Exam 16: Hierarchical and Randomized Block Analysis of Variance Models

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?

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

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

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. Pretest score block Type of classroom layout low middle high 1 65 75 90 2 80 85 95 3 70 80 85 4 75 85 100 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?

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?

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?

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

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

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?

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?

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 Source Type III SS df MS F 764.54 1 764.54 64.23993 () 944.22 4 236.06 19.83435 Within 1356.75 114 11.90 Total 3065.51 119 (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)

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

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?

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?

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 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. Source SS df MS F Critical Value Decision Flavor () 300 - - - - - Age () - - 50 - - - Interaction () - - - - - - Within - - 25 Total 2400 -

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?

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

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?

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?