Deck 16: Hierarchical and Randomized Block Analysis of Variance Models

Question 1

To study the effects of a new mathematics textbook, 30 students are randomly selected. Based on the scores of their achievement test, students are grouped into three groups (limited: 0-15, proficient: 16-30, advanced: 31-45). Half of the students in each group are then randomly assigned to use the new textbook, while the rest of the students continue to use the old textbook. Which of the following methods of blocking is employed here?

A) Predefined value blocking
B) Predefined range blocking
C) Sampled value blocking
D) Sampled range blocking
E) Post hoc blocking method

Answer 1

B

Question 2

In the scenario described above, instead of using the raw scores, the researcher used the percentile rank in the achievement test and grouped the students into three new groups: the top third, the middle third, and the bottom third. Then half of the students in each group were randomly assigned to use the new textbook. Which of the following methods of blocking is employed here?

A) Predefined value blocking
B) Predefined range blocking
C) Sampled value blocking
D) Sampled range blocking
E) Post hoc blocking method

Answer 2

A

Question 3

Ravi was studying the effect of a new medicine on subjects' blood pressure. He randomly sampled 60 laboratory rats and ranked them based on their current blood pressure. Those ranked from 1 to 3 (i.e., the three rats with the highest blood pressure) formed group 1, and those ranked from 4 to 6 formed group 2, etc. Ravi then randomly selects five groups (i.e., 15 rats). Within each group, rats were randomly assigned to three groups: new medicine, old medicine, and no medicine. Which of the following methods of blocking is employed here?

A) Predefined value blocking
B) Predefined range blocking
C) Sampled value blocking
D) Sampled range blocking
E) Post hoc blocking method

Answer 3

D

Question 4

Azita wants to evaluate the effects of two new types of word processors (Macrosoft word and Toggle doc) on employees' working efficiency. Twelve employees were randomly selected and grouped into four blocks based on the nature of the work (proofreading, copyediting, technical writing, data analysis). Within each block, each employee was randomly assigned to use one of the three word processors: Macrosoft word, Toggle doc, and the old word processor. Their working efficiency as measured by the number of files processed per day was compared. Which of the following statements is false?

A) Both the blocking factor and the treatment factor are fixed.
B) The blocking factor and the treatment factor are crossed.
C) It is expected that the blocking factor (nature of work) is related with the number of files processed per day.
D) We can conduct MCP on the interaction between nature of work and type of word processor if it is found to be significant in ANOVA.

Question 5

In a split-plot design, suppose A is the between-subjects factor, B is the within- subjects factor, and S is the subject. Which of the following statements is true?

A) Subject is nested within factor
B) Subject is nested within factor
C) Factor A is nested within subject.
D) Factor A is nested within factor

Question 6

To study the effects of diet plans on blood pressure, the researcher assigned 10 subjects to diet plan A, and 10 participants to diet plan B. Within each group, five of the subjects are male and five participants are female. Which of the following statement is true?

A) Gender is nested within diet plans.
B) Diet plan is nested within gender.
C) Gender and diet plan are crossed.
D) Diet plan is nested within subjects.

Question 7

If a design is denoted by A(BC), it means that

A) factor A is nested within factor B and factor
B) both factor B and factor C is nested within factor
C) factor A is the blocking factor and factor B and C are the treatment factors.
D) factor A is the treatment factor and factor B and C are the blocking factors.

Question 8

If a design is denoted by A(BC), and there are four observations in each cell, which of the following effects can be studied?

A) The A B interaction
B) The A C interaction
C) The B C interaction
D) The A B C interaction
E) All of the above

Question 9

To determine if statistical software A is uniformly superior to software B for the population of statistical consultants, from which random samples are taken to conduct a study, one needs

A) a nested design with a fixed-effects model.
B) a crossed design with a fixed-effects model.
C) a nested design with a random-effects model.
D) a crossed design with a random-effects model.
E) a nested design with a mixed-effects model.
F) a crossed design with a mixed-effects model.

Question 10

For the same course in statistics, two instructors are from the mathematics department, and two instructors are from the statistics department. Each instructor taught one session of the course (one student may only be enrolled in one session). The researcher is interested in comparing student evaluation of instructors from different departments. This is an example of which type of design?

