Chapter 1 An Introduction to Statistics and Research Design / Statistics for the Behavioral Sciences 6th Edition 2024 Susan Nolan solution manuals
SOLUTIONS TO END-OF-CHAPTER PROBLEMS
Chapter 1
1-1
Descriptive statistics organize, summarize, and communicate a group of numerical observations. Inferential statistics use sam-ple data to make general estimates about the larger population.
1-2
A sample is a set of observations drawn from the population of interest that, it is hoped, shares the same characteristics as the population of interest. A population includes all possible observations about which we’d like to know something.
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The four types of variables are nominal, ordinal, interval, and ratio. A nominal variable is used for observations that have cat-egories, or names, as their values. An ordinal variable is used for observations that have rankings (i.e., 1st, 2nd, 3rd) as their values. An interval variable has numbers as its values; the dis-tance (or interval) between pairs of consecutive numbers is assumed to be equal. A ratio variable meets the criteria for interval variables but also has a meaningful zero point. Interval and ratio variables are both often referred to as scale variables.
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Statisticians use scale as another term for an interval or ratio measure. They also use scale as a word for many measure-ment tools, particularly those that involve a series of items that test-takers must complete.
1-5
Discrete variables can only be represented by specific num-bers, usually whole numbers; continuous variables can take on any values, including those with great decimal precision (e.g., 1.597).
1-6
A predictor variable is a variable that we either manipulate or observe to determine its effects on the outcome variable; an outcome variable is the outcome variable that we hypothesize to be related to, or caused by, changes in the predictor variable.
1-7
A confounding variable (also called a confound) is any variable that systematically varies with the predictor variable so that we cannot logically determine which variable affects the outcome variable. Researchers attempt to control confounding variables in experiments by randomly assigning participants to conditions. The hope with random assignment is that the confounding vari-able will be spread equally across the different conditions of the study, thus neutralizing its effects.
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Reliability refers to the consistency of a measure. Validity refers to the extent to which a test actually measures what it was intended to measure. A measure that is valid absolutely must be reliable, but a reliable measure is not necessarily a valid one.
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An operational definition specifies the operations or procedures used to measure or manipulate a predictor variable or an out-come variable.
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In everyday language, people often use the word experiment to refer to something they are trying out to see what will happen. Re-searchers use the term to refer to a type of study in which partici-pants are randomly assigned to levels of the independent variable.
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An independent variable is a type of predictor variable that is used only in experiments.
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An dependent variable is a type of outcome variable that is used only in experiments.
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When conducting experiments, the researcher randomly assigns participants to conditions or levels of the indepen-dent variable. When random assignment is not possible, such as when studying something like gender or marital status, correlational research is used. Correlational research allows us to examine how variables are related to each other; experimental research allows us to make assertions about how an independent variable causes an effect in a dependent variable.
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In a between-groups research design, participants experience one, and only one, level of the independent variable. In a within- groups research design, all levels of the independent variable are experienced by all participants in the study.
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a.
b.
“the independent variable of caffeine” (not “the dependent variable of caffeine”)
c.
“A university assessed the validity” (not “A university assessed the reliability”)
d.
“In a between-groups experiment” (not “In a within-groups experiment”)
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a.
“the nominal variable ‘gender’” (not “the ordinal variable
b.
“A psychologist used a within-groups design” (not “A psy-chologist used a between-groups design”)
c.
“the effects of the independent variable” (not “the effects of the confounding variable”)
d.
“A researcher studied a sample of 20 rats” (not “A researcher studied a population of 20 rats”)
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Data ethics refer to best research practices that enable transpar-ency in research design and statistical analysis, as well as the fair and clear interpretation and reporting of findings. The push toward ethical data practices is sometimes called “open science.”
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Researchers worry about studies that have been designed in ways that allow researchers to analyze their data in a variety of ways until they “find” a result they want. They are also con-cerned about researchers using outdated statistics that have lim-itations. Both of these practices can lead to findings that other researchers cannot replicate. This may be why consumers so often read contradictory research findings.
