Question 1

In order to analyze any potential interactions between factors in an analysis of variance study, it is necessary to have at least two measurements at each level of each factor.

Accepted Answer

In an analysis of variance (ANOVA) study, having at least two measurements at each level of each factor is necessary to estimate the variability within groups and to analyze potential interactions between factors. Without multiple measurements, it's impossible to assess how factors interact with each other because there's no way to distinguish between the variability due to the interaction and the inherent variability within each level of the factors.

Question 2

An advertising company is interested in determining if there is a difference in the mean sales that will be generated for a soft drink company based on which shelf the soft drinks are located. There are four possible shelf levels. The ad company wants to control for store size. The following data reflect the sales for one week at each combination of shelf level and store size.  Based on the experimental design, the managers should conclude that they were justified in blocking on store size if they test using a 0.05 level of significance.

Accepted Answer

The answer of An advertising company is interested in determining...

Question 3

Six food critics each visited and rated four different restaurants. Each critic visited each restaurant on three separate occasions and recorded a score for each visit. The correct method for analyzing this data is two-factor ANOVA.

Accepted Answer

The correct method for analyzing this data is two-factor ANOVA because there are two independent variables (factors) involved: the critics and the restaurants, and the response variable is the score given by the critics. This allows for the assessment of the main effects of each factor as well as any interaction effect between the two factors on the scores.

Question 4

A study recently conducted by a marketing firm analyzed three different advertising designs and four different income levels of potential customers. At each combination of factor A and factor B, 5 customers are observed and the number of products produced are recorded. The total number of degrees of freedom associated with this two-factor ANOVA design is 59.

Accepted Answer

The total degrees of freedom for a two-factor ANOVA design is (r-1) * (c-1), where r is the number of rows and c is the number of columns. In this case, r = 4 and c = 3, so the total degrees of freedom is (4-1) * (3-1) = 3 * 2 = 6.

Question 5

In a two-factor ANOVA design with replications, there are three hypotheses to be tested; test for factor A, test for factor B, and test for interaction between factors A and B.

Accepted Answer

In a two-factor ANOVA with replication, there are indeed three hypotheses tested: one for each of the two factors (A and B) to see if they have significant effects independently, and one for the interaction between factors A and B to see if the effect of one factor depends on the level of the other factor.

Question 6

In a two-factor ANOVA design, the variances of the populations are assumed to be equal unless there is interaction present.

Accepted Answer

In a two-factor ANOVA design, the assumption of equal variances (homogeneity of variances) is required regardless of whether there is an interaction effect present. This assumption pertains to the variances within each of the groups formed by the combinations of factors, not to the interaction between factors.

Question 7

In a two-factor ANOVA, the minimum number of replications required in any cell is two, but all cells must have the same number of replications.

Accepted Answer

In a two-factor ANOVA, balanced design requires each cell to have the same number of replications to ensure equal variance and valid interaction effects analysis.

Question 8

A study recently conducted by a marketing firm analyzed three different advertising designs and four different income levels of potential customers. At each combination of factor A and factor B, 5 customers are observed and the number of products produced are recorded. The degrees of freedom for the MSE in this two-factor ANOVA design is 48.

Accepted Answer

The degrees of freedom for the MSE in a two-factor ANOVA design is calculated as (r-1) * (c-1), where r is the number of rows and c is the number of columns. In this case, there are 3 rows (advertising designs) and 4 columns (income levels), so the degrees of freedom for the MSE is (3-1) * (4-1) = 48.

Question 9

An advertising company is interested in determining if there is a difference in the mean sales that will be generated for a soft drink company based on which shelf the soft drinks are located. There are four possible shelf levels. The ad company wants to control for store size. The following data reflect the sales for one week at each combination of shelf level and store size.  Based on the experimental design, the number of treatments is two.

Accepted Answer

The answer of An advertising company is interested in determining...

Question 10

Six food critics each visited and rated four different restaurants. Each critic visited each restaurant on three separate occasions and recorded a score for each visit. The total number of degrees of freedom is 71.

Accepted Answer

The total number of observations is $6 \text{ critics} \times 4 \text{ restaurants} \times 3 \text{ visits} = 72$. Since the degrees of freedom are calculated as the total number of observations minus 1, we have $72 - 1 = 71$ degrees of freedom.

Question 11

In a two-factor ANOVA study, if the two factors do not interact, then neither factor A nor factor B can be considered statistically significant.

Accepted Answer

The lack of interaction between two factors in a two-factor ANOVA does not imply that neither factor is statistically significant. Each factor can still have a significant main effect on the dependent variable independently of the interaction effect.

Question 12

In a two-factor ANOVA, the total sum of squares can be partitioned into four parts; the variation due to factor A, the variation due to factor B, the variation due to blocking, and the error variation.

