Deck 15: Chi-Square Test

Question 1

Which of the following is the definition of the chi-square statistic?

A)The overall difference between the two variables under investigation.
B)The overall difference between the observed and expected frequencies.
C)The overall difference between the column frequencies and the row frequencies.
D)The overall difference between the observed frequencies and the Yates' correction.

Answer 1

B

Question 2

c² (1,N = 200)= 12.89,p < .05.
How many cells would be in a contingency table for this example?

A)4
B)6
C)8
D)cannot be determineD.

Answer 2

A

Question 3

The chi-square test is a nonparametric test designed to analyze relationships between variables using what type of information?

A)mean
B)frequencies
C)standard deviation
D)mode

Answer 3

B

Question 4

One of the assumptions of the chi-square test is that the expected frequencies be no lower than approximately 5.Which of the following is a strategy to ensure that this assumption is met?

A)conduct a goodness-of-fit test
B)add a third group to at least one of the variables
C)increase sample size
D)ensure that eta-squared is at least .15.

Question 5

If the researcher in the study above (examining gender and car preference)specifically designed the study so that 50 men and 50 women would be selected for the study,then in the data table,the marginal means for the car choice variable would be _____,but the marginal means for gender would be _____.

A)fixed;random
B)expected;determined
C)random;fixed
D)determined;independent

Question 6

16.c² (1,N = 200)= 12.89,p < .05.What is the value for the degrees of freedom?

A)4
B)3
C)2
D)1

Question 7

For the example in question 11,which is the more appropriate statistical test to analyze the data?

A)independent groups t test.
B)one-way between subjects analysis of variance
C)Pearson correlation coefficient
D)one-way within subjects analysis of variance

Question 8

To assess the strength of the relationship,Cramer's statistic is used when _____,and the fourfold point correlation coefficient is used when _____.

A)sample sizes are small;sample sizes are large
B)both variables have two levels;one or both variables have more than two levels
C)one or both variables have more than two levels;both variables have two levels
D)sample sizes are large;sample sizes are small

Question 9

A researcher is interested in investigating 3 types of interventions designed to increase physical activity.The independent variable is the type of intervention and the dependent variable is amount of physical activity,measured in minutes per week.If this researcher wanted to use chi-square to analyze the data,what modification would need to be made?

A)Formulas utilizing degrees of freedom need to be modified to N-3.
B)Subtract .5 from each of the differences between the observed and expected values.
C)At least double the amount of data should be collected.
D)The dependent variable needs to be collapsed into categories.

Question 10

As degrees of freedom for the sampling distribution of the chi-square statistic decreases the sampling distribution becomes

A)more platykurtic.
B)more skewed.
C)more leptokurtiC.
D)more normal in shape.

Question 11

Which of the following is the appropriate way to report a chi-square statistic in a research report?

A)c² (2,N = 200)= 15.71,p < .01.
B)c² (2,200)= 15.71,p = .01.
C)c² = 15.71,p < .01,(2,N = 200).
D)c² = 15.71,p < .01.

Question 12

The interpretation of the obtained value for the fourfold point correlation coefficient/Cramer's statistic is similar to _____.

A)a Pearson correlation coefficient
B)eta-squared
C)omega-squared
D)Tukey HSD

Question 13

AS N increases results of the chi-square test become more similar to which of the following alternatives?

A)Fisher's exact test
B)Yate's correction for continuity
C)the phi coefficient
D)Cramer's statistic

Question 14

Conceptually,what are the "expected frequencies" telling us?

A)The mean of the participants scores on the variable of interest.
B)The frequency that would be observed in each "cell" of the design if the null hypothesis were true.
C)The frequency that would be observed in each "cell" of the design if the null hypothesis were false.
D)the frequency of scores in the data collecteD.

Question 15

c² (1,N = 200)= 12.89,p < .05.
What is the value of the chi-square statistic?

A)200
B)12.89
C)1
D).05

Question 16

What is the possible range of values for the fourfold point correlation coefficient/Cramer's statistic?

A)-1.00 to +1.00
B)0 to 1.00
C)-1.00 to 0
D)0 to infinity

Question 17

The chi-square goodness of fit test is a _____ test.

A)descriptive
B)biased
C)bivariate
D)univariate

Question 18

Which of the following is an appropriate and viable approach to statistically analyzing the nature of the relationship for a statistically significant chi-square test?

