Deck 12: Relationships Between Categorical Variables

Question 1

For Questions use the following narrative
Narrative: Aspirin and polyps
A study done by the Ohio State University Medical Center examined whether or not taking an aspirin a day would help colon cancer patients reduce the chance of getting subsequent colon polyps.635 patients with colon cancer participated; 317 of them were randomly assigned to the aspirin group, and the other 318 patients were assigned to a placebo (non-aspirin) group.54 patients in the aspirin group developed subsequent polyps, compared to 86 patients in the non-aspirin group.Many confounding variables were controlled for in this well-designed randomized experiment.
{Aspirin and polyps narrative} What is the relative risk of developing polyps for colon cancer patients who don't take an aspirin a day (compared to those who do)? Interpret your answer.

Answer 1

1.59.The risk of developing subsequent polyps is 1.59 times greater for patients who do not take an aspirin a day, compared to those that do.

Question 2

For Questions , use the following narrative
Narrative: Genetic defect
Suppose a population contains 100,000 individuals, of which 500 are carriers of a certain genetic defect.
{Genetic defect narrative}Which of the following is an appropriate way to express this result in terms of odds?

A)The odds of carrying the genetic defect are 5 to 995.
B)The odds of carrying the genetic defect are 500 out of 100,000.
C)The odds of carrying the genetic defect are 500 to 1.
D)None of the above

Answer 2

The odds of carrying the genetic defect are 5 to 995.

Question 3

Which of the following is not one of the basic ways to express the chances that a randomly selected individual will fall into a particular category for a categorical variable?

A)The proportion of the total that falls into that group.
B)The percentage of the total that falls into that group.
C)Comparing one category to another category in the form of relative odds.
D)All of the above are appropriate.

Answer 3

All of the above are appropriate.

Question 4

For Questions , use the following narrative
Narrative: Aspirin and polyps
A study done by the Ohio State University Medical Center examined whether or not taking an aspirin a day would help colon cancer patients reduce the chance of getting subsequent colon polyps.635 patients with colon cancer participated; 317 of them were randomly assigned to the aspirin group, and the other 318 patients were assigned to a placebo (non-aspirin) group.54 patients in the aspirin group developed subsequent polyps, compared to 86 patients in the non-aspirin group.Many confounding variables were controlled for in this well-designed randomized experiment.
{Aspirin and polyps narrative} What percentage of all the patients in this study developed subsequent polyps?

A)140/635 = 22%
B)54/140 = 39%
C)140/495 = 28%
D)None of the above.

Question 5

When there is a treatment or behavior for which researchers want to study risk, they often compare it to the __________ risk, which is the risk without the treatment or behavior.

Question 6

A table that displays the number of individuals who fall into each combination of categorical variables is called a(n) __________ table.

Question 7

For Questions , use the following narrative
Narrative: Aspirin and polyps
A study done by the Ohio State University Medical Center examined whether or not taking an aspirin a day would help colon cancer patients reduce the chance of getting subsequent colon polyps.635 patients with colon cancer participated; 317 of them were randomly assigned to the aspirin group, and the other 318 patients were assigned to a placebo (non-aspirin) group.54 patients in the aspirin group developed subsequent polyps, compared to 86 patients in the non-aspirin group.Many confounding variables were controlled for in this well-designed randomized experiment.
{Aspirin and polyps narrative} Based on the results of this study, what can you conclude?

A)Taking an aspirin a day can help prevent subsequent polyps from developing in colon cancer patients.
B)Taking an aspirin a day has a causal effect on subsequent polyp development in colon cancer patients.
C)Taking an aspirin a day reduces the chances of developing subsequent polyps in colon cancer patients.
D)All of the above.

Question 8

For Questions , use the following narrative
Narrative: Aspirin and polyps
A study done by the Ohio State University Medical Center examined whether or not taking an aspirin a day would help colon cancer patients reduce the chance of getting subsequent colon polyps.635 patients with colon cancer participated; 317 of them were randomly assigned to the aspirin group, and the other 318 patients were assigned to a placebo (non-aspirin) group.54 patients in the aspirin group developed subsequent polyps, compared to 86 patients in the non-aspirin group.Many confounding variables were controlled for in this well-designed randomized experiment.
{Aspirin and polyps narrative} For colon cancer patients who take an aspirin a day, what is the expected rate for developing subsequent polyps?