A) Completely crossed design
B) Repeated measures design
C) Hierarchical design
D) Randomized block design

Question 11

In the scenario as described in Question 10, suppose the instructors from the same department are randomly assigned to use either the lecture-based method or the computer-based method. The researcher is primarily interested in the effects of different instructional methods on student outcomes. Which of the following statements is correct?

A) Instructional method is used as a blocking factor.
B) Department and instructional method are crossed.
C) Instructor is nested within department but crossed with method.
D) Instructor is nested within method but crossed with department.

Question 12

How many hypotheses are tested in a design denoted by A(B)?

A) 1
B) 2
C) 3
D) 4

Question 13

In which of the following designs can we test the A B interaction?

A) A and B are crossed, and n = 1.
B) A and B are crossed, and n = 2.
C) A is nested within B, and n = 1.
D) A is nested within B, and n = 2

Question 14

based on the following figure.
Each cell represents one combination of factor levels. The actual experiment assigns participants only to the combinations represented by the shaded cells. It is unknown whether the levels of the factors are fixed or randomly selected.
-Which of the following best describes the design of the experiment?

A) A B
B) B A
C) A(B)
D) B(A)

Question 15

based on the following figure.
Each cell represents one combination of factor levels. The actual experiment assigns participants only to the combinations represented by the shaded cells. It is unknown whether the levels of the factors are fixed or randomly selected.
-A is a random-effects factor and B is a fixed-effects factor. Each cell has 5 observations. The F_B ratio has degrees of freedom equal to?

A) 2, 3
B) 2, 10
C) 2, 24
D) 3, 72

Question 16

based on the following figure.
Each cell represents one combination of factor levels. The actual experiment assigns participants only to the combinations represented by the shaded cells. It is unknown whether the levels of the factors are fixed or randomly selected.
-Both A and B are fixed-effects factors. Each cell has 5 observations. The F_B ratio has degrees of freedom equal to?

A) 2, 3
B) 2, 10
C) 2, 24
D) 3, 72

Question 17

based on the following figure.
Each cell represents one combination of factor levels. The actual experiment assigns participants only to the combinations represented by the shaded cells. It is unknown whether the levels of the factors are fixed or randomly selected.
-Both A and B are random-effects factors. Each cell has 5 observations. The F_B ratio has degrees of freedom equal to?

A) 2, 3
B) 2, 10
C) 2, 24
D) 3, 72

Question 18

If the correlation between the concomitant variable and dependent variable is −.35, and the concomitant variable is measured on an interval scale, which of the following designs is recommended?

A) One-factor ANOVA.
B) ANCOVA.
C) Randomized block ANOVA.
D) Either ANCOVA or randomized block ANOVA.

Question 19

If the correlation between the concomitant variable and dependent variable is .05, and the concomitant variable is measured on an ordinal scale, which of the following designs is recommended?

A) One-factor ANOVA
B) ANCOVA
C) Randomized block ANOVA
D) Either ANCOVA or randomized block ANOVA.

Question 20

If the correlation between the concomitant variable and dependent variable is .5, and the concomitant variable is measured on an ordinal scale, which of the following designs is recommended?

A) One-factor ANOVA
B) ANCOVA
C) Randomized block ANOVA
D) Either ANCOVA or randomized block ANOVA.

Question 21

Suppose two researchers performed ANOVA on the same data. Researcher A used a one-factor model, whereas researcher B added a blocking factor in addition to the treatment factor to the model. Which researcher will get the smaller residual variation?

A) Researcher A
B) Researcher B
C) Both researchers will get the same residual variation.
D) It depends.

Question 22

Which of the following blocking methods is more precise in estimating the treatment effects for an ordinal blocking variable?

A) Predefined value blocking
B) Predefined range blocking
C) Sampled value blocking
D) Sampled range blocking
E) Post hoc blocking method

Question 23

Which of the following variables may be used as a treatment factor?

A) Teaching method.
B) Years of teaching experience.
C) Pretest score.
D) Gender.

Question 24

Compared to the two-factor fully-crossed ANOVA, the two-factor hierarchical ANOVA

A) has the same model assumptions.
B) has the same linear model.
C) has the same ANOVA table.
D) has the same hypotheses to be tested.

Question 25

Which assumption is required for the randomized block model, but not for the two-factor fully-crossed ANOVA?

