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fundamentals of statistics
Questions and Answers of
Fundamentals Of Statistics
Looking at a figure of cell means, what would indicate an interaction effect is present?
What is the difference between cell means and marginal means? What is represented by each of these two types of means?
What is the relationship between the presence or absence of main effects and the presence or absence of interaction effects?
Why does a determination of an interaction effect precede an examination of main effects?
Compared with the single-factor research design, what are the advantages and disadvantages of factorial research designs?
In each of the following figures, is an interaction effect present or not present? Anxiety level Anxiety level 5.00 (a) 4.00 3.00 2.00 a Anxiety level 5.00 (b) 4.00 3.00 2.00 1.00 1.00 Mon Wed Fri
For the figures in Exercise 3, develop a table of cell means and marginal means and determine whether the main effects and the interaction effect are present or absent.
What do the letters A and B represent in an “A × B factorial research design”?
In the two-factor research design, what is between-group variance composed of?
In the two-factor research design, what is within-group variance?
Why are there three sets of statistical hypotheses in a two-factor research design?
Why don’t the null and alternative hypotheses for the interaction effect specify the nature of the interaction effect?
Why are the degrees of freedom (df), critical values, and decision rules for main effects similar to those in the single-factor research design?
For each of the research situations below, identify the two independent variables and indicate the type of A × B design (e.g., 2 × 2, 3 × 3).a. An instructor teaches two courses: one taught in the
For each of the following tables of cell means, calculate marginal means (X̅A and X̅B) and the total mean(X̅T). a. b. Factor A a a2 bu 3.00 4.00 Factor B b2 2.00 2.00 Factor A a1 a2 b 8.50 6.50
For each of the following, calculate four degrees of freedom (dfA, dfB, dfA × B, dfWG) and identify the three critical values of the three F-ratios (FA, FB, FA × B) (assume α = .05). a. a=2, b=2,
Which descriptive statistic is used to calculate between-group variance in the two-way ANOVA? Which descriptive statistic is used to calculate within-group variance?
Why is the word Error included in an ANOVA summary table?
For each of the following, calculate the F-ratios (F) for the two-way ANOVA, create an ANOVA summary table, and calculate measures of effect size (R2). a. SSA=20.00, df = 1, SSB = 10.00, df = 1, SSAx
Does the type of car you own influence how attractive you are to someone of the opposite sex? Two researchers (Dunn & Searle, 2010) showed men and women a picture of a person of the opposite sex
What conclusion can you draw from a significant A x B interaction? What conclusion can you not draw?
What is the difference between a main effect and a simple effect?
What is the purpose of analyzing simple effects in the A x B research design?
For each of the research situations below, draw a figure such as those in Figure 12.11 that illustrate simple effects analyses appropriate to test the study's research hypothesis.a. An instructor
For each of the tables from Exercise 1, calculate the marginal means \(\left(\bar{X}_{\mathrm{A}}\right.\) and \(\left.\bar{X}_{\mathrm{B}}\right)\) and determine whether the main effects and
For each of the tables from Exercise 2, calculate the marginal means \(\left(\bar{X}_{\mathrm{A}}\right.\) and \(\left.\bar{X}_{\mathrm{B}}\right)\) and determine whether the main effects and
For each of the tables created in Exercise 3, calculate the marginal means \(\left(\bar{X}_{\mathrm{A}}\right.\) and \(\left.\bar{X}_{\mathrm{B}}\right)\) and determine whether the main effects and
For each of the tables created in Exercise 4, calculate the marginal means \(\left(\bar{X}_{\mathrm{A}}\right.\) and \(\left.\bar{X}_{\mathrm{B}}\right)\) and determine whether the main effects and
For each of the research situations below, identify the two independent variables and indicate the type of \(A \times B\) design (e.g., \(2 \times 2,3 \times 3)\).a. An instructor gives a final exam
For each of the research situations below, identify the two independent variables and indicate the type of \(A \times B\) design (e.g., \(2 \times 2,3 \times 3\) ).a. A gardener reads an article that