A)Goodman's procedure
B)Fisher's exact test
C)modified Bonferroni procedure
D)Cramer's statistic

Question 19

A researcher was interested in examining the relationship between gender (male and female)and car preference (SUV,sedan,or sports car).What type of table would be most appropriate for this data?

A)a two-way contingency table
B)a two-way table
C)a 2 X 3 table
D)all of these

Question 20

As the population value of Cramer's statistic increases,what happens to the sample size needed to achieve a desired power level?

A)The sample size requirement increases.
B)The sample size requirement decreases.
C)The sample size requirement is unchanged.
D)Cannot be determined without looking at the table.

Question 21

A researcher is interested in whether or not domestic violence occurs in the same proportion in families of alcoholics as it does in the population in general.If the relative frequency of domestic violence in the population is .05 and the relative frequency of no domestic violence in the population is .95,what is the chi-square goodness-of-fit value for the following data?
Alcohol Abuse Status O
Alcoholic 7
Nonalcoholic 23
Total 30

A)5.5
B)21.23
C)30
D)60.5

Question 22

When the marginal frequencies of both variables under study are random,the test is known as the chi-square test of:

A)heterogeneity
B)dependence
C)independence
D)homogeneity

Question 23

The chi-square test is typically used to analyze the relationship between two variables when

A)both variables are qualitative in nature.
B)the two variables have been measured on different individuals.
C)the observations on each variable are within-subjects in nature.
D)none of these

Question 24

If the researcher suspects that the strength of the relationship between two variables in the population is .50 as indexed by Cramer's statistic,what sample size should she use in a study involving a 3 x 3 contingency table and an alpha level of .05 to achieve a power of .70?

A)7
B)19
C)22
D)28

Question 25

A researcher is interested in whether frequencies of ice cream preference are evenly distributed across the three categories of vanilla,chocolate,and strawberry.What is the chi-square goodness-of-fit value of the following data?
Ice Cream Preference O
Vanilla 100
Chocolate 70
Strawberry 40
Total 210

A)0
B)5.99
C)25.71

Question 26

Each unique combination of _____ in a contingency table is referred to as a(n)_____.

A)variables;cell
B)cells;variable
C)rows;cell
D)cells;expected frequency

Question 27

Which level of measurement is appropriate for the independent and dependent variables when using a chi-square analysis?

A)nominal
B)ordinal
C)interval
D)ratio

Question 28

The entries within the cells of a contingency table represent the number of individuals in the sample who are characterized by the corresponding levels of the _____ and are referred to as _____.

A)marginal frequencies;observed frequencies
B)contingency table;unexpected frequencies
C)variables;expected frequencies
D)variables;observed frequencies

Question 29

If subjects in a gender and political party identification study were selected for participation without regard to gender or political party identification,the marginal frequencies for both of these variables would be:

A)fixed
B)constrained
C)random
D)unidentified

Question 30

Which of the following conditions would necessitate choosing a test other than chi-square test of independence?

A)observations are within subjects.
B)the independent variable is qualitative.
C)the dependent variable is qualitative.
D)the observations on each variable are between subjects in nature.

Question 31

The use of frequency information is predicated on the fact that the chi-square test is designed for use with _____ variables,and it is not appropriate to compute _____ for variables of this type.

A)quantitative;marginal frequencies
B)quantitative;contingency tables
C)qualitative;means
D)qualitative;degrees of freedom

Question 32

What are the degrees of freedom?

A)1
B)2
C)3
D)4

Question 33

A chi-square test can only be used to analyze the relationship between qualitative variables.

Question 34

The sum of the frequencies in the corresponding row or column are referred to as:

A)observed frequencies
B)marginal frequencies
C)expected frequencies
D)total frequencies

Question 35

When the marginal frequencies for both variables under study are random,the chi-square test of _____ is used,and when the marginal frequencies are random for one variable and fixed for the other,the chi-square test of _____ is used.

A)independence;heterogeneity
B)heterogeneity;dependence
C)independence;homogeneity
D)homogeneity;independence

Question 36

The basis of analysis for the chi-square test is a(n)_____ table (also called a frequency or crosstabulation table).

A)expected frequency
B)cellular
C)summary
D)contingency

Question 37

If the researcher suspects that the strength of the relationship between two variables in the population is .30 as indexed by Cramer's statistic,what sample size should she use in a study involving a 2 x 4 contingency table and an alpha level of .05 to achieve a power of .80?