A) Independence
B) Homogeneity of variance
C) Normality
D) Sphericity

Question 26

An experiment was conducted to compare the effects of four types of classroom layout on children's learning outcomes. Score on a pretest is used to form the blocks (low, middle, high). The mean scores on the dependent variable, children's score on a posttest quiz, are listed here for each cell.
Use these cell means to graph the interaction between type of classroom layout and pretest score block.
a. Is there an interaction between type of classroom layout and pretest score?
b. What kind of recommendation would you make to teachers?

Question 27

An experiment was conducted to compare the effect of three types of daily schedules on the employees' work performance. The schedules all contained the same amount of tasks, but the tasks were listed in different orders in each schedule. The day of the week was used as the blocking variable. The mean scores on the dependent variable, the percentage of tasks completed, are listed here for each cell.
Use these cell means to graph the interaction between type of schedule and the day of the week.
a. Is there an interaction between type of schedule and the day of the week?
b. What kind of recommendation would you make to the manager?

Question 28

A market researcher wanted to test three exotic flavors of cake (dragon fruit, root beer, and yam) on customers of different age groups (21-30, 31-40, 41-50, 51-60). Thus, age is a blocking variable. The dependent measure was the customer's rating on how much he/she liked the cake. There were six subjects in each cell. Complete the ANOVA summary table below, assuming a fixed-effects model, where $\alpha$ = .05.
$\begin{array}{ccccccc}\hline \text { Source } & \text { SS } & d f & M S & F & \text { Critical Value } & \text { Decision } \\\hline \text { Flavor }(\mathrm{A}) & 300 & - & - & - & - & - \\\text { Age }(\mathrm{B}) & - & - & 50 & - & - & - \\\text { Interaction }(\mathrm{AB}) & - & - & - & - & - & - \\\text { Within } & -& - & {25} & \\\text { Total } & 2400 & - & & & & \\\hline\end{array}$

Question 29

Azita wants to evaluate the effects of three new types of word processors (1: MacrosoftWork; 2: ToogleDoc, 3: WordTerrific) on the employees' working efficiency. 12 employees were randomly selected and grouped into four blocks based on the amount of their daily tasks (higher values indicate heavier work load). Within each block, each employee was randomly assigned to use one of the three word processors. Their working efficiency as measured by the number of files processed per day is listed in the table. Conduct a two-factor randomized block ANOVA ( $\alpha$ = .05) and Bonferroni MCPs using SPSS to determine the results of the study.
$\begin{array}{|c|c|c|c|}\hline \text { Subject } & \text { Word Processor } & \text { Workload } & \text { Number of files processed } \\\hline 1 & 1 & 1 & 8 \\\hline 2 & 1 & 2 & 13 \\\hline 3 & 1 & 3 & 18 \\\hline 4 & 1 & 4 & 26 \\\hline 5 & 2 & 1 & 3 \\\hline 6 & 2 & 2 & 10 \\\hline 7 & 2 & 3 & 13 \\\hline 8 & 2 & 4 & 20 \\\hline 9 & 3 & 1 & 5 \\\hline 10 & 3 & 2 & 12 \\\hline 11 & 3 & 3 & 14 \\\hline 12 & 3 & 4 & 20 \\\hline\end{array}$

Question 30

Dr. Numerus wanted to examine two different methods to teach number theory. He randomly selected six instructors from the department, and assigned three of them to use method 1 and three of them to use method 2. There were 20 students in each instructor's class. At the end of the semester, Dr. Numerus collected the test scores from all six classes and ran a two-factor hierarchical ANOVA. Below is the selected output generated by SPSS.
Test of Between-Subjects Effects
$\begin{array}{ccccc}\hline \text { Source } & \text { Type III SS } & \text { df } & \text { MS } & \text { F } \\\hline \mathrm{A} & 764.54 & 1 & 764.54 & 64.23993 \\\mathrm{~B}(\mathrm{~A}) & 944.22 & 4 & 236.06 & 19.83435 \\\text { Within } & 1356.75 & 114 & 11.90 & \\\text { Total } & 3065.51 & 119 & & \\\hline\end{array}$ (a) Identify factor A and factor
(b) For each factor, identify whether it is a fixed-effects or random-effects factor.
(c) Is the SPSS ANOVA summary table correct? If not, correct the erroneous part(s).
(d) What conclusions can you draw from the correct test results? (Use $\alpha$ = .05)