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essentials of statistics

Essentials Of Statistics For The Behavioral Sciences 5th Edition Susan A. Nolan, Thomas Heinzen - Solutions

13.1 What is a correlation coefficient?
12.49 Feedback and ANOVA: Stacey Finkelstein and Ayelet Fishbach (2012) examined the impact of feedback in the learning process. The following is an excerpt from their abstract: “This article explores what feedback people seek and respond to. We predict and find a shift from positive to negative
12.48 Skepticism, self-interest, and two-way ANOVA: A study on motivated skepticism examined whether participants were more likely to be skeptical when it served their self-interest (Ditto & Lopez, 1992). Ninety-three participants completed a fictitious medical test that told them they had high
12.47 Negotiation, an interaction, and a graph: German psychologist David Loschelder and his colleagues (2014) conducted an experiment on negotiations. They cited tennis player Andy Roddick’s agent, who thought it was always detrimental to make an initial offer: “The first offer gives you an
12.46 Gender, pizza, and an interaction: Researchers examined whether men and women eat different amounts of food in the company of same-sex dining partners versus opposite-sex dining partners (Kniffin et al., 2016). From an evolutionary perspective, the researchers wondered which of the following
12.45 College students, anxiety, depression, and a MANOVA: Jason Nelson and Noel Gregg (2012) conducted a study of college students with disabilities. They reported that: “A 3 × 3 × 2 MANOVA was conducted to determine the effect of level of educational attainment (transitioning adolescents and
12.44 Math performance and type of ANOVA: Imagine that a university professor is interested in the effects of a new instructional method on the math performance of first-year university students. All students take a math pretest and then are randomly assigned to a class in which the new
12.43 Body weight, salary, and the need for covariates: A nutritional software program called DietPower offers encouragement to its users when they sign in each day. In one instance, the program states that people at their ideal body weight tend to have higher salaries than do people who are
12.42 Exercise, well-being, and type of ANOVA: Cox and colleagues (2006) studied the effects of exercise on well-being. There were three independent variables: age (18–20 years old, 35–45 years old), intensity of exercise (low, moderate, high), and time point (15, 20, 25, and 30 minutes). The
12.41 Helping, payment, and interactions: Expanding on the work of Heyman and Ariely (2004) as described in the previous exercise, let’s assume a higher level of payment was included and the following data were collected. (Notice that all data are the same as earlier, with the addition of new
12.40 Helping, payment, and two-way between-groups ANOVA: Heyman and Ariely (2004) were interested in whether effort and willingness to help were affected by the form and amount of payment offered in return for effort. They predicted that when money was used as payment, in what is called a money
12.39 Age, online dating, and two-way between-groups ANOVA: The data below were from the same 25-year-old participants described in How It Works 12.1, but now the scores represent the oldest age that would be acceptable in a dating partner. 25-year-old women seeking men: 40, 35, 29, 35, 35
12.38 Grade-point average, fraternities, sororities, and two-way between-groups ANOVA: A sample of students from our statistics classes reported their grade-point averages (GPAs), indicated their genders, and stated whether they were in the university’s Greek system (i.e., in a fraternity or
12.37 The cross-race effect, main effects, and interactions: Hugenberg, Miller, and Claypool (2007) conducted a study to better understand the cross-race effect, in which people have a difficult time recognizing members of different racial groups—colloquially known as the “they all look the
12.36 Gender, negotiating a salary, and an interaction: Eleanor Barkhorn (2012) reported in The Atlantic about differences in women’s and men’s negotiating styles. She first explained that researchers did not find a significant difference in how likely women and men are to negotiate salaries.
