# Quiz 16: Analysis of Variance and

Business

Q 1Q 1

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

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Multiple Choice

D

Q 2Q 2

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 y

^{2}C) significance of the interaction effect D) significance of the overall effectFree

Multiple Choice

D

Q 3Q 3

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

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B

Q 4Q 4

The effects of X on Y is measured by .
A) SS

_{y}_{ }B) SS_{within}_{ }C) SS_{error}_{ }D) SS_{x}Free

Multiple Choice

Q 5Q 5

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.

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Multiple Choice

Q 6Q 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)

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Multiple Choice

Q 7Q 7

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.

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Multiple Choice

Q 8Q 8

If you are estimating y

^{2}, 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 significanceFree

Multiple Choice

Q 9Q 9

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) eta^{2}^{ }(y^{2})Free

Multiple Choice

Q 10Q 10

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

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Multiple Choice

Q 11Q 11

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

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Q 12Q 12

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

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Q 13Q 13

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.

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Multiple Choice

Q 14Q 14

In one- way ANOVA, the null hypothesis may be tested by _ .
A) F statistic
B) eta

^{2}^{ }C) chi- square D) the t statisticFree

Multiple Choice

Free

Multiple Choice

Q 16Q 16

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 significanceFree

Multiple Choice

Q 17Q 17

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) eta^{2}^{ }(4^{2})Free

Multiple Choice

Q 18Q 18

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

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Multiple Choice

Q 19Q 19

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)

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Multiple Choice

Q 20Q 20

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.

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Q 22Q 22

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

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Multiple Choice

Q 23Q 23

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 y

^{2}C) significance of the overall effect D) significance of the main effectFree

Multiple Choice

Q 24Q 24

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)

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Multiple Choice

Q 25Q 25

A covariate is a independent variable used in .
A) metric; ANOVA
B) categorical; ANCOVA
C) categorical; ANOVA
D) metric; ANCOVA

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Multiple Choice

Q 26Q 26

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 y

^{2}C) significance of the interaction effect D) significance of the main effectFree

Multiple Choice

Q 27Q 27

are contrasts made after the analysis.
A) Single comparison contrasts
B) Multiple comparison contrasts
C) A priori contrasts
D) A posteriori contrasts

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Multiple Choice

Q 28Q 28

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)

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Multiple Choice

Q 29Q 29

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.

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Multiple Choice

Q 30Q 30

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

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Multiple Choice

Q 31Q 31

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

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Multiple Choice

Q 32Q 32

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}Free

Multiple Choice

Q 33Q 33

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.Free

Multiple Choice

Q 34Q 34

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

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Multiple Choice

Q 35Q 35

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 y

^{2}^{ }D) significance of the main effectFree

Multiple Choice

Q 36Q 36

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

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Multiple Choice

Q 37Q 37

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

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Multiple Choice

Q 38Q 38

At what point does m

^{2 }begin to represent a larger experimental effect? A) )25 B) )15 C) )10 D) )06Free

Multiple Choice

Q 39Q 39

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

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Multiple Choice

Q 40Q 40

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

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Multiple Choice

Q 41Q 41

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.

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Multiple Choice

Q 42Q 42

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)

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Multiple Choice

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Multiple Choice

Q 44Q 44

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

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Multiple Choice

Q 45Q 45

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

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Q 46Q 46

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)

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Multiple Choice

Q 47Q 47

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

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Multiple Choice

Free

True False

Q 49Q 49

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

^{2}).Free

True False

Q 50Q 50

Omega squared, m

^{2}, indicates what proportion of the variation in the dependent variable is related to a particular independent variable or factor.Free

True False

Q 51Q 51

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

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True False

Q 52Q 52

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

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True False

Q 53Q 53

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.

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True False

Q 54Q 54

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

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True False

Q 55Q 55

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

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True False

Q 56Q 56

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.

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True False

Q 57Q 57

The estimated value of m

^{2 }can be negative, in which case the estimated value of m^{2 }is set equal to one.Free

True False

Q 58Q 58

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.

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True False

Q 59Q 59

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

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True False

Q 60Q 60

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

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True False

Q 61Q 61

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

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True False

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True False

Q 63Q 63

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.

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True False

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True False

Q 65Q 65

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."

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True False

Q 66Q 66

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

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True False

Q 67Q 67

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

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True False

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True False

Q 69Q 69

SS

_{between}_{ }is the portion of the sum of squares in Y related to the independent variable or factor X.Free

True False

Q 70Q 70

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

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True False

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True False

Q 72Q 72

y

^{2}^{ }assumes a value of 0 when all the category means are equal, indicating that X has no effect of X on Y.Free

True False

Q 73Q 73

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

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True False

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True False

Q 75Q 75

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

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True False

Q 76Q 76

In one- way analysis of variance, under the null hypothesis, SS

_{x}_{ }and SS_{error}_{ }come from different sources of variation.Free

True False

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True False

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True False

Q 79Q 79

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

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True False

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True False

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Essay

Q 82Q 82

Draw the ANOVA interactive cases listed below (Figure 16.5 in the text). Name your dependent variable Y and assume that there are two factors, X

_{1 }with three levels (X_{11}, X_{12}, and X_{13}), and X_{2 }with two levels (X_{21 }and X_{22}). Briefly discuss/describe the interaction shown in each of your drawings. 1. no interaction 2. ordinal interaction 3. disordinal interaction (noncrossover) 4. disordinal interaction (crossover)Free

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Essay