14.12: Exercises

Correlations

■ 1. Refer to the exercise in an earlier chapter about Lady Theresa.

Analyzing the data from the laboratory, you discover a statistically significant correlation between when Lady Theresa gets the right answer on the card tests and when she twitches her right hand. What do you recommend doing to determine, whether a statistically significant correlation holds the other way around—that is, between her right hand twitching and her getting the right answer on those card tests?

■ 2. If increases in the percentage of citizens in jail is caused by decreases in income among the citizenry, among other things, what can you say about the correlation between the citizens' income and the citizens' criminal convictions?

a. It is positive.
b. It is negative.

3. Create an original, nontrivial multiple-choice question, with answer, that requires an understanding of the notion of correlation of two discrete variables.

■ 4. How strong is the correlation mentioned in this passage? Comment also on any causal inferences.

The Surgeon General has determined that breathing is dangerous to our health. This conclusion was drawn from a survey of 100 prisoners in a New York prison who have died within the past five years. All were habitual breathers. A strong correlation; take heed and watch your breathing.

5. Barometers measure air pressure. When the air pressure is low, air from farther away rushes in to restore the imbalance. This new air is likely to bring with it new weather, especially rain. So, the height of mercury in an outside barometer is

a. positively correlated
b. negatively correlated
c. not correlated

with the probability of rain (in the vicinity of the barometer).

6. State something that, in the summer in mountainous states, is positively correlated with the amount of the previous winter's snowfall.

Identifying Causal Claims

1. Which phrase below is least likely to be used to say that A causes B?

a. A leads to B.
b. B is caused by A.
c. A makes B happen.
d. A occurs with B.
e. A produces B.
f. B is affected by A

■ 2. Rewrite the following causal claim using the word cause or causes explicitly.

Whenever the sun sets, it gets dark.

3. In an exercise in an earlier chapter, you are asked to analyze the conversation between Lesley and Rico about a measles vaccine. Identify the causal claim that they inferred from the finding that 1 out of 622 children receiving the vaccine had gotten measles within the next seven months.

■ 4. Which of the following sentences contain causal claims, and which contain merely correlational claims?

a. Money makes you happy.
b. Sniffing ragweed pollen triggers the creation of histamine in the blood of allergy sufferers.
c. It therefore is the case that lack of education is partly to blame for crime, at least in the United States if not necessarily elsewhere.
d. Putting an infant on a feeding schedule would probably make it cry until its feeding time.
e. The data on the height of corn are associated with the amount of water the corn gets during its growing season.
f. Adding water to corn plants usually leads to taller growth.
g. There are more smokers among Japanese-born Canadians than among other Canadians.

■ 5. David claims that there is a link between smoking and sugar consumption. He says he has noticed that people who avoid the sugar jar when offered a cup of coffee also are more apt to be a smoker than someone who does dip into the jar. If so, Davis is likely to have uncovered

a. a positive correlation
b. a negative correlation
c. a non-standard transverse Kurzweil correlation

■ 6. Following are three causal claims. Which claim is a specific, rather than general causal claim?

a. John Jameson stabbed her with his own kitchen knife.
b. PEOPLE kill people; bullets don't.
c. Anyone who drinks a cup of gasoline will get very sick.

7. Label the following passages:

i. Statistics reported by the Ugandan ministry of police establish that a person's age makes the person more susceptible to being mugged.

a. only an association
b. causal
c. ambiguous

ii. Our study has now uncovered a link between people's religion and their faith in the stability of their economy.

a. only an association
b. causal
c. ambiguous

iii. Medical doctors believe that high sugar consumption is associated with weight gain in rats and mice.

a. only an association
b. causal
c. ambiguous

iv. Medical doctors believe that having diarrhea is associated with eating too much licorice.

a. only an association
b. causal
c. ambiguous

v. Medical doctors now believe that eating too much licorice is associated with diarrhea.

