Deck 16: Analysis of Variance and

Question 1

Which statement about MANOVA is not true?

A) Multivariate analysis of variance is appropriate when there are two or more dependent variables that are correlated.
B) In MANOVA, the null hypothesis is that the vectors of means on multiple dependent variables are equal across groups.
C) MANOVA is most appropriate if there are multiple dependent variables that are uncorrelated or orthogonal.
D) MANOVA examines group differences across multiple dependent variables simultaneously.

Answer 1

C

Question 2

Suppose that four groups, each consisting of 100 randomly selected individuals, were exposed to four different commercials about Tide detergent. After seeing the commercial, each individual provided ratings on preference for Tide, preference for Proctor and Gamble (the company making Tide), and preference for the commercial itself. Because these three preference variables are correlated, should be conducted to determine which commercial is the most effective (produced the highest preferences across the three variables).

A) regression
B) n- way ANOVA
C) one- way ANOVA
D) MANOVA

Answer 2

D

Question 3

The strength of the effects of X (independent variable or factor) on Y (dependent variable) is measured by .

A) SS_within B) SS_y C) SS_x D) eta² (4²)

Answer 3

D

Question 4

In one- way ANOVA, separation of the variation observed in the dependent variable into the variation due to the independent variables plus the variation due to error is called _ .

A) one- way analysis of variance
B) analysis of covariance (ANCOVA)
C) decomposition of the total variation
D) n- way analysis of variance

Question 5

Which statement is correct concerning one- way ANOVA?

A) Only one categorical variable is involved.
B) A treatment is the same as a particular combination of factor levels.
C) The set of independent variables consists of both categorical and metric variables.
D) Both A and B are correct.

Question 6

is an ANOVA technique for examining the difference in the central tendencies of more than two groups when the dependent variable is measured on an ordinal scale.

A) Nonmetric ANOVA
B) Contrasts
C) Repeated measures ANOVA
D) Multivariate analysis of variance (MANOVA)

Question 7

Repeated measures analysis of variance may be thought of as an extension of the to the case of more than two related samples.

A) z test
B) paired samples t test
C) F test
D) t test

Question 8

Which of the statistical techniques below does not involve a metric independent variable (Figure 16.1 in the text)?

A) ANOVA
B) t test
C) regression
D) Both A and B are correct.

Question 9

A major advantage of is that it enables the researcher to examine interactions between the factors.

A) t tests
B) n- way ANOVA
C) one- way ANOVA
D) F tests

Question 10

are contrasts that enable the researcher to construct generalized confidence intervals that can be used to make pairwise comparisons of all treatment means.

A) Single comparison contrasts
B) Multiple comparison contrasts
C) A priori contrasts
D) A posteriori contrasts

Question 11

Which F test is used to test the significance of the overall effect?

Question 12

If you are estimating y², you are at which step in the procedure for conducting one- way analysis of variance?

A) decompose the total variation
B) interpret the results
C) measure the effects
D) test the significance

Question 13

Which statement is correct concerning the decomposition of the total variation?

A) By comparing the Y variance estimates based on between- group and within group variation, we can test the null hypothesis.
B) If the population mean is the same in all the groups, then the variation in the sample means and the sizes of the sample groups can be used to estimate the variance of Y.
C) Because it is not known that all the groups have the same mean, we cannot calculate the variance of all the observations together.
D) All statements are correct.

Question 14

In one- way ANOVA, the null hypothesis may be tested by _ .

A) F statistic
B) eta² C) chi- square
D) the t statistic

Question 15

are used to examine differences among two or more means of the treatment groups.

A) Contrasts
B) Nonmetric ANOVA
C) Repeated measures ANOVA
D) Multivariate analysis of variance (MANOVA)

Question 16

is a measure of variation in Y that is explained by the independent variable X.

A) SS_y B) SS_within C) SS_x D) eta² (y²)

Question 17

Which step are you on in the procedure for conducting one- way analysis of variance if you are decomposing SSy into two components using the equation SSy = SS_between + SS_within?

A) decompose the total variation
B) interpret the results
C) measure the effects
D) test the significance

Question 18

The effects of X on Y is measured by .

A) SS_y B) SS_within C) SS_error D) SS_x

Question 19

In determining how different price levels will affect a household's cereal consumption, it may be essential to take household size into account. This is best analyzed by .

A) ANCOVA
B) one- way ANOVA
C) regression
D) n- way ANOVA

Question 20

A test finding that some differences exist between some of the treatment groups is a test of the .

