Deck 16: Chi-Square Tests: Goodness-of-Fit and Independence

Question 1

As a general rule,the larger the degrees of freedom for a chi-square test,

A)the smaller the critical value will be
B)the larger the critical value will be
C)the smaller the level of significance will be
D)the larger the level of significance will be

Answer 1

the larger the critical value will be

Question 2

A researcher compares the frequency of participants who sleep primarily on their stomach,back,or side during the night.What is the critical value for a chi-square goodness-of-fit test at a .05 level of significance?

A)2
B)3
C)3.84
D)5.99

Answer 2

5.99

Question 3

Many nonparametric tests are called ________ because they make no assumptions regarding the shape of the distribution in the population.

A)parametric tests
B)skewed-distribution tests
C)significance-free tests
D)distribution-free tests

Answer 3

distribution-free tests

Question 4

A researcher selects a sample of 80 people and records the frequency of participants choosing a low,moderate,or high calorie dessert in a buffet.What are the degrees of freedom for this chi-square goodness-of-fit test?

A)2
B)3
C)79
D)80

Question 5

What is a key distinction between parametric tests and nonparametric tests in terms of scales of measurement?

A)Parametric tests are used for interval and ratio data,whereas nonparametric tests are used for nominal and ordinal data.
B)Parametric tests are used for ordinal and nominal data,whereas nonparametric tests are used for interval and ratio data.
C)Parametric tests are used for ordinal or interval data,whereas nonparametric tests are used for nominal data only.
D)There is no distinction;both types of tests are used to analyze data on any scale of measurement.

Question 6

A researcher records the frequency of participants selecting one of four new slogans for an advertising campaign.If it was expected that among 200 people polled there would be no preference for any one slogan,then what was the expected frequency for each slogan.

A)25 people
B)50 people
C)100 people
D)200 people

Question 7

A researcher conducts a chi-square goodness-of-fit test in which k = 5.What is the critical value for this test at a .05 level of significance?

A)4
B)5
C)9.49
D)11.07

Question 8

Which of the following is recorded using a chi-square goodness-of-fit test and a chi-square test for independence?

A)variance
B)frequency observed
C)frequency expected
D)both B and C

Question 9

A chi-square goodness-of-fit test shows that the frequencies observed fit well with those that were expected.Hence,the decision was to

A)reject the null hypothesis
B)retain the null hypothesis
C)no decision was made

Question 10

A researcher conducts a chi-square goodness-of-fit test in which k = 3 and = 4.32.What is the decision for this test at a .05 level of significance?

A)Retain the null hypothesis.
B)Reject the null hypothesis.
C)There is not enough information to answer this question.

Question 11

A researcher asks participants to taste each of three meals and to choose the one they like best.The same foods are in each meal,expect for the calorie total of the meal (which is low,moderate,or high calorie).Based on the observed frequencies given below,what is an appropriate conclusion for this test at a .05 level of significance?

A)Participants liked the high calorie meal more than the low calorie meal.
B)Participants liked the low calorie meal less than the moderate calorie meal.
C)Participants liked the high calorie meal more than was expected.
D)all of the above

Question 12

We compute the frequency expected in each category using known ________ stated in the null hypothesis.

A)hypothesis tests
B)proportions
C)variances
D)effect sizes

Question 13

A chi-square goodness-of-fit test shows that the frequencies observed equal those that were expected.Hence,the value of the test statistic is

A)equal to 0
B)less than 0
C)small;less than the critical value but not necessarily equal to 0
D)large;greater than the critical value

Question 14

To appropriately interpret the chi-square goodness-of-fit test,it is necessary to compare differences

A)at each level of the categorical variable
B)across the levels of the categorical variable
C)within and between expected frequencies

Question 15

Which of the following is a statistical procedure used to test hypotheses about the discrepancy between the observed and expected frequencies in two or more nominal categories?

A)one-way ANOVA
B)analysis of regression
C)chi-square test
D)all of the above

Question 16

The degrees of freedom for a chi-square goodness-of-fit test are

A)k - 1
B)n - 1
C)(k₁ - 1)(k₂ - 1)
D)(k - 1)(n - 1)

Question 17

A researcher conducts a chi-square goodness-of-fit test in which k = 2 and = 3.92.What is the decision for this test at a .05 level of significance?

A)Retain the null hypothesis.
B)Reject the null hypothesis.
C)There is not enough information to answer this question.

Question 18

A local ice cream shop wants to see if they should promote a new swizzleberry swirl or creamsicle flavored drink.In order to determine which one to promote,they took a sample of 80 patrons and asked them to choose which they preferred.The one that is significantly preferred over the other (at a .05 level of significance)will be promoted.It is expected that an equal number of patrons will choose each flavor.Based on the observed frequencies given below,what is the decision for this test?

A)Promote the swizzleberry swirl flavored drink.
B)Promote the creamsicle flavored drink.
C)Do not promote any flavored drinks.
D)There is not enough information to answer this question.

Question 19

Which of the following is an example of a nonparametric test?

A)analysis of variance
B)the t-tests
C)chi-square test
D)Pearson correlation

Question 20

Which of the following is an example of a parametric test?

