Question 1

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

(a) row, interaction (b) row, column (c) interaction (d) row, column, interaction (e) column

Question 2

(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 3

Thirty words are flashed on a screen, one at a time, under various combinations of type style (A, B, and C) and exposure time (60 milliseconds and 120 milliseconds). Two randomly assigned participants are used in each cell (considerably more participants would be required for a practical study). The results, given below, are numbers of words correctly recognized. 
(a) Compute  and  for each cell and display these values in a table. 
(b) Proceed to obtain

(c) Compute the variance estimates; perform the three F tests at  and  and draw statistical conclusions. Display your results in a summary analysis of variance table. 
(d) Construct a table showing cell and marginal means. Considering the F-test results, which means would be of interest? Why? Draw final conclusions concerning the treatment variables.

Accepted Answer

(a) Check cell sums 
  
 to see that they add up to 120; similarly, row sums and column sums should total 120;

Question 4

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 5

A human factors psychologist investigates which of two simulators (P and Q) results in improved task performance. Eight participants are randomly assigned to one of the two simulators and each participant's performance score is measured across five trials. The performance scores are given below (normally far more cases would be used in an actual study). (a) Compute the appropriate variance estimates; complete the F tests at and draw statistical conclusions. Show your results in a summary analysis of variance table (b) Construct a graph of the cell means. Draw final conclusions.

Accepted Answer

The answer of A human factors psychologist investigates which of...

Question 6

Which is not an advantage of two-factor analysis of variance?

Accepted Answer

Better experimental control of extraneous variables can be achieved in a simple experiment than in a two-factor analysis of variance.

Question 7

In terms of the two-way table layout for two-factor ANOVA, main effects are concerned solely with

Accepted Answer

Main effects in a two-factor ANOVA are concerned with the marginal means, which are the averages of each level of a factor, ignoring the other factor.

Question 8

A main effect is most precisely described as a(n)

Accepted Answer

A main effect refers to the average effect of one independent variable on the dependent variable, regardless of the levels of other variables in the experiment.

Question 9

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

Interaction is suggested when the effect of one factor (method) depends on the level of another factor (intelligence). If method A is better for brights but not for dulls, it indicates an interaction between method and intelligence level.

Question 10

In terms of the two-way table layout for two-factor ANOVA, interaction is concerned solely with

Accepted Answer

Interaction is concerned with the differences between cell means and marginal means.

Question 11

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

The answer of Suppose, in a two-way analysis of variance,...

Question 12

In a study investigating the effects of three different diets (Diet) on physical abilities, twelve participants were divided evenly into three groups. Each group was assigned a particular diet and each participant was measured on a physical ability test on seven consecutive days (Trials). What are the appropriate denominator degrees of freedom for the F-test on the Diet × Trials interaction?

Accepted Answer

The denominator degrees of freedom for the Diet × Trials interaction in a repeated measures ANOVA is calculated as (number of subjects - number of groups) × (number of trials - 1), which is (12 - 3) × (7 - 1) = 54.

Question 13

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

The answer of Suppose, in a two-way analysis of variance,...

Question 14

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

Accepted Answer

The answer of Suppose, in a two-way analysis of variance,...

Question 15

Using an equal number of cases per group is recommended practice

Accepted Answer

The answer of Using an equal number of cases per...

Question 16

A significant interaction becomes a matter of concern

Accepted Answer

A significant interaction is a concern regardless of the significance of main effects because it indicates that the effect of one independent variable depends on the level of another independent variable.

Question 17

Both main effects in a two-factor ANOVA turn out to be nonsignificant. Does this mean that the sample results showed no effects of the two factors beyond those expected by chance?

Accepted Answer

If the interaction is significant, it indicates that the effect of one factor depends on the level of the other factor, which means there are effects beyond those expected by chance, even if the main effects are nonsignificant.

Question 18

The finding of a significant main effect in two-way analysis of variance may not be open to straight-forward interpretation when

Accepted Answer

When there is a significant interaction effect, it means that the effect of one independent variable on the dependent variable depends on the level of the other independent variable, complicating the interpretation of main effects.

Question 19

In studying the outcome of a two-way ANOVA for which one or more F's turn out to be significant, one should always

Accepted Answer

Examining the various sample means helps to understand the nature of the significant effects and interactions found in the ANOVA.

Question 20

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

Parallel lines in a two-factor ANOVA graph suggest that there is very little, if any, interaction between the two factors. Interaction would typically cause the lines to diverge or converge.

Quiz 19: Factorial Analysis of Variance

Which is not an advantage of two-factor analysis of variance?

In terms of the two-way table layout for two-factor ANOVA, main effects are concerned solely with

A main effect is most precisely described as a(n)

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

In terms of the two-way table layout for two-factor ANOVA, interaction is concerned solely with

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

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

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

Using an equal number of cases per group is recommended practice

A significant interaction becomes a matter of concern

Both main effects in a two-factor ANOVA turn out to be nonsignificant. Does this mean that the sample results showed no effects of the two factors beyond those expected by chance?

The finding of a significant main effect in two-way analysis of variance may not be open to straight-forward interpretation when

In studying the outcome of a two-way ANOVA for which one or more F's turn out to be significant, one should always

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