12.35 Self-interest, ANOVA, and interactions: Ratner and Miller (2001) wondered whether people are uncomfortable when they act in a way that’s not obviously in their own self-interest. They randomly assigned 33 women and 32 men to read a fictional passage saying that government funding would soon
12.34 Racism, juries, and interactions: In a study of racism, Nail, Harton, and Decker (2003) had U.S. participants read a scenario in which a police officer assaulted a motorist. Half the participants read about a black officer who assaulted a white motorist, and half read about a white officer
12.33 Anger, culture, and choosing the type of ANOVA: Researchers explored the effect of the expression of anger on physical health in two cultures—the United States and Japan (Kitayama et al., 2015). They noted that previous research linked the expression of anger with health problems, but this
12.30 An app for tracking alcohol use, and ANOVA: Researchers investigated the use of an app for tracking alcohol consumption on the number of drinks a person consumed over a 3-week period. Participants logged each time they had a drink, and the researchers summed the number of drinks that each
12.29 Using the information in the source table provided here, compute R2 values for each effect. Using Cohen’s conventions, explain what these values mean.Source SS df MS F A (rows) 30.006 1 30.006 0.511 B (columns) 33.482 1 33.482 0.570 A × B 1.720 1 1.720 0.029 Within 587.083 10 58.708 Total
12.28 Using the information in the source table provided here, compute R 2 values for each effect. Using Cohen’s conventions, explain what these values mean.Source SS df MS F A (rows) 0.267 1 0.267 0.004 B (columns) 3534.008 2 1767.004 24.432 A × B 5.371 2 2.686 0.037 Within 1157.167 16 72.323
12.27 Using what you know about the expanded source table, fill in the missing values in the table shown here: Source SS df MS F Gender 248.25 1 Parenting style 84.34 3 Gender × style 33.60 Within 1107.20 36 Total
12.26 Use these data—incidents of reports of underage drinking at universities—to perform the following tasks: “Dry” campus, state school: 47, 52, 27, 50 “Dry” campus, private school: 25, 33, 31 “Wet” campus, state school: 77, 61, 55, 48 “Wet” campus, private school: 52, 68,
12.25 Use these “enjoyment” ratings to perform the following tasks:Ice Hockey Figure Skating Men 19, 17, 18, 17 6, 4, 8, 3 Women 13, 14, 18, 8 11, 7, 4, 14a. Calculate the cell and marginal means.b. Draw a bar graph.c. Calculate the five different degrees of freedom, and indicate the critical F
12.24 State how many cells there should be for each of these studies. Then, create an empty grid to represent those cells.a. Men’s and women’s enjoyment of two different sporting events, Sport 1 and Sport 2, are compared using a 20-point enjoyment scale.b. The amount of underage drinking, as
12.23 Identify the factors and their levels in the following research designs.a. Men’s and women’s enjoyment of two different sporting events, Sport 1 and Sport 2, are compared using a 20-point enjoyment scale.b. The amount of underage drinking, as documented in formal incident reports, is
12.22 For each of the following scenarios, what are two names for the ANOVA that would be conducted to analyze the data?a. A researcher examined the effect of gender and pet ownership (no pets, one pet, more than one pet) on a measure of loneliness.b. In a study on memory, participants completed a
12.21 What is a two-way mixed-design MANOVA?
12.20 When might a researcher decide to use an ANCOVA rather than an ANOVA?
12.19 When might a researcher decide to use a MANOVA rather than an ANOVA?
12.18 How is a MANOVA different from an ANOVA?
12.17 How is an ANCOVA different from an ANOVA?
12.16 What is a two-way mixed-design ANOVA?
12.15 What effect-size measure is used with two-way ANOVA?
12.14 In your own words, define the word interaction, first as you would use it in everyday conversation and then as a statistician would use it.
12.13 Explain the following formula in your own words: SSinteraction = SStotal − (SSrows + SScolumns + SSwithin).
12.12 When are post hoc tests needed for a two-way between-groups ANOVA?
12.11 In Step 6 of hypothesis testing for a two-way between-groups ANOVA, we make a decision for each F statistic. What are the three possible outcomes with respect to the overall pattern of results?
12.10 Why is a bar graph a better choice than a line graph for depicting the means of a two-way ANOVA?
12.9 How do bar graphs help us identify and interpret interactions? Explain how adding lines to the bar graph can help.
12.8 What are the three ways to identify a statistically significant interaction?
12.7 What is a marginal mean?
12.6 What are the three different F statistics in a two-way ANOVA?
12.5 What is the difference in information provided when we say twoway ANOVA versus 2 × 3 ANOVA?
12.4 What is a four-way within-groups ANOVA?
12.3 In your own words, define the word cell, first as you would use it in everyday conversation and then as a statistician would use it.