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Severe testing is holding your hypothesis to a high standard, using rigorous research methods and statistics to uncover any weaknesses in your hypothesis.
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Severe testing is an important data ethics tool because it helps researchers avoid falling prey to looking for ways to get the results they want. A severe test holds us to a high standard in that it forces us to look for weaknesses in our hypothesis.
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Preregistration is an ethical and transparent research practice in which researchers report their research design and analysis plan before they conduct a study. Researchers can preregister studies online by outlining their research design and statistical analyses. Preregistration is important because researchers have a time-stamped record of their plans. They cannot later claim that they in-tended to study and analyze different hypotheses in different ways.
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HARKing stands for “(H)ypothesizing (A)fter the (R)esults are (K)nown.” Researchers typically have a hypothesis before they begin a study. If their findings don’t match that hypothesis, it is tempting to pretend there was a different hypothesis all along. This fakery makes findings sound all the more compelling, and can fool people (and the media) into getting excited about what may be a fluke finding.
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The sample is the 2500 Canadians who work out every week. The population is all Canadians.
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The sample is the 225 students who completed the survey. The population is all of the student customers at the bookstore.
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The sample is the 100 customers who completed the survey. The population is all of the customers at the grocery store.
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a.
130 people
b.
All people living in urban areas in India
c.
Descriptive statistic
d.
Answers may vary, but one way is to rank people according to how far they walked, so that the person who walked the longest distance is ranked 1, the person who walked the second longest distance is ranked 2, and so on.
e.
Answers may vary, but pedometers could be used to mea-sure steps taken or distance walked, both of which are scale measures.
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a.
73 people
b.
All people who shop in grocery stores similar to the one where data were collected
c.
Inferential statistic
d.
Answer may vary, but here is one way that the amount of fruit and vegetable items purchased could be operational-ized as a nominal variable: People could be labeled as having a “healthy diet” or an “unhealthy diet.”
e.
Answers may vary, but one way is to rank people according to how many fruits and vegetables they purchased, so that the person who purchased the most is ranked 1, the person who purchased the second most is ranked 2, and so on.
f.
Answers may vary, but the number of items could be counted or weighed.
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Answers may vary, but one could look at the average rate of personal saving in various nations before and after the pandemic.
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a.
The predictor variables are pet ownership and social activity. The outcome variable is loneliness.
b.
There are two levels of pet ownership, owning no pets or owning at least one pet, and two levels of social activity, went out with friends or family either not at all or at least once over the past week.
c.
Answers may vary, but loneliness could be operationalized as responses to a questionnaire about each respondent’s feelings.
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a.
Skin tone
b.
Severity of facial wrinkles
c.
Three levels (light, medium, and dark)
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a.
250 million is based on a sample. The researchers would not have been able to assess the entire population — every single person in the world.
b.
The 250 million is an inferential statistic because it is being used to draw conclusions about the prevalence of depression in the population.
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a.
The sample is the 60,000 people they studied.
b.
The researchers would like to generalize their findings to the population of all Norwegians, or perhaps even more broadly.
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a.
Ordinal
b.
Scale
c.
Nominal
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a.
Ordinal
b.
Scale
c.
Scale
d.
Scale
e.
Nominal
f.
Nominal
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a.
Discrete
b.
Continuous
c.
Continuous
d.
Discrete
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a.
A reliable test is one that provides consistent results. If you take the test twice, you should get the same results, an indi-cation of reliability.
b.
A valid test is one that measures what it intends to measure. This test has the stated intention of measuring personality. If in fact it is measuring personality accurately, then it is a valid test.
c.
There are several possible answers to this question. The developers of this website might, for example, hypothesize that the region of the world in which one grew up predicts different personality profiles that are based on region.
d.
The predictor variable would be region and the outcome variable would be personality profile.
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a.
The predictor variables are temperature and rainfall. Both are continuous scale variables.
b.
The outcome variable is experts’ ratings. This is a discrete scale variable.
c.
The researchers wanted to know if the wine experts are consistent in their ratings — that is, if they’re reliable.
d.