A) significance of the main effect
B) multiple y²
C) significance of the interaction effect
D) significance of the overall effect

Question 21

How consumers' intentions to buy a brand vary with different levels of price and different levels of distribution is best analyzed via .

A) regression
B) ANCOVA
C) n- way ANOVA
D) one- way ANOVA

Question 22

An advanced analysis of variance procedure in which the effects of one or more metric- scaled extraneous variables are removed from the dependent variable before conducting the ANOVA is called .

A) decomposition of the total variation
B) one- way analysis of variance
C) n- way analysis of variance
D) analysis of covariance (ANCOVA)

Question 23

Categorical independent variables are . The independent variables must all be categorical (nonmetric) to use .

A) parameters; regression
B) items; ANOVA
C) covariates; ANOVA
D) factors; ANOVA

Question 24

A covariate is a independent variable used in .

A) metric; ANOVA
B) categorical; ANCOVA
C) categorical; ANOVA
D) metric; ANCOVA

Question 25

The refers to the fact that ordinarily the assumption in analysis of variance that the categories of the independent variable are fixed.

A) fixed- effects model
B) mixed- effects model
C) standard- effects model
D) random- effects model

Question 26

A test of the significance of the interaction between two or more independent variables is a test of the .

A) significance of the interaction effect
B) multiple y²
C) significance of the overall effect
D) significance of the main effect

Question 27

A test of the significance of the main effect for each individual factor is a test of the .

A) significance of the overall effect
B) multiple y²
C) significance of the interaction effect
D) significance of the main effect

Question 28

In ANOVA the relative contribution of a factor X is calculated as .

Question 29

At what point does m² begin to represent a larger experimental effect?

A) )25
B) )15
C) )10
D) )06

Question 30

The strength of the joint effect of two (or more) factors or the overall effect is known as .

A) significance of the overall effect
B) significance of the interaction effect
C) multiple y² D) significance of the main effect

Question 31

Also referred to as SS_error, is the variation in Y due to the variation within each of the categories of X. This variation is not accounted for by X.

A) SS_within B) SS_between C) SS_x D) SS_y

Question 32

The null hypothesis for ANOVA typically is that all .

A) means are unequal
B) proportions are equal
C) means are equal
D) proportions are unequal

Question 33

are determined before conducting the analysis, based on the researcher's theoretical framework.

A) Single comparison contrasts
B) Multiple comparison contrasts
C) A priori contrasts
D) A posteriori contrasts

Question 34

The total variation in Y, denoted by SSy, can be decomposed into which two components?

A) SS_y = SS_x - SS_error B) SS_y = SS_x + SS_error
C) SSy = SS_between + SS_within D) B and C are correct.

Question 35

Which statement is not true concerning interactions resulting from ANOVA?

A) Disordinal interactions of a crossover type represent the weakest interactions.
B) In disordinal interactions of a crossover type, the relative effect of the levels of one factor changes with the levels of the other.
C) Because it involves a change in rank order, disordinal interaction is stronger than ordinal interaction.
D) In ordinal interaction, the rank order of the effects related to one factor does not change across the levels of the second factor.

Question 36

How consumers' "intentions to buy the brand" varies with different price levels is best analyzed via .

A) regression
B) one- way ANOVA
C) t tests
D) ANCOVA

Question 37

Analysis of covariance includes at least one _ independent variable and at least one independent variable.

A) parametric; interval
B) categorical; interval
C) metric; interval
D) ordinal; categorical

Question 38

When using SPSS Windows, for nonmetric analysis of variance, including the k- sample median test and Kruskal- Wallis one way analysis of variance, the program _ _ should be used.

A) univariate
B) compare means
C) nonparametric tests
D) general linear model

Question 39

is an ANOVA technique used when respondents are exposed to more than one treatment condition and repeated measurements are obtained.

A) Nonmetric ANOVA
B) Contrasts
C) Repeated measures ANOVA
D) Multivariate analysis of variance (MANOVA)

Question 40

are contrasts made after the analysis.

A) Single comparison contrasts
B) Multiple comparison contrasts
C) A priori contrasts
D) A posteriori contrasts

Question 41

The total variation in y is _ .

A) SS_within B) SS_between C) SS_y D) SS_x

Question 42

Interactions occur when the effects of one factor on the dependent variable depend on the level (category) of the other factors.