A)Approximately 170 occurrences per 1,000 patients.
B)Approximately 54 occurrences per 635 patients.
C)Approximately 54 occurrences per 140 patients.
D)None of the above.

Question 9

For Questions use the following narrative
Narrative: Aspirin and polyps
A study done by the Ohio State University Medical Center examined whether or not taking an aspirin a day would help colon cancer patients reduce the chance of getting subsequent colon polyps.635 patients with colon cancer participated; 317 of them were randomly assigned to the aspirin group, and the other 318 patients were assigned to a placebo (non-aspirin) group.54 patients in the aspirin group developed subsequent polyps, compared to 86 patients in the non-aspirin group.Many confounding variables were controlled for in this well-designed randomized experiment.
{Aspirin and polyps narrative} What is the increased risk of developing polyps for colon cancer patients who don't take an aspirin a day? Interpret your answer.

Question 10

For Questions , use the following narrative
Narrative: Genetic defect
Suppose a population contains 100,000 individuals, of which 500 are carriers of a certain genetic defect.
{Genetic defect narrative}Which of the following is not an appropriate way to express this result as a portion of the total?

A)One half of one percent (0.5%) of all individuals in this population are carriers.
B)The proportion in this population who are carriers is 0.005.
C)The probability that a person randomly selected from this population is a carrier is 0.5%
D)All of the above are appropriate.

Question 11

When researchers report relative risks and/or odds ratios, they often adjust them to account for __________.

Question 12

For Questions use the following narrative
Narrative: Aspirin and polyps
A study done by the Ohio State University Medical Center examined whether or not taking an aspirin a day would help colon cancer patients reduce the chance of getting subsequent colon polyps.635 patients with colon cancer participated; 317 of them were randomly assigned to the aspirin group, and the other 318 patients were assigned to a placebo (non-aspirin) group.54 patients in the aspirin group developed subsequent polyps, compared to 86 patients in the non-aspirin group.Many confounding variables were controlled for in this well-designed randomized experiment.
{Aspirin and polyps narrative} What is the odds ratio of developing polyps for colon cancer patients who don't take an aspirin a day versus those that do?

Question 13

For Questions use the following narrative
Narrative: Aspirin and polyps
A study done by the Ohio State University Medical Center examined whether or not taking an aspirin a day would help colon cancer patients reduce the chance of getting subsequent colon polyps.635 patients with colon cancer participated; 317 of them were randomly assigned to the aspirin group, and the other 318 patients were assigned to a placebo (non-aspirin) group.54 patients in the aspirin group developed subsequent polyps, compared to 86 patients in the non-aspirin group.Many confounding variables were controlled for in this well-designed randomized experiment.
{Aspirin and polyps narrative} What are the odds of developing subsequent polyps for colon cancer patients who don't take an aspirin a day?

A)86 to 318
B)86 to 54
C)86 to 232
D)None of the above

Question 14

For Questions , use the following narrative
Narrative: Aspirin and polyps
A study done by the Ohio State University Medical Center examined whether or not taking an aspirin a day would help colon cancer patients reduce the chance of getting subsequent colon polyps.635 patients with colon cancer participated; 317 of them were randomly assigned to the aspirin group, and the other 318 patients were assigned to a placebo (non-aspirin) group.54 patients in the aspirin group developed subsequent polyps, compared to 86 patients in the non-aspirin group.Many confounding variables were controlled for in this well-designed randomized experiment.
{Aspirin and polyps narrative} Make a contingency table summarizing the data from this study, making the explanatory variable the row variable and the response variable the column variable.

Question 15

For Questions use the following narrative
Narrative: Aspirin and polyps
A study done by the Ohio State University Medical Center examined whether or not taking an aspirin a day would help colon cancer patients reduce the chance of getting subsequent colon polyps.635 patients with colon cancer participated; 317 of them were randomly assigned to the aspirin group, and the other 318 patients were assigned to a placebo (non-aspirin) group.54 patients in the aspirin group developed subsequent polyps, compared to 86 patients in the non-aspirin group.Many confounding variables were controlled for in this well-designed randomized experiment.
{Aspirin and polyps narrative} What is the baseline risk of developing subsequent polyps? Interpret your answer.

