Deck 13: Chi-Square Tests

Question 1

The distribution that is always greater than 0 and positively skewed is the distribution for

A)Z .
B)t .
C)χ² .
D)U .

Answer 1

χ² .

Question 2

In a chi-square test,the variables are

A)rank-order.
B)equal-interval.
C)quantitative.
D)nominal.

Answer 2

nominal.

Question 3

In a chi-square test for independence,the null hypothesis is that

A)the two population variances are independent.
B)the two variables are independent in the population.
C)the means of the populations are not equal.
D)the means of the populations are equal.

Answer 3

the two variables are independent in the population.

Question 4

"(N_Columns-1)(N_Rows-1)" is the formula for the degrees of freedom for

A)the chi-square test for goodness of fit.
B)the chi-square test for independence.
C)the chi-square statistic estimated from a one-way analysis of variance.
D)the chi-square statistic estimated from a two-way analysis of variance .

Question 5

In a chi-square test of independence,the term "expected frequency" generally refers to

A)the distribution of people over categories on the measured variables under the assumption of equal numbers of people in all cells.
B)the distribution of people over categories on one variable expected if the distribution of people over categories on the other variable is completely unrelated to it.
C)the examination of the spread of the grouping variable to see if it is truly an independent variable.
D)the population's distribution of the scores on the measured variable as estimated by the sample data.

Question 6

When discussing the pattern in a contingency table,the word "independence" means

A)the distribution of one variable varies over different levels of the other.
B)the variables in the table should not be compared.
C)the observed frequencies are larger than the expected frequencies.
D)there is no relationship between the variables.

Question 7

The degrees of freedom for the chi-square test for goodness of fit is

A)the number of categories minus one.
B)the mean number of individuals per category minus the number of categories.
C)the mean number of individuals per category minus one.
D)the total number of individuals minus the number of categories.

Question 8

The degrees of freedom for the chi-square test for independence is

A)the number of categories minus one.
B)the number of columns minus one multiplied by the number of rows minus one.
C)the total number of category levels minus one.
D)the number of people minus the number of cells.

Question 9

In a 3 × 4 contingency table,there are

A)four levels of each variable.
B)two levels of one variable,and three levels of the other.
C)three levels of one variable,and four levels of the other.
D)four levels of one variable,and five levels of the other.

Question 10

When carrying out a chi-square test for independence,a good check on the arithmetic in figuring the expected frequencies is to make sure that

A)the expected frequency of each cell is no larger than the observed frequency.
B)the sum of all the expected frequencies times the degrees of freedom equals the sum of all the observed frequencies.
C)within any one row or column,the sum of the observed frequencies and the sum of the expected frequencies are the same.
D)the sum of all the expected frequencies for each row equals the sum of all the observed frequencies for each column minus 1.

Question 11

Although similar in some ways,one difference between contingency tables and the tables used in factorial designs is

A)the factorial analysis of variance tables display marginal figures,whereas contingency tables do not.
B)the cells in contingency tables hold frequencies,whereas the cells in factorial analysis of variance tables represent means.
C)contingency tables,but not factorial analysis of variance tables,rely on marginal figures.
D)the numbers in the cells of factorial analysis of variance tables are means for the measured variable,whereas the numbers in the cells of contingency tables represent the means for grouping variables.

Question 12

A way to determine the number of people expected to be in any one cell of a chi-square contingency table is to

A)multiply the number of people for the cell's column by its row proportion,figuring its row proportion as the number of people for the cell's row divided by the total number of people.
B)divide the total number of people by the number of people in the cell and multiply this result by a row proportion,figuring its row proportion as the number of people for the cell's row divided by the total number of people.
C)multiply the number of people in the cell's row by the number of people in the cell's column.
D)divide the number of people in the cell's row by the number of people in the cell's column.

Question 13

The main difference between the test for goodness of fit and the test for independence is that

A)the goodness of fit test can be used only for 2 × 2 designs whereas the independence test is not limited to a particular design type.
B)expected frequencies are calculated for the independence test but not for the goodness of fit test.
C)the goodness of fit test is limited to one nominal variable whereas the independence test is not.
D)observed frequencies are compared to expected frequencies for the independence test but not for the goodness of fit test.

Question 14

Which calculation is necessary for figuring the chi-square statistic?

A)dividing the absolute differences between observed and expected frequencies by the expected frequency in each cell
B)dividing the absolute differences between observed and expected frequencies by the observed frequency in each cell
C)dividing the squared differences between observed and expected frequencies by the expected frequency in each cell
D)dividing the squared differences between observed and expected frequencies by the observed frequency in each cell

Question 15

The main idea of a chi-square test is to

A)test the estimated degree of fit (proportion of variance accounted for)of one variable to the other variable.
B)compare the estimated population means,to see if they vary from each other by more than chance.
C)compare estimated population variances,to see if they vary from each other by more than chance.
D)test how well the pattern of observed frequencies fits some expected pattern of frequencies.

