Deck 16: Analysis of Variance and Covariance

Question 1

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

Answer 1

False

Question 2

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

Answer 2

True

Question 3

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

Answer 3

True

Question 4

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

Question 5

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

Question 6

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

Question 7

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

Question 8

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

Question 9

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 10

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 11

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

Question 12

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

Question 13

SS_within is referred to as SS_error.

Question 14

The value of η² varies between 0 and 1.

Question 15

SS_between is also denoted as SS_y.

Question 16

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

Question 17

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

Question 18

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

Question 19

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

Question 20

η² assumes a value of 0 when all the category means are equal, indicating that X has no effect of X on Y.

Question 21

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

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

Question 22

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 23

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

Question 24

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

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

Question 25

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

Question 26

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

Question 27

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 28

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

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

Question 29

The null hypothesis for ANOVA typically is that all ________.

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

Question 30

A covariate is a ________ independent variable used in ________.

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

Question 31

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

Question 32

The most commonly used measure in ANOVA indicating the relative importance of factors is omega squared, (ω²).

Question 33

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

Question 34

Omega squared, ω², indicates what proportion of the variation in the dependent variable is related to a particular independent variable or factor.

Question 35

The estimated value of ω² can be negative, in which case the estimated value of ω² is set equal to one.

Question 36

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

Question 37

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 38

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 39

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

Question 40

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 41

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

A)eta² (η²)
B)SS_x
C)SS_y
D)SS_within

Question 42

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

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

Question 43

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)random-effects model
C)mixed-effects model
D)standard-effects model

Question 44

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

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

Question 45

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)measure the effects
C)test the significance
D)interpret the results

Question 46

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

A)eta² (η²)
B)SS_x
C)SS_y
D)SS_within

Question 47

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

A)significance of the overall effect
B)significance of the main effect
C)multiple η²
D)significance of the interaction effect

Question 48

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

A)F =
B)F =
C)F =
D)F =

Question 49

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

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

Question 50

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)random-effects model
C)mixed-effects model
D)standard-effects model

Question 51

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

A)Because it is not known that all the groups have the same mean, we cannot calculate the variance of all the observations together.
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)By comparing the Y variance estimates based on between-group and within group variation, we can test the null hypothesis.
D)All statements are correct.

Question 52

If you are estimating η², you are at which step in the procedure for conducting one-way analysis of variance?

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

Question 53

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_x
B)SS_within
C)SS_between
D)SS_y

Question 54

The total variation in y is ________.

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

Question 55

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

Question 56

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

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

Question 57

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 main effect
C)multiple η²
D)significance of the interaction effect

Question 58

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

Question 59

The effects of X on Y is measured by ________.

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

Question 60

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

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

Question 61

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

Question 62

________ 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 63

________ are contrasts made after the analysis.

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

Question 64

________ 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 65

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

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

Question 66

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

Question 67

________ 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 68

Which statement is not true concerning interactions resulting from ANOVA?

A)In disordinal interactions of a crossover type, the relative effect of the levels of one factor changes with the levels of the other.
B)Because it involves a change in rank order, disordinal interaction is stronger than ordinal interaction.
C)Disordinal interactions of a crossover type represent the weakest interactions.
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 69

Which statement about MANOVA is not true?

A)MANOVA examines group differences across multiple dependent variables simultaneously.
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)Multivariate analysis of variance is appropriate when there are two or more dependent variables that are correlated.

Question 70

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

Question 71

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

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

Question 72

________ 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 73

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

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

Question 74

At what point does ω² begin to represent a larger experimental effect?

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

Question 75

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

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

Question 76

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

A)ω² _{x =}
B)ω² _{x =}
C)ω² _{x =}
D)ω² _{x =}

Question 77

________ 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 78

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)significance of the main effect
C)multiple η²
D)significance of the interaction effect

Question 79

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)F test
C)t test
D)paired samples t test

Question 80

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

A)significance of the overall effect
B)significance of the main effect
C)multiple η²
D)significance of the interaction effect