Question 1

In two-factor analysis of variance, the denominator of the F-test is

Accepted Answer

A)   
B)   
C)   depending on the test to be made 
D)   depending on the test to be made

Question 2

Two approaches, S (structured) and U (unstructured), to teaching a required undergraduate course in social research methods are to be compared with regard to their effects on student interest in social research. Students signing up for the course are classified as Type C (conforming) or Type I (independent) individuals according to personality test results. On a random basis, half of each type of student are assigned to section S of the course and half to section U. At the end of the course, scores are obtained on a scale of interest in social research and are analyzed using a two-factor analysis of variance.

The interest (in social research) scores are given below (normally far more cases would be used). 
(a)Compute the variance estimates; complete the F tests at  and  ; and draw statistical conclusions. Show your results in a summary analysis of variance table 
(b)Construct a table showing cell and marginal means. Considering the F-test results, which means would be of interest? Why? 
(c)Construct a graph of the cell means. Draw final conclusions concerning the two treatment variables.

Accepted Answer

The answer of Two approaches, S (structured) and U (unstructured),...

Question 3

Suppose, in a two-way analysis of variance, based on 15 cases per cell, the indicated cell means were observed. We might expect to find that there will be a significant

Accepted Answer

A)  main effect for factor 1 
B)  main effect for factor 2 
C)  interaction effect 
D)  effect in none of the above situations

Question 4

We are studying the effect of two methods of learning, using bright students and dull students, in a two-way analysis of variance. Interaction between method and level of intelligence would be suggested if we found that

Accepted Answer

A)  method A was better for brights, but not for dulls 
B)  method A was better for brights and better for dulls 
C)  there is no difference between method A and method B, but there is a difference between brights and dulls 
D)  there is no difference between methods, and there is no difference between brights and dulls

Question 5

In general, the number of degrees of freedom for the within-cells variance estimate is

Accepted Answer

A)   
B)   
C)   
D)  (R - 1)(C - 1)

Question 6

A graph is made of the cell means for a two-factor ANOVA. The lines connecting the means for each row are reasonably parallel. This suggests

Accepted Answer

A)  very little, if any, row effect 
B)  very little, if any, column effect 
C)  very little, if any, interaction 
D)  all F tests probably turned out nonsignificant

Question 7

Using an equal number of cases per group is recommended practice

Accepted Answer

A)  for one-way analysis of variance 
B)  when it is desirable to avoid Type I errors 
C)  when it is desirable to avoid an interaction effect 
D)  for two-factor analysis of variance

Question 8

(a) -(e)Draw a graph of the cell means for each of the tables above. Let the horizontal axis represent the column variable. In each case, see if you can arrive at correct conclusions concerning the presence (or absence) of row, column, and interaction effects from the graph alone. Bear in mind that the tables of Problem 1 are highly artificial; they are population values and do not reflect the effects of the sampling variation that would be encountered in practice.

Accepted Answer

The answer of (a) -(e)Draw a graph of the cell...

Question 9

In the tables below, population (not sample) means are given for the cells. In each case, compute the marginal means and indicate whether the table shows (1) a main row effect, (2) a main column effect, (3) an interaction effect. Remember: population values do not show the effects of sampling variation.

Accepted Answer

The answer of In the tables below, population (not sample)...

Question 10

In general, the number of degrees of freedom for row by column interaction is given by

Accepted Answer

A)  (R - 1)(C - 1) 
B)  (R - 1) + (C - 1) 
C)  (R + 
C)  - 1 
D)  (R)(
C)

Exam 19: Factorial Analysis of Variance