A)analysis of variance
B)one-sample t-test
C)Pearson correlation
D)all of the above

Question 21

A researcher tests whether job security and life satisfaction are related.In this study,he observes the following frequencies.If he computes a test for independence at a .05 level of significance,then what is the decision for this test?

A)Job security and job satisfaction are related.
B)Job security and job satisfaction are dependent.
C)Job security and job satisfaction are independent.
D)Both A and B are appropriate.

Question 22

The interpretation of a 2 $\times$ 2 chi-square test for independence is similar to what other type of statistical test?

A)goodness-of-fit chi-square test
B)2 $\times$ 2 analysis of variance
C)phi correlation coefficient
D)two-independent sample t-test

Question 23

To compute the expected frequencies for a chi-square test for independence,we use which of the following formulas?

A)k - 1
B)p(n)
C)(row total + column total)/grand total
D)(row total column total)/grand total

Question 24

A researcher computes a 3 $\times$ 5 chi-square test for independence.What are the degrees of freedom for this test?

A)3
B)5
C)8
D)15

Question 25

The degrees of freedom for a chi-square test for independence test are

A)k - 1
B)n - 1
C)(k₁ - 1)(k₂ - 1)
D)(k - 1)(n - 1)

Question 26

A researcher tests whether levels of education and income levels are related.In this study,he observes the following frequencies.If he computes a chi-square test for independence at a .05 level of significance,then what is the decision for this test?

A)Education and income level are related.
B)Education and income level are not related.
C)Education and income level are independent.
D)Both B and C are appropriate.

Question 27

A researcher conducts two chi-square tests.The 2 $\times$ 2 chi-square was $\chi$ ² = 3.82.The 2 $\times$ 3 chi-square was $\chi$ ² = 5.02.Which chi-square test resulted in a decision to reject the null hypothesis at a .05 level of significance?

A)the 2 $\times$ 2 chi-square
B)the 2 $\times$ 3 chi-square
C)both chi-square tests results in a decision to reject the null hypothesis
D)none;both chi-square tests result in a decision to retain the null hypothesis

Question 28

What is the key assumption for a chi-square goodness-of-fit test?

A)The population is normally distributed.
B)Observed frequencies are independently recorded in each cell.
C)Expected frequencies are homogeneous.
D)all of the above

Question 29

A researcher can correct for having expected frequencies smaller than five by

A)increasing the number of cells
B)increasing the sample size
C)decreasing the observed frequency
D)both A and B

Question 30

To appropriately interpret the chi-square goodness-of-fit test,it is necessary to compare differences _________ of the categorical variable.

A)outside the levels
B)across the levels
C)at each level
D)between the levels

Question 31

One way a researcher can correct for having expected frequencies smaller than five is to increase the sample size such that

A)it is equal to the number of cells
B)it is three times larger than the number of cells
C)it is five times larger than the number of cells
D)it is seven times smaller than the number of cells

Question 32

Which of the following is a key assumption for a chi-square goodness-of-fit test?

A)The observed frequencies are independently recorded in each cell.
B)The variance between groups is equal.
C)There is no mean difference between groups.
D)The proportion in each cell is equal to zero.

Question 33

A chi-square goodness-of-fit test leads to a decision to retain the null hypothesis.Which of the following correctly explains this decision?

A)frequencies observed were significantly different from frequencies expected at each level of the categorical variable
B)frequencies observed were significantly different from frequencies expected across the levels of the categorical variable
C)frequencies observed were significantly different from frequencies expected within and between expected frequencies
D)Frequencies observed were statistically similar to the frequencies expected at each level of the categorical variable

Question 34

If the expected frequencies equal to observed frequencies for a chi-square test for independence,what do we conclude?

A)the degrees of freedom for the test are equal to 0
B)the test statistic value is equal to 0
C)the frequencies observed fit well with the frequencies expected
D)both B and C

Question 35

When computing a chi-square goodness-of-fit test,the frequency expected in a given cell should never be less than

A)the sample size
B)the number of cells
C)the frequency observed
D)five

Question 36

A researcher computes a 2 $\times$ 2 chi-square test for independence.What is the critical value for this test at a .05 level of significance?

A)3.84
B)5.99
C)7.81
D)9.49

Question 37

One way a researcher can correct for having expected frequencies smaller than five is to increase the levels of the categorical variable such that the number of levels

A)is equal to the sample size
B)is greater than four
C)is less than five
D)is minimal

Question 38

A researcher computes a 2 $\times$ 4 chi-square test for independence.What are the degrees of freedom for this test?

A)2
B)3
C)4
D)8

Question 39

A researcher computes a 2 $\times$ 3 chi-square test for independence.What is the critical value for this test at a .05 level of significance?

A)3.84
B)5.99
C)7.81
D)12.59

Question 40

A researcher conducts two chi-square tests.The 2 $\times$ 2 chi-square was $\chi$ ² = 3.92.The 2 $\times$ 3 chi-square was $\chi$ ² = 5.92.Which chi-square test resulted in a decision to reject the null hypothesis at a .05 level of significance?