Question 16

Each row and column combination in a contingency table is called a(n) __________

Question 17

For Questions , use the following narrative
Narrative: Aspirin and polyps
A study done by the Ohio State University Medical Center examined whether or not taking an aspirin a day would help colon cancer patients reduce the chance of getting subsequent colon polyps.635 patients with colon cancer participated; 317 of them were randomly assigned to the aspirin group, and the other 318 patients were assigned to a placebo (non-aspirin) group.54 patients in the aspirin group developed subsequent polyps, compared to 86 patients in the non-aspirin group.Many confounding variables were controlled for in this well-designed randomized experiment.
{Aspirin and polyps narrative} Does taking aspirin appear to be related to the chance of developing subsequent polyps in colon cancer patients? Justify your answer using percentages.

Question 18

For Questions , use the following narrative
Narrative: Aspirin and polyps
A study done by the Ohio State University Medical Center examined whether or not taking an aspirin a day would help colon cancer patients reduce the chance of getting subsequent colon polyps.635 patients with colon cancer participated; 317 of them were randomly assigned to the aspirin group, and the other 318 patients were assigned to a placebo (non-aspirin) group.54 patients in the aspirin group developed subsequent polyps, compared to 86 patients in the non-aspirin group.Many confounding variables were controlled for in this well-designed randomized experiment.
{Aspirin and polyps narrative} What percentage of patients on the placebo did not develop subsequent polyps?

A)232/495 = 47%
B)232/318 = 73%
C)232/635 = 37%
D)None of the above.

Question 19

For Questions , use the following narrative
Narrative: Aspirin and polyps
A study done by the Ohio State University Medical Center examined whether or not taking an aspirin a day would help colon cancer patients reduce the chance of getting subsequent colon polyps.635 patients with colon cancer participated; 317 of them were randomly assigned to the aspirin group, and the other 318 patients were assigned to a placebo (non-aspirin) group.54 patients in the aspirin group developed subsequent polyps, compared to 86 patients in the non-aspirin group.Many confounding variables were controlled for in this well-designed randomized experiment.
{Aspirin and polyps narrative} How many cells will the contingency table have for the data presented by this study?

Question 20

For Questions , use the following narrative
Narrative: Aspirin and polyps
A study done by the Ohio State University Medical Center examined whether or not taking an aspirin a day would help colon cancer patients reduce the chance of getting subsequent colon polyps.635 patients with colon cancer participated; 317 of them were randomly assigned to the aspirin group, and the other 318 patients were assigned to a placebo (non-aspirin) group.54 patients in the aspirin group developed subsequent polyps, compared to 86 patients in the non-aspirin group.Many confounding variables were controlled for in this well-designed randomized experiment.
{Aspirin and polyps narrative} Which variable is the explanatory variable and which is the response variable in this study?

Question 21

Simpson's Paradox makes it clear that it is dangerous to __________ information across groups, especially if the subjects or experimental units were not __________ assigned to those groups.

Question 22

For Questions , use the following narrative
Narrative: Audition qualifications
Suppose an audition process requires applicants to first meet a series of qualifications before they can be accepted for an audition.Suppose 88% of the women met these qualifications, and 86% of the men met these qualifications.Also assume that there were 100 men and 100 women who applied.
{Audition qualifications narrative} What is the odds ratio for being accepted (versus rejected) for women compared to men?

Question 23

For Questions , use the following narrative
Narrative: Audition qualifications
Suppose an audition process requires applicants to first meet a series of qualifications before they can be accepted for an audition.Suppose 88% of the women met these qualifications, and 86% of the men met these qualifications.Also assume that there were 100 men and 100 women who applied.
{Audition qualifications narrative} What is the odds ratio for being accepted (versus rejected) for men compared to women?

Question 24

Suppose you hear a report that says the chances of developing lung cancer increase by 10 times, just by living in the city versus the country.How do you interpret this?

A)You had better move to the country; 10 times is a huge difference.
B)You need to find out what the baseline risk is and what confounding variables were adjusted for before you can determine how serious this is for you.
C)You should just stay put; no one could possibly come up with a valid statistic that measures this.
D)You should ignore the results.Your increased risk should depend on whether or not your house contains radon gas, not on whether the house is in the city or the country.

Question 25

For Questions , use the following narrative
Narrative: Blood clot risk
Suppose you hear on the news that sitting on an airplane for five hours or more without getting up and walking around increases your chances of developing blood clots by 10 times.
{Blood clot risk narrative} The baseline risk is missing.Explain what that means in terms of what conclusions you can make about the results.