For each of the following tables of cell means, calculate marginal means \(\left(\bar{X}_{\mathrm{A}}\right.\) and \(\left.\bar{X}_{\mathrm{B}}\right)\) and the total mean
For each of the following tables of cell means, calculate marginal means \(\left(\bar{X}_{\mathrm{A}}\right.\) and \(\left.\bar{X}_{\mathrm{B}}\right)\) and the total mean
For each of the following, calculate four degrees of freedom \(\left(d f_{\mathrm{A}}, d f_{\mathrm{B}}, d f_{\mathrm{A} \times \mathrm{B}}, d f_{\text {WG }}\right)\) and identify the three critical
For each of the following, calculate four degrees of freedom \(\left(d f_{\mathrm{A}}, d f_{\mathrm{B}}, d f_{\mathrm{A}} \times \mathrm{B}, d f_{\text {WG }}\right)\) and identify the three critical
For each of the following, calculate the \(F\)-ratios \((F)\) for the two-way ANOVA, create an ANOVA summary table, and calculate measures of effect size \(\left(R^{2}\right)\).a. \(S
For each of the following, calculate the \(F\)-ratios \((F)\) for the two-way ANOVA, create an ANOVA summary table, and calculate measures of effect size \(\left(R^{2}\right)\).a. \(S
For the examples in Exercise 15, indicate the type of \(\mathrm{A} \times \mathrm{B}\) design (e.g., \(2 \times 2,3 \times 3\) ) and the number of scores in each combination of the two factors
For the examples in Exercise 16, indicate the type of A \(\times \mathrm{B}\) design (e.g., \(2 \times 2,3 \times 3\) ) and the number of scores in each combination of the two factors
One study examined parents' use of discipline with their children (McKee et al., 2007). They asked, "Do rates of harsh verbal and physical discipline differ by gender of parent and child?" (p. 188).
Does playing violent video games lead to greater aggressive behavior? A team of researchers believed greater amount of time playing these games leads to higher feelings of hostility (Barlett, Harris,
A researcher is interested in examining how teachers' expectations of their students' scholastic abilities might affect students' self-perceptions of their own ability and whether this effect varies
Concerns regarding the possibility of getting skin cancer have influenced beliefs regarding the positive benefits of getting a suntan. One study examined whether men and women have similar beliefs
Characteristics of students may influence how favorably they're perceived by their teachers. One study examined whether teachers' perceptions of students may be influenced by the student's gender
When children see adults arguing, what do they think or expect will happen? Two researchers had elementary school children watch a videotape of a man and a woman arguing (El-Sheikh \&
One way of improving job performance in organizations is through the use of "self-managed work teams": teams of employees given a certain amount of control (autonomy) over how they conduct their work
Earlier in this chapter, we mentioned a study looking at students' use of rituals related to taking exams (Rudski \& Edwards, 2007). The researchers believed that two factors related to students'
For each of the research situations described in Exercises 19 to 22, draw a figure that illustrates simple effects analyses appropriate to test the study's research hypothesis.Exercises 19One study
For each of the research situations described in Exercises 23 to 25, draw a figure that illustrates simple effects analyses appropriate to test the study's research hypothesis.Exercises
For what reasons would you create a scatterplot for a set of data?
What three aspects can be used to describe the relationship between variables?
What is the difference between a linear relationship and a nonlinear relationship?
What is the difference between a positive relationship and a negative relationship? Is a positive relationship better than a negative relationship?
What is the difference between a perfect relationship, a moderate relationship, and a zero relationship?
What does the Pearson correlation coefficient (r) measure?
What are the main features of the Pearson r?
What is covariance? What roles do covariance and variance play in calculating the Pearson r?
For each of the following situations, create a scatterplot of the data and describe the nature, direction, and strength of the relationship.a. A teacher hypothesizes that the more days of school a
In testing the Pearson r, what is implied by the null hypothesis (H0)?
What three things are represented in calculating the Pearson r?