12.2 What is a factor?
12.1 What is a two-way ANOVA?
11.49 ANOVA, award-winning television, and the theory of mind: Can watching high-quality television dramas improve our theory of mind—our ability to understand others? Psychologists Jessica Black and Jennifer Barnes (2015) explored this question in a study in which participants were randomly
11.48 Orthodontics and one-way between-groups ANOVA: Iranian researchers studied factors affecting patients’ likelihood of wearing orthodontic appliances, noting that orthodontics is perhaps the area of health care with the highest need for patient cooperation (Behenam & Pooya, 2006). Among their
11.47 Trust in leadership and one-way between-groups ANOVA: In Chapter 10, we introduced a study by Steele and Pinto (2006) that examined whether people’s level of trust in their direct supervisor was related to their level of agreement with a policy supported by that leader. Steele and Pinto
11.46 ANOVA and taking notes: Researchers studied the type of note taking that would lead to the best performance on conceptual questions on a test (Mueller & Oppenheimer, 2014). Conceptual questions are those in which students have to apply the material, rather than just answer fact-based
11.45 Post hoc tests, bilingualism, and language skills: Researchers Raluca Barac and Ellen Bialystok (2012) conducted a study in which they compared the language skills of 104 six- year-old children who were in one of four groups. Some children spoke only English. Others were bilingual, speaking
11.44 Post hoc tests and p values: The most recent version of the Publication Manual of the American Psychological Association (American Psychological Association, 2020) recommends reporting the exact p values for all statistical tests to two decimal places (previously, it recommended reporting p <
11.43 Instructors on Facebook and one-way ANOVA: Researchers investigated whether the amount of self-disclosure on Facebook affected student perceptions of the instructor, the class, and the classroom environment (Mazer et al., 2007). Students were randomly assigned to view one of three Facebook
11.42 Consideration of Future Consequences and two kinds of hypothesis testing: Two samples of students, one composed of social science majors and one composed of students with other majors, completed the Consideration of Future Consequences scale (CFC). The tables on the next page include the
11.41 Grade-point average and comparing the t and F distributions: Based on your knowledge of the relation of the t and F distributions, complete the software output tables below. The table for the independent-samples t test and the table for the one-way between-groups ANOVA were calculated using
11.40 Exercise and post hoc tests: Use the same data from the previous exercise in this exercise.a. Explain why it is necessary to conduct a post hoc test such as a Tukey HSD test when an ANOVA is statistically significant.b. Conduct a Tukey HSD test. Show all calculations.c. Explain why we cannot
11.39 Exercise and education programs: Irwin and colleagues (2004) conducted research on adherence to an exercise regimen. Participants were asked to attend a monthly group education program to help them change their exercise behavior. Participants were divided into three categories: those who
11.38 Type of ANOVA in study of remembering names: Do people remember names better under different circumstances? In a fictional study, a cognitive psychologist studied memory for names after a group activity that lasted 20 minutes. Participants were not told that this was a study of memory. After
11.37 International students and type of ANOVA: Catherine Ruby (2006), a doctoral student at New York University, conducted an online survey to ascertain the reasons that international students chose to attend graduate school in the United States. One of several dependent variables that she
11.36 Links among distributions: The z, t, and F distributions are closely linked. In fact, it is possible to use an F distribution in all cases in which a t or a z could be used.a. If you calculated an F statistic of 4.22 but you could have used a t statistic (i.e., the situation met all criteria
11.35 The comparison distribution: For each of the following situations, state whether the distribution of interest is the z distribution, a t distribution, or an F distribution. Explain your answer.a. A student reads in her Introduction to Psychology textbook that the mean IQ is 100. She asks 10
11.34 The comparison distribution: For each of the following situations, state whether the distribution of interest is the z distribution, a t distribution, or an F distribution. Explain your answer.a. A city employee locates a U.S. Census report that includes the mean and standard deviation for
11.33 Comedy versus news and hypothesis testing: Focusing on coverage of the U.S. presidential election, Julia R. Fox, a telecommunications professor at Indiana University, wondered whether The Daily Show, despite its comedy format, was a valid source of news. She coded a number of half-hour
11.32 A researcher designs an experiment in which the single independent variable has five levels. If the researcher performed an ANOVA and rejected the null hypothesis, how many post hoc comparisons would he make (assuming he was making all possible comparisons)?
11.31 A researcher designs an experiment in which the single independent variable has four levels. If the researcher performed an ANOVA and rejected the null hypothesis, how many post hoc comparisons would she make (assuming she was making all possible comparisons)?
11.30 Each of the following is a calculated F statistic with its degrees of freedom. Using the F table, estimate the level of significance for each. You can do this by indicating whether its likelihood of occurring is greater than or less than an alpha level shown in the table.a. F = 4.11, with 3
11.29 Use the source table in Exercise 11.27 to answer the following questions.a. What is R2 for these data?b. What is ω 2 for these data?
11.28 Use the source table in Exercise 11.26 to answer the following questions.a. What is R 2 for these data?b. What is ω 2 for these data?