Question 26

For Questions , use the following narrative
Narrative: Talent and gender
Suppose a talent contest is looking for people who can either sing or act.900 people tried out for the first round of auditions, 300 women and 600 men.Of the men who tried out, 55% of them were allowed to go on to the next round, compared to 42% of the women.However, if you break the data down by singing versus acting auditions, the relationship changes.For acting, 20% of the women made it through, compared to 15% of the men; for singing, 85% of the women made it through, compared to 75% of the men.
{Talent and gender narrative}What is the statistical phenomena that occurred in this situation?

A)A statistical error; these results cannot be correct.
B)Simpson's Paradox.
C)The Empirical Rule.
D)Selection Bias.

Question 27

One of the common ways the media misrepresent statistics about risk is that the reported risk is not necessarily your risk.What is the underlying problem that causes this?

A)Not establishing a causal link between the variables.
B)Confounding variables, which may differ for you and those in the study.
C)Unless you personally participated in the study, your personal risk cannot be calculated.
D)Since risks describe what proportion of the population will encounter a certain situation, they cannot be used to find any individual's chances of encountering that situation.

Question 28

When omitting a third variable masks the relationship between two categorical variables, this phenomenon is called __________.

Question 29

What does Simpson's Paradox teach us?

A)The nature of an association can reverse direction when data from several groups are combined to form a single group.
B)Omitting a third variable can mask the true relationship between two categorical variables.
C)It is dangerous to summarize information over groups, especially if the individuals were not randomly assigned to those groups.
D)All of the above.

Question 30

Suppose you are on a jury in a trial someday.How could you encounter Simpson's Paradox?

A)You could see data that were collected from two different studies, giving you two different results.
B)One side could present the data using two variables, and the other side could break the same data down by a third variable that reverses the direction of the results.
C)One side could use counts to summarize the data, and the other side could use percentages or rates, reversing the direction of the relationship.
D)All of the above.

Question 31

For Questions , use the following narrative
Narrative: Blood clot risk
Suppose you hear on the news that sitting on an airplane for five hours or more without getting up and walking around increases your chances of developing blood clots by 10 times.
{Blood clot risk narrative} Does this increased risk apply to anyone and everyone? Explain why or why not.

Question 32

For Questions , use the following narrative
Narrative: Blood clot risk
Suppose you hear on the news that sitting on an airplane for five hours or more without getting up and walking around increases your chances of developing blood clots by 10 times.
{Blood clot risk narrative} The timeline for the risk is not given.Explain what that means in terms of what conclusions you can make about the results.

Question 33

When you see a group of individuals summarized into a single contingency table containing only one row variable and one column variable, what should your reaction be?

A)Great; this data is clear and easy to understand.
B)I need to find out if the data have been collapsed over some important third variable.
C)This is garbage; there is always more to a statistical relationship than just two simple variables.
D)None of the above.

Question 34

Suppose a new medical study at a research university shows that a woman's chance of developing breast cancer triples if she is overweight.You know that the American Cancer Society says that the chance of a woman developing breast cancer in her lifetime is 1 in 9.Does being overweight now increase a woman's chance to 1 in 3 of developing breast cancer?

A)Yes; 1/9 × 3 = 1/3.
B)No; the baseline risk for women like the ones in this study may have been different from the American Cancer Society's lifetime risk.
C)No; unless a causal relationship is established, you should just ignore all risk statistics.
D)None of the above.

Question 35

For Questions , use the following narrative
Narrative: Audition qualifications
Suppose an audition process requires applicants to first meet a series of qualifications before they can be accepted for an audition.Suppose 88% of the women met these qualifications, and 86% of the men met these qualifications.Also assume that there were 100 men and 100 women who applied.
{Audition qualifications narrative} What is the selection ratio for men compared to women? Interpret your answer.

Question 36

For Questions , use the following narrative
Narrative: Talent and gender
Suppose a talent contest is looking for people who can either sing or act.900 people tried out for the first round of auditions, 300 women and 600 men.Of the men who tried out, 55% of them were allowed to go on to the next round, compared to 42% of the women.However, if you break the data down by singing versus acting auditions, the relationship changes.For acting, 20% of the women made it through, compared to 15% of the men; for singing, 85% of the women made it through, compared to 75% of the men.
{Talent and gender narrative}What do we call this phenomenon, and how could this have happened?