A)58
B)76
C)121
D)172

Question 38

Yates' correction for continuity should not be used because it tends to reduce statistical power while adding little control over Type I errors.

Question 39

The chi-square test is typically used to analyze the relationship between two variables when:

A)both variables are quantitative in nature and are measured on a level that at least approximates interval characteristics
B)there is an extremely small sample size
C)the observations on each variable are within-subjects in nature
D)none of these

Question 40

A chi-square test may be used to analyze the relationship between two variables when ______.

A)both variables are qualitative in nature
B)the two variables have been measured on the same subjects
C)the observations on each variable are between-subjects in nature
D)all of these

Question 41

Recent studies have shown that Yates' correction of continuity should not be used,as it tends to reduce _____ with little gain over _____ control.

A)cell frequencies;standard error
B)alpha levels;statistical
C)statistical power;Type I error
D)sample size;random error

Question 42

Although the issue is controversial,statisticians generally recommend that the lowest _____ one should have in order to use the chi-square statistic is somewhere around _____.

A)expected frequency;5
B)observed frequency;20
C)number of cells;5
D)degrees of freedom;10

Question 43

When the marginal frequencies are random for one variable and fixed for the other,the test is referred to as the chi-square test of:

A)heterogeneity
B)dependence
C)independence
D)homogeneity

Question 44

There are different chi-square distributions depending on the _____ associated with them.

A)standard errors
B)marginal frequencies
C)number of cells
D)degrees of freedom

Question 45

The chi-square statistic is an index that reflects the overall difference between the _____ and the _____ frequencies.

A)observed;total
B)observed;expected
C)expected;marginal
D)expected;total

Question 46

Research has generally found _____ to be preferable to the chi-square test in small sample situations.

A)Yates' Correction for Continuity
B)Fisher's Exact Test
C)Fisher's alpha test
D)None of these

Question 47

In a chi-square test,the null hypothesis states that ______.

A)the two variables of interest are related in the population
B)the two variables of interest are unrelated in the population
C)the column frequencies equal the row frequencies
D)the sum of the row and column frequencies equal the total frequency

Question 48

Because of sampling error,a chi-square computed from sample data might be _____ even when the null hypothesis is true.

A)less than 0
B)uninterpretable
C)greater than 0

Question 49

When both of the variables under study have only two levels,the sampling distribution of the chi-square statistic corresponds _____ to a chi-square distribution than when one or both variables have more than two levels.

A)more precisely
B)exactly
C)more closely
D)less closely

Question 50

As long as the _____ assumption is met,observed frequencies can be as low as _____.

A)homogeneity of variance;10
B)normality;1.0
C)observed frequency;0
D)expected frequency;0

Question 51

Which of the following situations refers to a chi-square test of homogeneity?

A)when the marginal frequencies of both variables are random
B)when one of the marginal frequencies for a variable is fixed but the other is random
C)when both the variables have marginal frequencies that are fixed
D)all of these apply

Question 52

The alternative hypothesis for the chi-square test is _____ in nature.

A)directional
B)nondirectional
C)mathematical
D)computational

Question 53

One of the assumptions of the chi-square test is that the expected frequency for each cell is:

A)zero
B)nonzero
C)independent
D)random

Question 54

As the observed and expected frequencies become more dissimilar,then we are more likely to ______.

A)accept the null
B)reject the null
C)increase the sample size
D)reject H₁

Question 55

Application of the chi-square test requires computation of a(n)_____ for each cell under the assumption of no relationship between the two variables.

A)expected frequency
B)observed frequency
C)mean
D)standard error

Question 56

Which of the following situations refers to a chi-square test of independence?

A)when the marginal frequencies of both variables are random
B)when one of the marginal frequencies for a variable is fixed
C)when both of the variables have marginal frequencies that are fixed
D)all of these

Question 57

The alternative hypothesis for chi-square test states that ______.

A)the two variables of interest are related in the population
B)the two variables of interest are unrelated in the population
C)the column frequencies equal the row frequencies
D)the sum of the row and column frequencies equals the total frequency

Question 58

As the discrepancy between the observed and expected frequencies becomes larger,the magnitude of the chi-square statistic ______.