11.27 An incomplete one-way between-groups ANOVA source table is shown below. Compute the missing values.Source SS df MS F Between — 2 — — Within 89 11 — Total 132 —
11.26 An incomplete one-way between-groups ANOVA source table is shown below. Compute the missing values.Source SS df MS F Between 191.450 — 47.863 — Within 104.720 32 — Total — 36
11.25 Calculate the F statistic, writing the ratio accurately, for each of the following cases:a. Between-groups variance is 321.83 and within-groups variance is 177.24b. Between-groups variance is 2.79 and within-groups variance is 2.20c. Within-groups variance is 41.60 and between-groups variance
11.24 Calculate the F statistic, writing the ratio accurately, for each of the following cases:a. Between-groups variance is 29.4 and within-groups variance is 19.1b. Within-groups variance is 0.27 and between-groups variance is 1.56c. Between-groups variance is 4595 and within-groups variance is
11.23 For the following data, assuming a between-groups design, determine: 1990: 45, 211, 158, 74 2000: 92, 128, 382 2010: 273, 396, 178, 248, 374a. dfbetweenb. dfwithinc. dftotald. The critical value, assuming a p value of 0.05e. The mean for each group and the grand meanf. The total sum of
11.22 For the following data, assuming a between-groups design, determine: Group 1: 11, 17, 22, 15 Group 2: 21, 15, 16 Group 3: 7, 8, 3, 10, 6, 4 Group 4: 13, 6, 17, 27, 20a. dfbetweenb. dfwithinc. dftotald. The critical value, assuming a p value of 0.05e. The mean for each group and the grand
11.21 Find the incorrectly used symbol or symbols in each of the following statements or formulas. For each statement or formula, (i) state which symbol(s) is/are used incorrectly, (ii) explain why the symbol(s) in the original statement is/are incorrect, and (iii) state which symbol(s) should be
11.20 Find the incorrectly used symbol or symbols in each of the following statements or formulas. For each statement or formula, (i) state which symbol(s) is/are used incorrectly, (ii) explain why the symbol(s) in the original statement is/are incorrect, and (iii) state which symbol(s) should be
11.19 Find the error in the statistics language in each of the following statements about z, t, or F distributions or their related tests. Explain why it is incorrect and provide the correct word.a. The professor reported the mean and standard error for the final exam in the statistics class.b.
11.18 Define the symbols in the following formula: N ′ = Ngroups Σ(1/N)
11.17 What does post hoc mean, and when are these tests needed with ANOVA?
11.16 Why are researchers increasingly calculating omega squared rather than R2?
11.15 What is omega squared?
11.14 What are Cohen’s conventions for interpreting effect size using R2?
11.13 What do we typically use to measure effect size for a z test or a t test? What do we use to measure effect size for an ANOVA?
11.12 How do we calculate the between-groups sum of squares?
11.11 What is the grand mean?
11.10 The total sum of squares for a one-way between-groups ANOVA is found by adding which two statistics together?
11.9 Explain the concept of sum of squares.
11.8 Define the word source as you would use it in everyday conversation. Provide at least two different meanings that might be used. Then define the word as a statistician would use it.
11.7 Why is the F statistic always positive?
11.6 The null hypothesis for ANOVA posits no difference among population means, as in other hypothesis tests, but the research hypothesis in this case is a bit different. Why?
11.5 What are the three assumptions for a between-groups ANOVA?
11.4 What is the difference between a within-groups (repeatedmeasures) ANOVA and a between-groups ANOVA?
11.3 The F statistic is a ratio of between-groups variance and within-groups variance. What are these two types of variance?
11.2 What do the F distributions allow us to do that the t distributions do not?
11.1 What is an ANOVA?
10.43 Independent-samples t test and the perils of informal email addresses: Is your email address something like hotstuff@fake-mail.com? You may not want to use it when you apply for a job or email your professors. Dutch psychologists studied the effect of using informal email addresses on the
10.42 Graphic warnings, sugary beverages, and hypothesis testing: Researchers asked soda drinkers to view either the logo for their favorite soda or a graphic warning demonstrating the harmful effects of sugary beverages (e.g., tooth decay, obesity; Donnelly et al., 2018). They found that those
10.41 School lunches: Alice Waters, owner of the Berkeley, California, restaurant Chez Panisse, has long been an advocate for the use of simple, fresh, organic ingredients in home and restaurant cooking. She has also turned her considerable expertise to school cafeterias. Waters (2006) praised

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