Accepted Answer

In a two-factor ANOVA, the total sum of squares is partitioned into three parts: the variation due to factor A, the variation due to factor B, the interaction between factors A and B, and the error variation. There is no separate partition for "blocking" in the standard two-factor ANOVA model.

Question 13

Interaction is the term that is used in a two-factor ANOVA design when the two factors have different means.

Accepted Answer

Interaction in a two-factor ANOVA design refers to a situation where the effect of one factor on the dependent variable depends on the level of the other factor, not just when the two factors have different means.

Question 14

Based on the partially completed ANOVA table below, we know that 3 samples are being compared using 9 blocks.

Accepted Answer

The answer of Based on the partially completed ANOVA table...

Question 15

The number of cells in a two-factor analysis of variance design is equal to the number of levels of factor A plus the number of levels of factor B.

Accepted Answer

The number of cells in a two-factor analysis of variance design is equal to the product of the number of levels of factor A and the number of levels of factor B.

Question 16

An advertising company is interested in determining if there is a difference in the mean sales that will be generated for a soft drink company based on which shelf the soft drinks are located. There are four possible shelf levels. The ad company wants to control for store size. The following data reflect the sales for one week at each combination of shelf level and store size.  Based on the experimental design, the calculated F-test statistic value for testing whether blocking on store size was effective is approximately 16.3.

Accepted Answer

The answer of An advertising company is interested in determining...

Question 17

Given the partially completed ANOVA table below, the test statistic for determining if there is any blocking effect is F = 4.38.

Accepted Answer

The answer of Given the partially completed ANOVA table below,...

Question 18

Six food critics each visited and rated four different restaurants. Each critic visited each restaurant on three separate occasions and recorded a score for each visit. The critical value for testing whether there is any difference among the four restaurants, using the 0.05 level of significance is approximately F = 2.8.

Accepted Answer

The critical value for an F-test depends on the degrees of freedom for the numerator and the denominator, which are determined by the number of groups (restaurants) and the number of observations. With four restaurants and multiple observations, a critical value around F = 2.8 is plausible for a 0.05 significance level.

Question 19

Six food critics each visited and rated four different restaurants. Each critic visited each restaurant on three separate occasions and recorded a score for each visit. The number of degrees of freedom in the interaction row of the ANOVA table is 15.

Accepted Answer

The degrees of freedom for interaction in a two-way ANOVA is calculated as (number of levels of factor A - 1) * (number of levels of factor B - 1). Here, there are 6 critics and 4 restaurants, so (6-1)*(4-1) = 5*3 = 15.

Question 20

To test for the stopping distances of four brake systems, 10 of the same make and model of car are selected randomly and then are assigned randomly to each of four brake systems. This is a randomized complete block design.

Accepted Answer

The answer of To test for the stopping distances of...

Quiz 12: Analysis of Variance

In order to analyze any potential interactions between factors in an analysis of variance study, it is necessary to have at least two measurements at each level of each factor.

Six food critics each visited and rated four different restaurants. Each critic visited each restaurant on three separate occasions and recorded a score for each visit. The correct method for analyzing this data is two-factor ANOVA.

In a two-factor ANOVA design with replications, there are three hypotheses to be tested; test for factor A, test for factor B, and test for interaction between factors A and B.

In a two-factor ANOVA design, the variances of the populations are assumed to be equal unless there is interaction present.

In a two-factor ANOVA, the minimum number of replications required in any cell is two, but all cells must have the same number of replications.

Six food critics each visited and rated four different restaurants. Each critic visited each restaurant on three separate occasions and recorded a score for each visit. The total number of degrees of freedom is 71.

In a two-factor ANOVA study, if the two factors do not interact, then neither factor A nor factor B can be considered statistically significant.

In a two-factor ANOVA, the total sum of squares can be partitioned into four parts; the variation due to factor A, the variation due to factor B, the variation due to blocking, and the error variation.

Interaction is the term that is used in a two-factor ANOVA design when the two factors have different means.

Based on the partially completed ANOVA table below, we know that 3 samples are being compared using 9 blocks.

The number of cells in a two-factor analysis of variance design is equal to the number of levels of factor A plus the number of levels of factor B.

Given the partially completed ANOVA table below, the test statistic for determining if there is any blocking effect is F = 4.38.

Six food critics each visited and rated four different restaurants. Each critic visited each restaurant on three separate occasions and recorded a score for each visit. The number of degrees of freedom in the interaction row of the ANOVA table is 15.

To test for the stopping distances of four brake systems, 10 of the same make and model of car are selected randomly and then are assigned randomly to each of four brake systems. This is a randomized complete block design.