A)decreases
B)does not change
C)increases
D)increases by a factor of the square of the difference

Question 59

If two variables are unrelated in the population,the _____ value of chi-square will equal _____ a.sample;0

A)population;1.0
B)sample;1.0
C)population;0

Question 60

The alternative hypothesis in a chi-square test is _____.

A)nondirectional
B)directional

Question 61

The most common index of the strength of the relationship between two variables in a contingency table is the:

A)fourfold point correlation coefficient
B)Cramér's statistic
C)a and b
D)neither a nor b

Question 62

A correct example of a null hypothesis is stated: H_o: Gender and political party identification are unrelated in the sample.

Question 63

Yates' correction for continuity involves which of the following procedures?

A)subtracting 5 from the absolute value of ?Oj-Ej?
B)subtracting .5 from the absolute value of ?Oj-Ej?
C)subtracting .5 from the absolute value of ?Oj-Ej?²
D)subtracting 5 from the absolute value of ?Oj-Ej?²

Question 64

Which of the following occurs when using Yates' correction procedure?

A)The power of the chi-square test increases.
B)The degrees of freedom are further reduced.
C)The power of the chi-square is reduced.
D)None of these

Question 65

Using Table J,what decision would you make if you observed a chi-square statistic was 36.08 and your sample size was 20?

A)p<.05,reject H₀
B)p<.02,reject H₀
C)p>.01,fail to reject H₀
D)need more information

Question 66

When analyzing data from a 2?2 contingency table,a correction factor has been suggested so that _______.

A)the sampling distribution better approximates the chi-square distribution
B)the power to reject the null increases
C)the degrees of freedom are correct
D)all of these

Question 67

The analytical procedures for the chi-square test of independence and the chi-square test of homogeneity are identical.

Question 68

The degrees of freedom for the chi-square statistic for the test of independence depends on the _____.

A)number of levels of both variables
B)sample size
C)number of levels of the independent variable
D)number of levels of the dependent variable

Question 69

The test of the chi-square statistic applies to the data as a whole and provides _____ as to which cells are causing rejection of H₀.

A)no information
B)partial information
C)complete information
D)none of these

Question 70

As the degrees of freedom increase,the shape of the sampling distribution of the chi-square statistic will become more _____.

A)positively skewed
B)negatively skewed
C)normal in shape
D)peaked in shape

Question 71

When the degrees of freedom of a chi-square statistic are small (for example,2),the shape of the sampling distribution will be _______.

A)extremely positively skewed
B)highly negatively skewed
C)very normal
D)unknown

Question 72

If a variable has been measured on a multi-valued quantitative scale,then creating categories and using a chi-square procedure will usually _____.

A)violate the assumptions of the chi square test
B)result in using a less powerful statistical test than alternatives
C)increase the sensitivity of the test
D)none of these

Question 73

When trying to decide the sample size necessary to achieve a particular level of statistical power,what information is needed?

A)size of the contingency table
B)population value of Cramer's statistic
C)the alpha level
D)all of these

Question 74

For the chi-square goodness-of-fit test,statisticians recommend that the lowest _____ frequency of any cell be between 5 and 10 in a 2X2 table and 5 in larger tables.

A)unexpected
B)total
C)observed
D)expected

Question 75

The power of the chi-square test is further reduced when quantitative variables are collapsed into categories because _____ by placing individuals with different scores into the same group.

A)considerable information is likely to be lost
B)more Type I errors are likely to be made
C)sampling difficulties may arise
D)all of these

Question 76

The fourfold point correlation coefficient is used when _____.

A)one of the variables has three levels
B)both of the variables have three or more levels
C)the variables are ordinal in nature
D)both variables have two levels each

Question 77

Which of the following indices measure the strength of the relationship between two variables in a contingency table when both variables have three levels?

A)the phi coefficient
B)Pearson correlation
C)Cramer's statistic
D)the fourfold point correlation coefficient

Question 78

Which of the following is not an assumption of the chi-square test?

A)The observations are independently drawn from the population
B)The observations are randomly sampled from the population
C)The observed frequency of any cell must be greater than zero
D)The expected frequency of each cell is nonzero

Question 79

Which of the following is the recommended lowest expected frequency per cell one should have in order to use the chi-square test?

A)0
B)5
C).5
D)none of these

Question 80

The question addressed by the _____ test is whether a distribution of frequencies across categories for a variable in a population are distributed in a specified manner.

A)nonparametric
B)goodness-of-fit
C)F
D)distribution-specific