Question 1.1

Question 1.2

Question 1.3

Question 1.4

Question 1.5

Question 1.6

Question 1.7

Question 1.8

Question 1.9

Question 1.10

Question 1.11

Question 1.12

Question 1.13

In statistics, it is important to pay close attention to language. The following statements are wrong but can be corrected by substituting one word or phrase. For example, the sentence “Only correlational studies can tell us something about causality” could be corrected by changing “correlational studies” to “experiments.” Identify the incorrect word or phrase in each of the following statements and supply the correct word.

1. In a study on exam preparation, every participant had an equal chance of being assigned to study alone or with a group. This was a correlational study.

2. A psychologist was interested in studying the effects of the dependent variable of caffeine on hours of sleep, and she used a scale measure for sleep.

3. A university assessed the reliability of a commonly used scale—a mathematics placement test—to determine if it were truly measuring math ability.

4. In a within-groups experiment on calcium and osteoporosis, participants were assigned to one of two levels of the independent variable: no change in diet or supplementing the diet with calcium.

Question 1.14

The following statements are wrong but can be corrected by substituting one word or phrase. (See the instructions in Exercise 1.13.) Identify the incorrect word or phrase in each of the following statements and supply the correct word.

1. A researcher examined the effect of the ordinal variable “gender” on the scale variable “hours of reality television watched per week.”

2. A psychologist used a between-groups design to study the effects of an independent variable—a workout video—on the dependent variable—the weight—of a group of undergraduate students before and after viewing the video.

3. In a study on the effects of the confounding variable of noise level on the dependent variable of memory, researchers were concerned that the memory measure was not valid.

4. A researcher studied a population of 20 rats to determine whether changes in exposure to light would lead to changes in the dependent variable of amount of sleep.

Question 1.15

When John Snow investigated the 1854 outbreak of cholera in London, he paid particular attention to outliers.

1. What is an outlier?

2. What are potential benefits of outlier analysis?

Question 1.16

Question 1.17

Question 1.18

A researcher studies the average distance that 130 people living in U.S. urban areas walk each week.

1. What is the size of the sample?

2. Identify the population.

3. Is this “average” a descriptive statistic or an inferential statistic if it is used to describe the 130 people studied?

4. How might you operationalize the average distance walked in 1 week as an ordinal measure?

5. How might you operationalize the average distance walked in 1 week as a scale measure?

Question 1.19

As they leave a popular grocery store, 73 people are stopped and the number of fruit and vegetable items they purchased is counted.

1. What is the size of the sample?

2. Identify the population.

3. Is this number of items counted as a descriptive statistic or an inferential statistic if it is used to estimate the diets of all shoppers?

4. How might you operationalize the amount of fruit and vegetable items purchased as a nominal measure?

5. How might you operationalize the amount of fruit and vegetable items purchased as an ordinal measure?

6. How might you operationalize the amount of fruit and vegetable items purchased as a scale measure?

Question 1.20

Question 1.21

A researcher might be interested in evaluating how a person’s physical and emotional distance from Manhattan at the time of the 9/11 terrorist attacks relates to the accuracy of memory about the event.

1. Identify the independent variables and the dependent variable.

2. Imagine that physical distance is assessed as within 100 miles or beyond 100 miles; also, imagine that emotional distance is assessed as knowing no one who was affected, knowing people who were affected but lived, and knowing someone who died in the attacks. How many levels do the independent variables have?

3. How might you operationalize the dependent variable, accuracy of memory about the event?

Question 1.22

A study of the effects of skin tone (light, medium, and dark) on the severity of facial wrinkles in middle age might be of interest to cosmetic surgeons.

1. What would the independent variable be in this study?

2. What would the dependent variable be in this study?

3. How many levels would the independent variable have?

Question 1.23

Question 1.24

Question 1.25

Average weights in the United States: The CDC reported very large weight increases for U.S. residents of both genders and all age groups over the past four decades. Go to the Web site that reports these data (http://www.cdc.gov) and search for the article titled “Americans Slightly Taller, Much Heavier Than Four Decades Ago.”

1. What were the average weights of 10-year-old girls in 1963 and in 2002?

2. Do you think the CDC weighed every girl in the United States to get these averages? Why would this not be feasible?

3. How does the average weight of 10-year-old girls in 2002 or the average weight of 10-year-old boys in 1963 represent both a descriptive and an inferential statistic?

Question 1.26

Sample versus population in Norway: The Nord-Trøndelag health study surveyed more than 60,000 people in a Norwegian county and reported that gastrointestinal symptoms, depression, and anxiety disorders are strongly related (Haug, Mykletun, & Dahl, 2002).