Question 43

When using SPSS Windows one- way ANOVA can be efficiently performed using the program.

A) NONPARAMETRIC TESTS
B) GENERAL LINEAR MODEL
C) COMPARE MEANS
D) UNIVARIATE

Question 44

A statistical technique for examining the differences among means for two or more populations is called .

A) cross- tabulation
B) independent samples t test
C) chi- square
D) analysis of variance (ANOVA)

Question 45

Analysis of variance and analysis of covariance are tests of differences between two means or median.

Question 46

The value of y² varies between 0 and 1.

Question 47

Which statement is correct if the null hypothesis for a one- way ANOVA is rejected?

A) The effect of the independent variable is significant.
B) The independent variable does not have a significant effect on the dependent variable.
C) The mean value of the dependent variable will be the same for different categories of the independent variable.
D) Both B and C are correct.

Question 48

An interaction effect occurs when the effect of an independent variable on a dependent variable is different for different categories or levels of another independent variable.

Question 49

The estimated value of m² can be negative, in which case the estimated value of m² is set equal to one.

Question 50

Omega squared, m², indicates what proportion of the variation in the dependent variable is related to a particular independent variable or factor.

Question 51

In the , the categories or treatments are considered to be random samples from a universe of treatments. Inferences are made to other categories not examined in the analysis.

A) fixed- effects model
B) mixed- effects model
C) random- effects model
D) standard- effects model

Question 52

Modest departures from the assumptions in analysis of variance do not seriously affect the validity of the analysis.

Question 53

The most commonly used measure in ANOVA indicating the relative importance of factors is omega squared, (m²).

Question 54

is an ANOVA technique using two or more metric dependent variables.

A) Nonmetric ANOVA
B) Contrasts
C) Repeated measures ANOVA
D) Multivariate analysis of variance (MANOVA)

Question 55

The most common use of the covariate is to remove extraneous variation from the dependent variable.

Question 56

Analysis of variance is so named because it examines the variability or variation in the sample (dependent variable) and, based on the variability, determines whether there is reason to believe that the population means differ.

Question 57

In examining the differences among means, one- way analysis of variance involves the decomposition of the total variation observed in the independent variable.

Question 58

Important issues involved in the interpretation of ANOVA results include all of the following except .

A) determining the appropriateness of the test
B) interactions
C) relative importance of factors
D) multiple comparisons

Question 59

Nonmetric analysis of variance examines the difference in the central tendencies of more than two groups when the dependent variable is measured on a nominal scale.

Question 60

ANOVA and ANCOVA include one independent variable and t tests include more than one independent variable.

Question 61

The null hypothesis for ANOVA is that all means are not equal.

Question 62

The Kruskal- Wallis one- way analysis of variance also examines the difference in medians.

Question 63

In analysis of variance, it is assumed that all the groups have the same variation in the population.

Question 64

A particular combination of factor levels, or categories, is called a treatment.

Question 65

In one- way analysis of variance, under the null hypothesis, SS_x and SS_error come from different sources of variation.

Question 66

SS_within is the variation in Y related to the variation within each category of X.

Question 67

A marketing survey conducted by EgeBank in Istanbul, Turkey used analysis of variance techniques to help identify affective and perceptual factors that differentiate alternative tourist destinations.

Question 68

When using n- way ANOVA the significance of the overall effect may be tested by a t test.

Question 69

The last step in the procedure for conducting one- way analysis of variance is to test the significance.

Question 70

SS_between is also denoted as SS_y.

Question 71

y² assumes a value of 0 when all the category means are equal, indicating that X has no effect of X
on Y.

Question 72

SS_between is the portion of the sum of squares in Y related to the independent variable or factor X.

Question 73

Multivariate analysis of variance is appropriate when there are two or more dependent variables that are correlated.

Question 74

Contrasts are used in ANOVA to determine which of the means are statistically different.

Question 75

The Kruskal- Wallis one- way analysis of variance and the k- sample median test have the same null hypothesis -"medians of the k populations are equal."

Question 76

ANOVA and ANCOVA can include more than one independent variable and at least one of the independent variables must be categorical.

Question 77

Analysis of covariance is most useful when the covariate is not linearly related to the dependent variable and is not related to the factors.

Question 78

Ordinal interaction involves a change in the rank order of the effects of one factor across the levels of another.

Question 79

SS_within is referred to as SS_error.

Question 80

The n- way ANOVA assumes that the design was orthogonal, or balanced (the number of cases in each cell was the same).