by Side Comparative Bar Graph ResponseWomenMen Almost no chance4.1%4% Some chance but probably not18.0%11.6% A 50-50 chance29.4%29.3% A good chance28%30.8% Almost certain20.5%24.3%

24. Segmented Comparative Bar Graph ResponseWomenMen Almost no chance4.1%4% Some chance but probably not18.0%11.6% A 50-50 chance29.4%29.3% A good chance28%30.8% Almost certain20.5%24.3%

25. 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.

26. 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.

27. 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.

28. Accident victims are sometimes taken by helicopter from the accident scene to a hospital. Helicopters save taim. Do they also save lives? HelicopterRoad Victim Died64260 Victim survived136840 Total2001100 32% of helicopter patients died, but only 24% of the others did. This seems discouraging!

29. Helicopter is sent mostly to serious accidents. Serious Accident HelicopterRoad Died4860 Survived5240 Total100 Less Serious Accident HelicopterRoad Died16200 Survived84800 Total1001000

30. Titanic Disaster

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