a. only an association
b. causal
c. ambiguous

9. What causal claim is the speaker, Huckleberry Finn, making in the following quotation?

I’ve always reckoned that looking at the new moon over your left shoulder is one of the carelessest and foolishest things a body can do. Old Hank Bunker done it once, and bragged about it; and in less than two years he got drunk and fell off of the shot tower, and spread himself out so that he was just a kind of a layer, as you may say; and they slid him edgeways between two barn doors for a coffin, and buried him so, so they say, but I didn't see it. Pap told me. But anyway it all come of looking at the moon that way, like a fool."

a. Looking at the new moon over your left shoulder causes most cases of drunkenness.
b. Drunkenness causes looking at the new moon.
c. Carelessness or drunkenness on the shot tower was stupid.
d. Looking at the new moon over his left shoulder caused Bunker to die.

Inferring from Correlation to Cause

■ 1. If scientific studies were to show that 80 percent of juvenile delinquents are from homes under the poverty line, could being from a home under the poverty line be a determinate cause of juvenile delinquency? Why?

■ 2. If there is a causal connection between two variables, then there must be a positive correlation between them.

a. true
b. false

3. Given that you have observed a correlation between A and B and have noticed that A doesn't occur after B, you then need to consider whether A causes B. Which one of the following would be the worst methodology to adopt to find out?

a. Look to see whether the causal connection between A and B can be deduced from other acceptable theories.
b. Try to eliminate alternative hypotheses about the connection between A and B by running tests on those hypotheses.
c. Consider whether some third factor C is causing A and also causing B.
d. Check to see whether the probability of A equals the probability of B.

■ 4. The following comment was made as a joke, but if it were made seriously, what would be wrong with it?

All muskrats walk single file; at least the only one I ever saw did.

5. Explain why the correlation between monthly ice cream revenues in New York City and monthly revenues in Utah from snow ski rentals is spurious. Be specific; don't merely restate the definition of spurious.

■ 6. The stronger a correlation between two variables...

a. the more likely there is
b. the less likely there is
c. still does not affect the probability of

... a causal connection between them

■ 7. The "scientific method" is the method of guessing possible explanations of interesting phenomena of nature and attempting to refute them by running experiments or making observations.

a. more or less true
b. clearly false

■ 8. Dr. Thomas Pyne has noticed a correlation between the color of the chairs in his college classrooms and the handedness of the chairs. The chairs for left-handers are always black, never the bright colors of the other chairs. What is most likely to be correct about the situation?

a. The color of the chair is causing its handedness.
b. The handedness of the chair causes it to receive the paint color it does.
c. Decisions by chair manufacturers affect paint manufacturing, often causing paint supplies to run out of all colors except black.
d. The correlation does not cohere with our background knowledge.

9. Write an essay about a significant piece of scientific research that uncovers a correlation and then tries to establish a causal connection. Begin by describing the research and its results in your own words. Use a footnote to indicate the source of your information. Then show how various points made in this chapter apply to the research. The essay should contain at least four of the terms from the glossary at the end of this chapter.

10. Write an essay that describes an experiment you yourself designed and ran in order to test the significance of a suspected correlation. The correlation need not have great social or scientific importance. Within your essay, argue for why your test does establish that the correlation is or is not significant.

11. What is the name of the fallacy that is committed in this reasoning?

I have noticed a pattern about all the basketball games I've been to this year. Every time I buy a good seat, our team wins. Every time I buy a cheap, bad seat, we lose. My buying a good seat must somehow be causing those wins.

Explanations

1. Write an essay explaining one of the following:

How to torpedo a non-money bill in the state legislature before it reaches the floor for a vote. Audience: fellow lobbyists.

How the game of basketball has changed since its creation. Audience: college physical education majors.

How to build a fireplace in a new house. Audience: homeowners.

Why World War I was not won by the Germans. Audience: high school seniors in a history class.

How a refrigerator refrigerates. Audience: high school science class at the sophomore level.

