Deck 11: Analysis of Variance

Question 1

A larger F obtained statistic means that there is more ______ variance than ______ variance.

A)between-group;within-group
B)within-group;between-group
C)explained;observed
D)mean square;sum of square

Answer 1

between-group;within-group

Question 2

Which of the following is an assumption of ANOVA?

A)The population is not normally distributed.
B)The dependent variable is a nominal level of measurement.
C)The population variances are statistically significant.
D)Independent random samples are used.

Answer 2

Independent random samples are used.

Question 3

What does the between-group sum of squares measure?

A)The sum of the squared deviations between each group mean and every other group mean
B)The sum of the squared deviations between each group mean and the mean across all groups
C)The sum of the squared deviations between each individual observation and its group mean
D)The sum of the squared deviations between each individual observation and the mean across all groups

Answer 3

The sum of the squared deviations between each group mean and the mean across all groups

Question 4

What is the research hypothesis when using ANOVA procedures?

A)
B)
C)At least one of the group means is significantly different from the others.
D)All of the group means are significantly different from all other group means.

Question 5

What does the within-group sum of squares measure?

A)The sum of the squared deviations between each group mean and every other group mean
B)The sum of the squared deviations between each group mean and the mean across all groups
C)The sum of the squared deviations between each individual observation and its group mean
D)The sum of the squared deviations between each individual observation and the mean across all groups

Question 6

ANOVA allows us to determine whether the variance between samples is larger than the variance within samples.If the variance is larger between samples,what can we say about the group differences we are interested in analyzing?

A)There are no group differences.
B)There may be group differences.
C)The dependent variables vary significantly across groups.
D)The dependent variables vary significantly within groups.

Question 7

In order to determine whether the differences between group means are statistically significant,ANOVA examines the differences

A)between groups.
B)within groups.
C)between and within groups.
D)neither between nor within groups.

Question 8

The test statistic for ANOVA is

A)t
B)r²
C)µ
D)F

Question 9

ANOVA is best suited for comparing the means of ______ group(s)at once.

A)identical
B)one
C)at least two
D)deviant

Question 10

In which academic field is ANOVA most commonly used?

A)Marine science
B)Social psychology
C)Forensic anthropology
D)Health research

Question 11

The amount of variation in the dependent variable that can be attributed to or explained by the independent variable is called the

A)between-group sum of squares.
B)within-group sum of squares.
C)total sum of squares.
D)correlation coefficient.

Question 12

What is the null hypothesis when using ANOVA procedures?

A)
B)
C)
D)

Question 13

The between-group sum of squares and the within-group sum of squares compose the
a.aggregate group sum of squares.
b.ratio sum of squares.
c.total sum of squares.
d.mean level of variance.

Question 14

The F-test statistic that is calculated is called

A)F obtained.
B)alpha.
C)F critical.
D)eta-squared.

Question 15

An analysis of variance with one dependent and one independent variable is referred to as a

A)single correlation.
B)multiple regression.
C)one-way ANOVA.
D)multiple ANOVA.

Question 16

Why is the F statistic also called an F ratio?

A)It is the ratio of one group mean to another.
B)It is the ratio of the mean square between to the mean square within.
C)It is the ratio of the within-group sum of squares to the between-group sum of squares
D)It is the ratio of degrees of freedom for the within-group sum of squares to the degrees of freedom for the between-group sum of squares

Question 17

The formula, ,calculates the ______ sum of squares.

A)between-group
B)within-group
C)total
D)perceived

Question 18

Differences between samples,or within a single sample,are referred to as the

A)variance.
B)mean.
C)parameter.
D)deviation.

Question 19

After calculating the between-group sum of squares and the within-group sum of squares,the next step is to calculate the mean square between and the mean square within.This is achieved by

A)calculating the average group mean.
B)multiplying the between-group sum of squares and the within-group sum of squares.
C)adding the between-group sum of squares and the within-group sum of squares.
D)dividing each sum of squares by its respective degrees of freedom.

Question 20

The formula, ,calculates the ______ sum of squares.

A)between-group
B)within-group
C)total
D)perceived

Question 21

A researcher is interested in comparing the mean education levels of recent immigrant groups by origin country.She is particularly interested in comparing the mean education levels of immigrants from China,Ecuador,Mexico,and Vietnam.The researcher uses an ANOVA design and calculates an F statistic of 29.275.What two statistical quantities comprise the numerator and denominator of this statistic?

Question 22

SELECT ALL THAT APPLY.The within-group sum of squares

A)measures the scores within a single sample.
B)is the sum of squared deviation between each sample mean to the overall mean score.
C)is calculated using .
D)is a tedious and cumbersome set of calculations.