This observation would suggest that Robert Parker’s judg-ments are valid. His ratings seem to be measuring what they intend to measure — wine quality.
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a.
“Best rapper” is operationalized as the rapper whose lyrics have the highest rhyme density.
b.
Other variables could include ratings of flow and delivery when performing, measures of influence or impact, ratings of storytelling and lyricism, record or song sales, awards won, number of downloads, critic reviews and ratings, listener rat-ings, and so on.
c.
Ranking is an ordinal variable; rhyme density is a scale variable.
d.
They added cultural relevance and how interesting the rap-per is to their operational definition.
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a.
Forbes is operationalizing earnings as all of a comedian’s pre-tax gross income from all sources, provided that he earned the majority of his money from live performances.
b.
isn’t a brofest because men 100% dominate the top echelons of comedy . . . [It] employs an outdated definition of what comedy is and who is earning money from it that is always going to skew male. The game is rigged.”Erin Gloria Ryan likely has a problem with this definition because not all comedians perform live as their primary source of income. In her article, she explains: “The Forbes list
c.
Forbes could operationalize the earnings of comedians as pretax gross income, as they are already doing, but they could include all comedians, whether they earned most of their money from concerts, TV or Internet shows, movies, books, social media, or any other comedy-related source. This would remove the restriction that most income must come from concert sales. According to Ryan, this broader definition would have put Ellen DeGeneres in first place; she earned $53 million in 2013. Other female comedians who would have leaped onto this list include Sofía Vergara, Tina Fey, Amy Poehler, and Chelsea Handler.
1-40
a.
A between-groups research design could involve randomly assigning different participants to each speed.
b.
All participants could watch videos at each speed, complet-ing a comprehension test after each speed.
c.
The primary confound is that participants are likely to earn higher scores each time they watch the video, so it is the repeated viewing and testing, rather than the different video speeds, that would lead to any differences in comprehension.
1-41
a.
An experiment requires random assignment to conditions. It would not be ethical to randomly assign some people to vape and some people not to vape, so this research had to be correlational.
b.
Other unhealthy behaviors may be associated with vaping, such as drinking alcohol or using illegal drugs. These other unhealthy behaviors might be confounded with vaping.
c.
The e-cigarette industry could claim it was not the vaping that was harming people, but rather the other activities in which vapers tend to engage or fail to engage.
d.
You could randomly assign people to either a vaping group or a nonvaping group and assess their health over time.
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a.
This research is correlational because participants could not be randomly assigned to be high in individualism or collectivism.
b.
The sample is the 32 people who tested high for individu-alism and the 37 people who tested high for collectivism.
c.
Answers may vary, but one hypothesis could be “On average, people high in individualism will have more relationship conflict than those high in collectivism.”
d.
Answers may vary, but one way to measure relationship conflict could be counting the number of disagreements or fights per month.
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a.
Answers may vary, but one hypothesis could be “Charging for plastic bags increases the likelihood that a customer will bring their own bags.”
b.
You could observe the number of customers who bring their own bags at stores that do not charge for plastic bags
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C-4 Appendix C
and at other stores that do charge for plastic bags. You could then determine the percentages of customers who bring their own bags in each situation.
c.
You could randomly assign certain days of the week to charge for plastic bags, and other days to not charge for plastic bags. As in part (b), you could then determine the percentages of customers who bring their own bags in each situation.
1-44
a.
For too long, researchers, including Wansink, did not have to say anything about their work until the final report. There was no transparency and researchers didn’t have to outline exactly what they planned to do in their studies.
b.
If Wansink and other researchers had been required to pre-register their studies, as good data ethics practices suggest, they could not have “played” with their data after the fact, thereby reducing the number of questionable findings reported. Moreover, maybe Wansink would not have had to retract published papers. Transparent and ethical data practices can help ward off such problems.
c.