How to get shelf space in U.S. supermarkets for the new cereal your company is planning to manufacture. Audience: your manager.

■ 2. Which comment below most accurately characterizes the following letter to the editor:

Dear Editor:

You smeared the public relations trade in your editorial when you said, "If Ollie North is lying to the U.S. Senate, he's lying very well, which would make him a highly excellent PR guy." This is a terrible indictment!

In my eighteen years as a public relations consultant, working on some very controversial issues, I have never found it necessary to lie on behalf of a client, nor have I ever been asked to. Lying is not an important criterion for becoming an "excellent PR guy."

a. The writer believes most public relations people do lie to help their clients.
b. The writer is appealing to anecdotal evidence.
c. The writer believes that lying for one's client usually causes bad public relations for that client.
d. The writer is committing the black-white fallacy.
e. The writer is committing the straw man fallacy.

3. What is the main principle of good explanation construction that is violated in this explanation?

Reporter: Why do you suppose that National Football Conference teams always win the Super Bowl, and the American Football Conference teams always lose?

Coach: I think it has something to do with the caliber of the teams in each conference. The AFC teams such as the Buffalo Bills just aren't as good as the Redskins and Giants of the NFC.

a. The explanation is supposed to fit the facts to be explained and not conflict with other facts.
b. A good explanation doesn't just rephrase what it is trying to explain.
c. Good explanations will explain something in terms of something else that we can understand to be relevant.
d. Good explanations will explain something unfamiliar in terms of something familiar.
e. Explanations should be consistent with well-established results except in extraordinary cases.

4. Discuss the pros and cons of the explanation in this letter to the editor. Begin by clearly identifying the explanation—that is, by saying what is being used to explain what.

There is an evil current running throughout history. People haven't been nice to each other. Take a look most recently at Nazism in Germany and Stalinism in the Soviet Union. Look at all the cases of demon possession in the files of the Catholic Church. It's time for your readers to wake up to the fact that the Devil is at work.

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Solutions

Correlations

1 You need to do nothing. If A is correlated with B, then B must be correlated with A.

2 Answer (b).

4 Would you find less death if you looked at nonbreathers? There is no significant correlation. This passage is a variation on a joke by Howard Kahane, Logic and Contemporary Rhetoric: The Use of Reason in Everyday Life, 4th ed. (Wadsworth, 1984), p. 111.

Identifying Causal Claims

2 The setting of the sun causes darkness.

4 a. causal
b. causal
c. causal
d. causal
e. correlational
f. causal
g. correlational

5 The more apt a person is to consume sugar the LESS apt the person is to be a coffee drinker. A group with many coffee drinkers would be a group with relatively fewer sugar consumers. So, this is a negative correlation.

6 Answer (a). It makes a specific causal claim rather than a general one.

Inferring from Correlation to Cause

1 To be a determinate cause, the statistic would have to be 100%, not 80%.

2 Answer (b). Why couldn’t it be negative?

4 First, by making a universal generalization from just one example, the speaker is committing the fallacy of hasty generalization. In addition, there is no file at all if there is just one member of the file. If you noticed that one muskrat cannot walk single file, then you realized that the generalization is an inconsistent remark. By the principle of charity, you might consider assuming that the one muskrat was walking single file with other non-muskrats; however, this assumption probably violates the principle of fidelity because it lessens the impact of the original joke and because there is no other indication that any other animals were observed. The joke was told to the author by Robert Garmston.

6 Answer (a).

7 Answer (a). This description of the scientific method as being the method of conjectures and refutations was first clearly stated by Karl Popper.

8 Answer (b). Some manufacturer has probably decided to paint all the left-handed chairs black. The chair’s being black is caused in part by its being left-handed and caused in part by the painter in the plant following the manufacturer’s decision.

Explanations

2 Answer (b). The anecdotal evidence is his own experience. It is true that most PR people are not primarily liars, although they are experts at shaping a sentence so that it emphasizes the good aspects of the client’s product and the bad aspects of the opponent’s.