Which of these determines whether the value for the Pearson r is a positive or negative number: SPXY, SSX, or SSY? Why?
Why is there a square root symbol in the denominator of the formula for the Pearson r?
For each of the following, calculate the degrees of freedom (df) and identify the critical values of r (assumeα = .05 [two-tailed]).a. Ni = 6b. Ni = 9c. Ni = 18
For each of the following, calculate the Pearson correlation (r).a. SPXY = 7.00, SSX = 11.00, SSY = 14.00b. SPXY = –1.25, SSX = 2.00, SSY = 4.00c. SPXY = 12.57, SSX = 135.31, SSY = 109.68
What does r2 for the Pearson correlation represent?
Students applying to graduate school may be asked to take an admissions test. To study how well these tests predict performance in grad school, one study hypothesized a positive relationship between
What is the purpose of a computational formula?
Calculate the Pearson correlation coefficient for each set of data below using the computational formulas: a. Participant X Y Participant X Y 1 8 7 4 6 2 2 3 1 5 8 3 3 7 6 10 6 4 LO 5
How do variables measured at the ordinal level of measurement differ from variables measured at the interval or ratio level of measurement?
What research situations may involve the use of ranked variables?
How are ranks assigned when there is a tie between two or more ranks?
What are the main similarities and differences between the Spearman rank-order correlation (rs) and the Pearson correlation (r)?
Calculate the Spearman rank-order correlation (rs) for each of the following pairs of ranks. Rank Order 1 Rank Order 2 4 1 4 2 21 3 2 3
One study examined the preferences of girls and boys for different musical instruments (Abeles, 2009). As part of the study, the number of sixth-grade girls and boys playing eight different
How is making the decision whether to reject the null hypothesis similar to making the decision regarding guilt in a criminal trial?
What are the different ways of describing a Type I error?
If you conducted a study comparing two groups, what would be a Type I error?
Why is the probability of Type I error equal to alpha (α)?
Why is the probability of not making a Type I error equal to 1 − alpha (1 − α)?
Why is Type I error a concern?
Why do researchers allow for the possibility of making Type I errors?
For each of the situations below, describe what would be considered a Type I error.
A restaurant owner wants to see if his customers can tell if they are drinking alcoholic or nonalcoholic beer.
A dentist tests two types of anesthesia on her patients to see which type is better at alleviating pain.
A consumer protection agency wants to know if computer users are less likely to get infected if they pay for virus protection software rather than download free software.
Why is Type II error a concern?
Why do Type II errors occur?
For each of the situations below, identify an example of a Type II error.a. A snowboarder tries two different kinds of wax to see which one lasts longer.b. A high school counselor wants to see
For each of the following hypotheses, create a chart that shows the four possible outcomes that could occur as a result of hypothesis testing. There should be two correct decisions and two incorrect
What is the main method used to control Type I error? What are concerns with this method?
What are some methods for controlling Type II error? What are concerns with each of these methods?
What is the relationship between the probability of making Type I and Type II errors?
What happens to the critical values and the region of rejection when you control Type I error by lowering alpha or control Type II error by raising alpha?
What happens to the critical values and the region of rejection when you control Type II error by using a directional alternative hypothesis?
What methods for increasing the statistical power of an analysis require the least amount of effort from a researcher? What methods require the greatest amount of effort?
What is the difference between between-group variability and within-group variability?
Imagine two studies are independently conducted regarding the same topic. Somehow, both studies find the same means and standard deviations for two groups: X̅1 = 7.00, s1 = 2.00, and X2 = 5.00, s2 =
Two researchers set out to test the same research hypothesis. Both studies are based on the same sample size (Ni = 23), and somehow both studies end up with the same standard deviations for the two
Why is it inappropriate to use terms such as highly significant to describe analyses significant at the p < .01 or .001 level?
Why is it useful to include a measure of effect size when reporting the results of a statistical analysis such as the t-test?
Conceptually, what does it mean for one variable to account for the variance of another variable?
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