A)the 2 $\times$ 2 chi-square
B)the 2 $\times$ 3 chi-square
C)both chi-square tests results in a decision to reject the null hypothesis
D)none;both chi-square tests result in a decision to retain the null hypothesis

Question 41

A chi-square goodness-of-fit test with five levels of a categorical variable will have four degrees of freedom.

Question 42

A researcher reports the following results for a chi-square test: $\chi$ ²(1)= 5.386,p < .05 (V = 0.224).If this test were a test for independence,then how many groups were observed?

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

Question 43

The value of the test statistic for a chi-square test is equal to 0 when there is no difference between observed and expected frequencies,and it gets larger,or more positive,as the differences get larger.

Question 44

A researcher selects a sample of 110 participants and computes the following phi correlation coefficient: = 0.31.What is the value of ?

A)3.84
B)10.57
C)34.10
D)There is not enough information to answer this question.

Question 45

To summarize the chi-square goodness-of-fit test,which of the following is reported?

A)test statistic
B)p value
C)degrees of freedom
D)all of the above

Question 46

Parametric tests are often called distribution-free tests.

Question 47

When k = 3,then the critical value for a chi-square goodness-of-fit test is 7.81.

Question 48

Nonparametric tests do not make inferences about population parameters,although these tests can be used to test hypothesized relationships in the population.

Question 49

A researcher reports the following results for a chi-square test: $\chi$ ²(1)= 5.386,p < .05 (V = 0.224).If this test were a goodness-of-fit test,then how many groups were observed?

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

Question 50

The larger the value of the chi-square test statistic,the more likely the discrepancy between observed and expected frequencies was due to chance or error.

Question 51

Which of the following measures of effect size can be reported with a 3 $\times$ 4 chi-square test for independence?

A)proportion of variance
B)the phi coefficient
C)Cramer's V
D)all of the above

Question 52

If a researcher computes a chi-square goodness-of-fit test in which k = 4 and n = 40,then the degrees of freedom for this test is 3.

Question 53

A researcher computes a 4 $\times$ 6 chi-square test for independence with a sample of 120 participants,with = 14.79.What is the effect size for this result?

A)0.04
B)0.20
C)0.12
D)0.35

Question 54

The formula for the chi-square test measures the size of the discrepancy between observed and expected frequencies.

Question 55

Variance is not computed using the chi-square tests.

Question 56

A researcher computes a 3 $\times$ 4 chi-square test for independence with a sample of 50 participants,with = 8.43.What is the effect size for this result?

A)0.08
B)0.17
C)0.29
D)0.41

Question 57

The chi-square test is an example of a parametric test.

Question 58

The observed frequencies can be summarized,

A)in a table
B)in a figure
C)in the main text
D)all of the above

Question 59

Which of the following is an appropriate measure of effect size for a 2 $\times$ 2 chi-square test for independence?

A)proportion of variance
B)the phi coefficient
C)Cramer's V
D)all of the above

Question 60

A researcher computes a 4 $\times$ 4 chi-square test for independence and estimates the following effect size: V = 0.36.This effect size is

A)small
B)medium
C)large

Question 61

A chi-square goodness-of-fit test is used to determine how well a set of observed frequencies "fits" with what was expected.

Question 62

When at least one categorical variable has more than two levels,Cramer's V is used to estimate effect size for a chi-square test for independence.

Question 63

To interpret a chi-square goodness-of-fit test,we compare observed and expected frequencies at each level of the categorical variable,and not across the levels of the categorical variable.

Question 64

To summarize the chi-square test,report the test statistic,the degrees of freedom,and the p value.

Question 65

A 2 $\times$ 3 chi-square test for independence has 2 degrees of freedom.

Question 66

When the chi-square test for independence is significant,this indicates that two categorical variables are independent.

Question 67

The test statistic is the same for a chi-square goodness-of-fit test and a chi-square test for independence.

Question 68

The phi coefficient can be used to estimate the effect size of a 2 $\times$ 2 chi-square test for independence.

Question 69

For a 2 $\times$ 2 chi-square test for independence,the value of a phi coefficient will equal the value of Cramer's V for a given data set.

Question 70

Homogeneity of variance is one assumption for the chi-square goodness-of-fit test.

Question 71

A key assumption for a chi-square goodness-of-fit test is that observed frequencies are independently recorded in each cell.

Question 72

A 2 $\times$ 2 chi-square test for independence has 4 degrees of freedom.

Question 73

When the chi-square test for independence is significant,this indicates that two variables are related.

Question 74

If = 4.79,then a chi-square goodness-of-fit test would be significant when k = 2,but not when k = 3.

Question 75

A researcher computes a 2 $\times$ 3 chi-square test for independence.In this example,the degrees of freedom are 2.

Question 76

The degrees of freedom for the chi-square test for independence are k - 1.

Question 77

One restriction for measuring frequency data is that the size of expected frequencies should never be less than five in a given cell.

Question 78

It is most appropriate to report effect size for the chi-square goodness-of-fit test,but not for the chi-square test for independence.

Question 79

A chi-square goodness-of-fit test with 3 levels of a categorical variable will have 3 degrees of freedom.

Question 80

When the chi-square test for independence is significant,this indicates that there is significant variability between groups.