1. What is the sample used by these researchers?

2. What is the population to which the researchers would like to extend their findings?

Question 1.27

Types of variables and Olympic swimming: At the 2012 London Summer Olympics, American Michael Phelps won four gold medals, bringing his overall Olympic career total to 18 gold medals, the all-time career record for Olympic gold medals in any sport. One of the events he won was the 100-meter butterfly. For each of the following examples, identify the type of variable—nominal, ordinal, or scale.

1. Phelps of the United States came in first, and Chad le Clos of South Africa and Evgeny Korotyshkin of Russia tied for second place.

2. Phelps finished in 51.21 seconds, and le Clos and Korotyshkin finished in 51.44 seconds.

3. One might examine the hemisphere from which swimmers hailed. Phelps and Korotyshki live in the Northern Hemisphere, whereas le Clos lives in the Southern Hemisphere.

Question 1.28

Types of variables and the Kentucky Derby: The Kentucky Derby is perhaps the premier event in U.S. horse racing. For each of the following examples from the derby, identify the type of variable—nominal, ordinal, or scale.

1. As racing fans, we would be very interested in the variable finishing position. A horse called Orb won in 2013, followed by Golden Soul in second and Revolutionary in third.

2. We also might be interested in the variable finishing time. Orb won in 2 minutes, 2.89 seconds.

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3. Derby attendance was 151,616 in 2013, not as high as the record-setting 165,307 people who attended in 2012.

4. If we were the betting type, we might examine the variable payoffs. For each $2.00 bet on Orb, a gambler won $12.80.

5. We might be interested in the history of the Derby and the demographic variables of jockeys, such as gender or race. For example, in the first 28 runnings of the Kentucky Derby, 15 of the winning jockeys were African American.

6. In the luxury boxes, high fashion reigns; we might be curious about the variable hat wearing, observing how many women wear hats and how many do not.

Question 1.29

Discrete versus continuous variables: For each of the following examples, state whether the scale variable is discrete or continuous.

1. The capacity, in terms of songs, of an iPod

2. The playing time of an individual song

3. The cost in cents to download a song legally

4. The number of posted reviews that a CD has on Amazon.com

5. The weight of an MP3 player

Question 1.30

Reliability and validity: Go online and take the personality test found at http://www.outofservice.com/ starwars. This test assesses your personality in terms of the characters from the original Star Wars series. (You may have to scroll down to get to the questions.)

1. What does it mean for a test to be reliable? Take the test a second time. Does it seem to be reliable?

2. What does it mean for a test to be valid? Does this test seem to be valid? Explain.

3. The test asks a number of demographic questions at the end, including “In what country did you spend most of your youth?” Can you think of a hypothesis that might have led the developers of this Web site to ask this question?

4. For your hypothesis in part (c), identify the independent and dependent variables.

Question 1.31

Reliability, validity, and wine ratings: You may have been in a wine store and wondered just how useful those posted wine ratings are. (They are usually rated on a scale from 50 to 100, with 100 being the top score.) After all, aren’t ratings subjective? Corsi and Ashenfelter (2001) studied whether wine experts are consistent. Knowing that the weather is the best predictor of price, the researchers wondered how well weather predicted experts’ ratings. The variables used for weather included temperature and rainfall, and the variable used for wine experts’ ratings was the number they assigned to each wine.

1. Name one independent variable. What type of variable is it? Is it discrete or continuous?

2. Name the dependent variable. What type of variable is it? Is it discrete or continuous?

3. How does this study reflect the concept of reliability?

4. Let’s say that you frequently drink wine that has been rated highly by Robert Parker, one of this study’s wine experts. His ratings were determined to be reliable, and you find that you usually agree with Parker. How does this observation reflect the concept of validity?

Question 1.32

Operationalizing variables and rap statistics: The Web site Rap Genius analyzes rap music using what they call RapMetrics (http://rapgenius.com/posts/63-Introducing-rapmetricstm-the-birth-of-statistical-analysis-of-rap-lyrics). It has developed a measure called rhyme density, which is the proportion of all syllables that are part of the rhyme. Eminem’s Without Me, for example, has a rhyme density of 0.49 (49%) because almost half of the lyrics are part of the rhyme, whereas Notorious B.I.G.’s Juicy only has a rhyme density of 0.23 (23%). The people behind Rap Genius say, “Over the course of a career, the rappers with the highest rhyme densities are basically the best technical rappers.”

1. How does Rap Genius operationalize the best rapper?

2. List at least three other variables that might be considered in determining the best rapper.

3. Across all songs, MF Doom came in first with an overall rhyme density of 0.44, and Cam’ron came in second with a rhyme density of 0.41. What kind of variable is the ranking, and what kind of variable is the rhyme density?

