Question 1

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?

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

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

Accepted Answer

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. A

Question 4

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.
 $\begin{array}{c }
  \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad{\text { Pretest score block }} \
\begin{array}{cccc}
\hline \text { Type of classroom layout }& \text { low } & \text { middle } & \text { high } \
\hline 1 & 65 & 75 & 90 \
2 & 80 & 85 & 95 \
3 & 70 & 80 & 85 \
4 & 75 & 85 & 100 \
\hline
\end{array}\end{array}$ 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?

Accepted Answer

The answer of An experiment was conducted to compare the...

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?

Accepted Answer

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

Question 6

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?

Accepted Answer

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 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

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 9

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 FB ratio has degrees of freedom equal to?

Accepted Answer

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

Question 10

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?

Accepted Answer

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

Question 11

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)

Accepted Answer

The answer of Dr. Numerus wanted to examine two different...

Question 12

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

Accepted Answer

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

Question 13

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?

Accepted Answer

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

Question 14

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?

Accepted Answer

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

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.
-Both A and B are fixed-effects factors. Each cell has 5 observations. The FB ratio has degrees of freedom equal to?

Accepted Answer

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

Question 16

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.
 $\begin{array}{ccccccc}
\hline \text { Source } & \text { SS } & d f & M S & F & \text { Critical Value } & \text { Decision } \
\hline \text { Flavor }(\mathrm{A}) & 300 & - & - & - & - & - \
\text { Age }(\mathrm{B}) & - & - & 50 & - & - & - \
\text { Interaction }(\mathrm{AB}) & - & - & - & - & - & - \
\text { Within } & -& - & {25}  & \
\text { Total } & 2400 & - & & & & \
\hline
\end{array}$

Accepted Answer

The answer of A market researcher wanted to test three...

Question 17

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?

Accepted Answer

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

Question 18

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

Accepted Answer

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 19

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?

Accepted Answer

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

Question 20

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?

Accepted Answer

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

Exam 16: Hierarchical and Randomized Block Analysis of Variance Models