This is a fun finding that might attract clicks to a headline. As such, journalists might report this finding without exploring whether the researcher followed transparent and ethical practices. Indeed, until recently, there was no push for journalists to ask questions about ethical practices related to data. So, if this ultimately unsupported finding is overturned, then readers lose trust in research. And if it isn’t overturned, then an unsupported finding might enter the mainstream.
1-45
a.
This is a good analogy because it describes the process by which researchers “aim” at a hypothesis, find something else entirely, then pretend that the “something else entirely” was what they were shooting at all along. The scientific method can’t work if the researchers change the target to match the finding.
b.
If researchers preregistered their research, then everyone would know if they moved their “target” after they knew their findings. HARKing wouldn’t be possible!
1-46
a.
Participants in the Millennium Cohort Study
b.
Parents in the United Kingdom, or possibly all parents globally
c.
This is a correlational study, as individuals were not random-ly assigned to the condition of being a married couple or a cohabiting couple.
d.
Marital status — married or cohabiting
e.
Length of relationship
f.
1-47
There are several possible answers to this question. For example, economic status or financial well-being may be a confounding factor, as those who are more likely to have the money to marry and raise a family may have fewer life stressors than those who have less money, do not marry, and choose to cohabit. One way this variable could be opera-tionalized and measured is via household income.
a.
Researchers could have randomly assigned some people who are HIV-positive to take the oral vaccine and other people who are HIV-positive not to take the oral vaccine. The second group would likely take a placebo.
b.
This would have been a between-groups experiment because the people who are HIV-positive would have been in only one group: either vaccine or no vaccine.
c.
This limits the researchers’ ability to draw causal conclusions because the participants who received the vaccine may have been different in some way from those who did not receive the vaccine. There may have been a confounding variable that led to these findings. For example, those who received the vaccine might have had better access to health care and better sanitary conditions to begin with, making them less likely to contract cholera regardless of the vaccine’s effectiveness.
d.
The researchers might not have used random assignment because it would have meant recruiting participants, likely immunizing half, then following up with all of them. The researchers likely did not want to deny the vaccine to people who were HIV-positive because they might have contracted cholera and died without it.
e.
If the researchers preregistered their study, that would mean that they detailed, in advance, exactly how they would recruit their participants, how they would assign them to groups (if they were indeed using random assignment), and how they would analyze their results statistically.
1-48
a.
Ability level, graduate level (high school versus university), and race
b.
Wages
c.
12,000 adults in the United States who were between 14 and 22 years old in 1979
d.
All high school and university graduate adults in the United States
e.
Participants were studied over time to measure change during that period.
f.
Age could be a confounding variable, as those who are older will have more exposure to the various areas measured via the AFQT, in addition to the education they received at the university level.
g.
Ability could be operationalized by having managers rate each participant’s ability to perform their job. Another way ability could be operationalized is via high school and uni-versity grades or a standardized ability test.
1-49
a.
A “good charity” is operationally defined as one that spends more of its money for the cause it is supporting and less for fundraising or administration.
b.
The rating is a scale variable, as it has a meaningful zero point, has equal distance between intervals, and is continuous.
c.
The tier is an ordinal variable, as it involves ranking the organizations into categories (1st, 2nd, 3rd, 4th, or 5th tier) and it is discrete.
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Appendix C C-5
d.
The type of charity is a nominal variable, as it uses names or categories to classify the values (e.g., health and medical needs) and it is discrete.
e.
Measuring finances is more objective and easier to measure than some of the criteria mentioned by Ord, such as impor-tance of the problem and competency and honesty.
f.
Charity Navigator’s ratings are more likely to be reliable than GiveWell’s ratings because they are based on an objec-tive measure. It is more likely that different assessors would come up with the same rating for Charity Navigator than for GiveWell.
g.
GiveWell’s ratings are likely to be more valid than Charity Navigator’s, provided that they can attain some level of reli-ability. GiveWell’s more comprehensive rating system incor-porates a better-rounded assessment of a charity.
h.
This would be a correlational study because donation funds, the independent variable, would not be randomly assigned based on country but measured as they naturally occur.
i.
This would be an experiment because the levels of donation funds, the independent variable, are randomly assigned to
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