4. Rap Genius summarized its rhyme density discussion by saying: “MF Doom surprised us a little. First the big New Yorker profile and now this…it’s too much! Cam’ron is much more culturally relevant and interesting (plus he doesn’t need to wear a mask, he’s naturally silly), so we at RapMetrics™ consider him the G.O.A.T. (greatest of all time) MC [rapper] overall.” Rap Genius, therefore, changed its operational definition a bit. What has it added to its operational definition of the overall G.O.A.T. MC?

Question 1.33

Identifying and operationalizing variables: For each of the following hypotheses, identify the independent variable and the most likely levels of that independent variable. Then identify the likely dependent variable and a likely way to operationalize that dependent variable. Be specific.

1. Teenagers are better at video games, on average, than are adults in their 30s.

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2. Spanking children tends to lead them to be more violent.

3. Weight Watchers leads to more weight loss, on average, for people who go to meetings than for those who only participate online.

4. Students do better in statistics, on average, if they study with other people than if they study alone.

5. Drinking caffeinated beverages with dinner tends to make it harder to get to sleep.

Question 1.34

Between-groups versus within-groups and exercise: Noting marked increases in weight across the population, researchers, nutritionists, and physicians have struggled to find ways to stem the tide of obesity in many Western countries. They have advocated a number of exercise programs, and there has been a flurry of research to determine the effectiveness of these programs. Pretend that you are in charge of a research study to examine the effects of an exercise program on weight loss in comparison with a program that does not involve exercise.

1. Describe how you could study the exercise program using a between-groups research design.

2. Describe how you could study the exercise program using a within-groups design.

3. What is a potential confound of a within-groups design?

Question 1.35

Correlational research and smoking: For decades, researchers, politicians, and tobacco company executives debated the relation between smoking and health problems such as cancer.

1. Why was this research necessarily correlational in nature?

2. What confounding variables might make it difficult to isolate the health effects of smoking tobacco?

3. How might the nature of this research and these confounds buy time for the tobacco industry with regard to acknowledging the hazardous effects of smoking?

4. All ethics aside, how could you study the relation between smoking and health problems using a between-groups experiment?

Question 1.36

Experimental versus correlational research and culture: A researcher interested in the cultural values of individualistic and collectivist societies collects data on the rate of relationship conflict experienced by 32 people who test high for individualism and 37 people who test high for collectivism.

1. Is this research experimental or correlational? Explain.

2. What is the sample?

3. Write a possible hypothesis for this researcher.

4. How might we operationalize relationship conflict?

Question 1.37

Experimental versus correlational research and recycling: A researcher wants to know if people’s concerns about the environment vary as a function of incentives provided for recycling. Students living on a university campus are recruited to participate in a study. Some students are randomly assigned to a group in which they are rewarded financially for their recycling efforts for one month. The other students are randomly assigned to a group in which they are assessed a fine that is based on the amount of material that they could have, but did not, recycle.

1. Is this research experimental or correlational? Explain.

2. Write a hypothesis for this researcher.

Question 1.38

Outliers, exercise, and weight gain: Imagine that you conducted the study described in Exercise 1.34 and that one person had gained many, many pounds while in the exercise program.

1. Why would this individual be considered an outlier?

2. Explain why outlier analysis might be useful in this situation.

3. What kinds of things are we looking for in an outlier analysis?

Question 1.39

Outliers and response time: Imagine that a researcher is measuring the time it takes participants to identify whether a string of letters constitutes a word (e.g., duke) or a nonword (e.g., dake). She measures the response time of 40 participants. She finds that most participants took from ½ to 1 second to make their decision but that one participant took 3 minutes to make a decision.

1. Why would the participant who took 3 minutes be considered an outlier?

2. What kinds of things might the researcher look for in an outlier analysis of this situation?

Question 1.40

Romantic relationships: Goodman and Greaves (2010) reported findings from the Millennium Cohort Study, a large research project in the United Kingdom. They stated that “while it is true that cohabiting parents are more likely to split up than married ones, there is very little evidence to suggest that this is due to a causal effect of marriage. Instead, it seems simply that different sorts of people choose to get married and have children, rather than to have children as a cohabiting couple, and that those relationships with the best prospects of lasting are the ones that are most likely to lead to marriage” (p. 1).

1. What is the sample in this study?

2. What is the likely population?

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3. Is this a correlational study or an experiment? Explain.

4. What is the independent variable?

5. What is the dependent variable?

6. What is one possible confounding variable? Suggest at least one way in which the confounding variable might be operationalized.

