Deck 16: Analysis of Variance and Covariance

Question 1

SSbetween is also denoted as SSy.

Answer 1

False

Question 2

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

Answer 2

True

Question 3

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

Answer 3

True

Question 4

SSwithin is referred to as SSerror.

Question 5

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

Question 6

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

Question 7

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

Question 8

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 9

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

Question 10

The value of η2 varies between 0 and 1.

Question 11

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

Question 12

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

Question 13

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

Question 14

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

Question 15

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

Question 16

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

Question 17

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

Question 18

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

Question 19

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 20

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

Question 21

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

Question 22

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

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

Question 23

Which statement is correct concerning one-way ANOVA?

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

Question 24

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 25

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

Question 26

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

Question 27

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

Question 28

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

Question 29

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 30

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

Question 31

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 32

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 33

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

Question 34

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

Question 35

A covariate is a ________ independent variable used in ________.

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

Question 36

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 37

The null hypothesis for ANOVA typically is that all ________.

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

Question 38

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

Question 39

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) decomposition of the total variation
D) n-way analysis of variance

Question 40

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

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

Question 41

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

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

Question 42

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

A) eta2 (η2)
B) SSy
C) SSx
D) SSwithin

Question 43

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

A) F = $$\frac { S S _ { x 1 x } 2 / d f _ { n } } { S S _ { \text {error } } / d f _ { d } }$$
B) F = $$\frac { S S _ { X } / ( c - 1 ) } { S S _ { \text {error } } / ( N - c ) }$$
C) F = $$= \frac { \left( S S _ { x 1 } + S S _ { x 2 } + S S _ { x 1 \times 2 } \right) \left( d f _ { n } \right. } { S S _ { c r r o r } / d f _ { d } }$$
D) F = $$\frac { S S _ { x } 1 / d f _ { n } } { 5 S _ { e r r o v } d f _ { d } }$$

Question 44

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

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

Question 45

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 46

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

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

Question 47

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

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

Question 48

The total variation in y is ________.

A) SSwithin
B) SSy
C) SSbetween
D) SSx

Question 49

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

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

Question 50

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

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

Question 51

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

A) SSy = SSx - SSerror
B) SSy = SSx + SSerror
C) SSy = SSbetween + SSwithin
D) B and C are correct.

Question 52

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 = SSbetween + SSwithin?

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

Question 53

Also referred to as SSerror,________ 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) SSy
B) SSbetween
C) SSwithin
D) SSx

Question 54

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

A) SSwithin
B) SSx
C) SSy
D) eta2 (η2)

Question 55

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

Question 56

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

Question 57

The effects of X on Y is measured by ________.

A) SSwithin
B) SSx
C) SSy
D) SSerror

Question 58

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

Question 59

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) standard-effects model
D) mixed-effects model

Question 60

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

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

Question 61

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

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

Question 62

________ 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) A priori contrasts
C) Multiple comparison contrasts
D) A posteriori contrasts

Question 63

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

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

Question 64

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

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

Question 65

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

A) $$\omega ^ { 2 } x = \frac { S S _ { x } / d f _ { x } } { S S _ { e r r o r } }$$
B) $$\omega ^ { 2 } x = \frac { S S _ { x } - \left( d f _ { x } \times M S _ { \text {crror } } \right) } { S S _ { \text {total } } + M S _ { \text {crror } } }$$
C) $$\omega ^ { 2 } x = \frac { \left( S S _ { x 1 } + S S _ { x 2 } + S S _ { x 1 x 2 } \right) / d f _ { x 1 } } { S S _ { \text {total } } + M S _ { \text {error } } }$$
D) $$\omega ^ { 2 } x = \frac { S S _ { x } / ( c - 1 ) } { S S _ { c r r o r } / ( N - c ) }$$

Question 66

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

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

Question 67

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

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

Question 68

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) univariate
C) compare means
D) nonparametric tests

Question 69

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

Question 70

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

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

Question 71

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

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

Question 72

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

Question 73

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

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

Question 74

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

Question 75

Which statement about MANOVA is not true?

A) In MANOVA,the null hypothesis is that the vectors of means on multiple dependent variables are equal across groups.
B) Multivariate analysis of variance is appropriate when there are two or more dependent variables that are correlated.
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.

Question 76

________ are contrasts made after the analysis.

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

Question 77

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

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

Question 78

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

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

Question 79

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

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

Question 80

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