Question 23

SELECT ALL THAT APPLY.The between-group sum of squares

A)measures differences in variance between the groups.
B)is the sum of squared deviation between each sample mean to the overall mean score.
C)is calculated using .
D)is the amount of variation in the dependent variable that can be attributed to the independent variable.

Question 24

SST = SSB - SSW

Question 25

Imagine you are interested in whether there is a significant difference between the mean age of marriage across educational groups.If the critical value for an F statistic of 8.49 is 2.99,are these results statistically significant or not?

Question 26

SELECT ALL THAT APPLY.The assumptions of ANOVA test are:

A)independent random samples.
B)nominal level of measurement of variables.
C)population distribution is normal.
D)population variances are not equal.

Question 27

SELECT ALL THAT APPLY.ANOVA

A)is one-way if it is applied to one dependent and one independent variable.
B)Requires non-homogeneity of variance.
C)examines difference between the samples only and not differences within a single sample.
D)allows us to determine whether the variance between samples is different than variances within the samples.

Question 28

A researcher is interested in whether there is a significant difference between the mean age of marriage across three racial groups.Based on the data below,calculate the value of the between-group sum of squares (SSB).

Question 29

A researcher is interested in whether there is a significant difference between the mean age of marriage across three racial groups.Based on the data below,the mean square between and the mean square within are 313.01 and 36.87 respectively.Calculate the F statistic.

Question 30

A researcher is interested in whether there is a significant difference between the mean age of marriage across three racial groups.If the F statistic calculated for these data is 8.49,what is the value of the mean square within?

Question 31

In an ANOVA,the population variances are assumed to be equal.

Question 32

SELECT ALL THAT APPLY.Degrees of freedom:

A) where k is the number of samples.
B) where N is the Population size and k is the number of samples.
C) .
D) .

Question 33

The F statistic is the ratio of between-group variance to within-group variance.

Question 34

A researcher is interested in whether there is a significant difference between the mean age of marriage across three racial groups in the 2006 General Social Survey.The data are provided in the accompanying data.If the value of the mean square within is 36.87,calculate the within-group sum of squares and the number of degrees of freedom for the within-group sum of squares.

Question 35

A researcher is interested in whether there is a significant difference between the mean age of marriage across three racial groups.Based on the data below,calculate the degrees of freedom for the between-group sum of squares.Then,use this quantity to calculate the mean square between.

Question 36

SELECT ALL THAT APPLY.The correlation ratio or eta square

A)allows the researcher to make a statement about the strength of the relationship.
B)represents the proportions of variance that is explained by the independent variables.
C)is the ratio of SST to SSB.
D)ranges from 0.0 to ±1.

Question 37

If alpha = 0.05 and,F critical is 3.55 and the obtained critical is 5.43,we reject the null hypothesis since 3.55 < 5.43.

Question 38

A researcher is interested in comparing the mean education levels of recent immigrant groups by country of origin.She is particularly interested in comparing the mean education levels of immigrants from China,Ecuador,Mexico,and Vietnam.What is the null hypothesis?

Question 39

As eta square approaches zero,the relationship between the variables is weaker.

Question 40

ANOVA is a test of the null hypothesis of no difference between any of the means.

Question 41

List the four assumptions of ANOVA.

Question 42

What is the corresponding F critical when =3, =20 and alpha level= .01?

Question 43

Imagine you are interested in whether there is a significant difference between the mean age of marriage across educational groups.Use the data in the accompanying table to calculate the value of the between-group sum of squares.

Question 44

What can you say about the relationship if eta square is 0.85?

Question 45

Imagine you are interested in whether there is a significant difference between the mean age of marriage across educational groups in the 2010 General Social Survey.If the value of the mean square within for these data is 36.87,calculate the within-group sum of squares and the number of degrees of freedom for the within-group sum of squares.

Question 46

If the F critical is 4.94 while the F obtained is 3.97,when = 3, = 20 and alpha level = .01,do we accept or reject the null hypothesis?

Question 47

Imagine you are interested in whether there is a significant difference between the mean age of marriage across educational groups.Calculate the degrees of freedom for the between-group sum of squares.Then,use this quantity to calculate the mean square between.

Question 48

Imagine you are interested in whether there is a significant difference between the mean age of marriage across educational groups.If the F statistic is 6.10,use the data below to determine the value of the mean square within.

Question 49

What is the F critical?

Question 50

If SSB = 15.62 and SSW = 6.39 ,then calculate the F statistic.