Question 1.41

Experiments, HIV, and cholera: Several studies have documented the susceptibility of people who are HIV-positive to cholera, likely because of weakened immune systems. Researchers in Mozambique (Lucas et al., 2005), a country where an estimated 20% to 30% of the population is HIV-positive, wondered whether an oral vaccine for cholera would work among people who are HIV-positive. Cholera immunization was administered to 14,000 people in Mozambique who tested positive for HIV. Soon thereafter, an epidemic of cholera spread through the region, giving the researchers an opportunity to test their hypothesis.

1. Describe a way in which the researchers could have conducted an experiment to examine the effectiveness of the cholera vaccine among people who are HIV-positive.

2. If the researchers did conduct an experiment, would this have been a between-groups or a within-groups experiment? Explain.

3. The researchers did not randomly assign participants to vaccine or no-vaccine conditions; rather, they conducted a general mass immunization. Why does this limit their ability to draw causal conclusions? Include at least one possible confounding variable.

4. The researchers did not use random assignment when conducting this study. List at least one practical reason and at least one ethical reason that they might not have used random assignment.

Question 1.42

Ability and wages: Arcidiacono, Bayer, and Hizmo (2008) analyzed data from a national longitudinal survey called NLSY79, which includes data from over 12,000 men and women in the United States who were in the 14- to 22-year age range in 1979. The researchers reported that ability is related to wages in early career jobs for university graduates but not for high school graduates. In line with this, research has found that racial discrimination with respect to wages is more prevalent against high school graduates than college graduates, because when ability is not the primary reason for determining wages, other irrelevant factors, such as race, play in. The researchers suggest that their findings might explain why, on average, a black person is more likely to earn a college degree than is a white person of the same ability level.

1. List any independent variables.

2. List any dependent variables.

3. What is the sample in this study?

4. What is the population about which researchers want to draw conclusions?

5. What do the authors mean by “longitudinal” in this study?

6. The researchers used the Armed Forces Qualification Test (AFQT) as their measure of ability. The AFQT combines scores on word knowledge, paragraph comprehension, arithmetic reasoning, and mathematics knowledge subscales. Can you suggest at least one confounding variable in the relation between ability and wages when comparing college graduates to high school graduates?

7. Suggest at least two other ways in which the researchers might have operationalized ability.

Question 1.43

Assessing charitable organizations: Many people do research on charitable organizations before deciding where to donate their money. Tina Rosenberg (2012) reported that traditionally many people have used sources such as Charity Navigator or the Better Business Bureau’s Web sites. Both of these sites rate organizations more highly if the organizations use less of their donation money for fundraising or administration and more of it for the cause they are supporting. On Charity Navigator, for example, Doctors Without Borders, a nonprofit focused on health and medical needs, gets a rating of 57.11 out of 70 based on its financial practices, accountability, and transparency; this puts that organization in the second of Charity Navigator’s five tiers (http://www.charitynavigator.org/).

1. How does Charity Navigator operationalize a good charity?

2. What kind of variable is the score of 57.11 out of 70, nominal, ordinal, or scale? Explain your answer.

3. What kind of variable is the tier, second out of five—nominal, ordinal, or scale? Explain your answer.

4. There are many types of charities. Doctors Without Borders focuses on health and medical needs. What kind of variable is its type of charity—nominal, ordinal, or scale? Explain your answer.

5. According to Rosenberg (2012), Toby Ord, a moral philosopher from Oxford University, thinks the traditional operational definition of what constitutes a good charity is too limited. He has five criteria that he sees as important for a good charity: It targets the most serious problems (disease over art, for example). It uses evidence-based practices. It uses cost-effective interventions. It is competent and honest. And it “can make good use of each additional dollar.” Ord touts an organization called GiveWell as a source for ratings that incorporates many of his criteria (http://www.givewell.org/). Doctors Without Borders fares less well on GiveWell; the site reports: “We believe that the overall cost-effectiveness of [Doctors Without Borders’] activities are unlikely to compare well with those of our top charities.” Explain why Web sites like Charity Navigator might look just at measures relating to finances, as opposed to a fuller definition such as that described by Ord.

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6. Which is more likely to be reliable, the rating by Charity Navigator or the verdict by GiveWell? Explain your answer.

7. Which is more likely to be valid, the rating by Charity Navigator or the verdict by GiveWell? Explain your answer.

8. If you were to monitor whether increased donation funds led to a lower death rate in a country, would that be an experiment or a correlational study? Explain your answer.

9. If you were to randomly assign some regions to receive more donation funds and other regions to receive fewer, and then track the death rate in both sets of regions, would that be an experiment or a correlational study? Explain your answer.