Question 16

The formula for the chi-squared statistic is

A)Σ[(O-E)²/E]
B)[Σ(O-E)²]/E
C)O/[Σ(O-E)²]
D)E/[Σ(O-E)²]

Question 17

The inventor of the chi-square test was

A)Karl Pearson.
B)W.S.Gossett.
C)Ronald Fisher.
D)Francis Galton.

Question 18

The values in a chi-square distribution are always greater than 0 and

A)are normally distributed.
B)less than 1.
C)can be quite large.
D)are negatively skewed.

Question 19

A contingency table is a table in which

A)the distributions of two nominal variables are laid out so that you have the frequencies of their combinations and totals can be seen.
B)chi-squares for each category are displayed over each level of the predictor variable.
C)χ² distributions are translated into t distributions.
D)χ² distributions are translated into F distributions.

Question 20

In a chi-square test for goodness of fit,the null hypothesis is that

A)the number of people in one category is no greater than the number of people in the other.
B)the variances of the populations of categories are the same.
C)the proportion of people over categories breaks down the same for the two populations.
D)the means of the two populations of categories are the same.

Question 21

based on the following scenario.
In a third world country, 100 randomly selected people were surveyed about their socioeconomic class and religious affiliation. The results and an excerpt from this fictitious study follow:

Excerpt: "Based on a chi-square test for independence, the working class differed from the middle class in the distribution of religious identification, χ² (4, N = 100) = 11.73, p < .05."
The percentage of the middle class respondents who were Catholic was

A)7.5/34 = 22.1%.
B)5/100 = 5.0%.
C)5/34 = 14.7%.
D)7.5/100 = 7.5%.

Question 22

A school psychologist surveyed 75 students (both boys and girls) who had been reported as "bullies" and asked them which bullying method they used most often: physical, verbal, psychological, or cyber-bullying. The results and an excerpt from this fictitious study follow:
Excerpt: "Based on a chi-square test for independence, there was a significant association between gender and bullying method, χ² (3, N = 75) = 11.85, p < .05."
Which bullying method was expected to be the most common among girls?

A)physical
B)verbal
C)psychological
D)cyber

Question 23

When a chi-square test is reported in a research article,which information is typically missing?

A)the degrees of freedom
B)the number of observed cases in each cell
C)the significance of χ²
D)the expected value for each cell

Question 24

One unsettled controversy regarding chi-square tests has to do with

A)large observed frequencies.
B)large expected frequencies.
C)small observed frequencies.
D)small expected frequencies.

Question 25

Which of the following statements about the phi coefficient is incorrect?

A)It is symbolized by the Greek letter "φ".
B)It ranges from 0 to 1.
C)It can be interpreted in the same manner as a correlation coefficient.
D)It is based on the chi-square statistic and the degrees of freedom.

Question 26

One advantage of the chi-square test over most other inferential statistical procedures is that it

A)can use the comparison distribution of any other statistical procedure.
B)does not require as many participants.
C)can be easily applied to repeated-measures designs.
D)has minimal assumptions.

Question 27

based on the following scenario.
In a third world country, 100 randomly selected people were surveyed about their socioeconomic class and religious affiliation. The results and an excerpt from this fictitious study follow:

Excerpt: "Based on a chi-square test for independence, the working class differed from the middle class in the distribution of religious identification, χ² (4, N = 100) = 11.73, p < .05."
The phi coefficient for this study is

A)√(11.73²/100)= 1.17
B)√(11.73/100²)= .03
C)√(11.73/100)= .34
D)√[11.73²/(100-1)] = 1.18

Question 28

A chi-square test would be appropriate for examining the relationship between

A)gender (male or female)and political orientation (measured on a 5-point Likert scale).
B)gender (male or female)and political orientation (conservative,liberal,or other).
C)education (in years)and political orientation (measured on a 5-point Likert scale).
D)education (in years)and political orientation (conservative,liberal,or other).

Question 29

According to Cohen's conventions for the phi coefficient,a large effect size is

A).10
B).15
C).40
D).50

Question 30

√(χ²/N)is the formula for

A)δ.
B)α.
C)φ.
D)μ.

Question 31

based on the following scenario.
In a third world country, 100 randomly selected people were surveyed about their socioeconomic class and religious affiliation. The results and an excerpt from this fictitious study follow:

Excerpt: "Based on a chi-square test for independence, the working class differed from the middle class in the distribution of religious identification, χ² (4, N = 100) = 11.73, p < .05."
Of the total sample,the percentage of agnostics,atheists,and others was

A)(12 + 13 + 22)/100 = 47%.
B)(4 + 6 + 18)/100 = 28%.
C)(8 + 7 + 4)/34 = 56%.
D)(12 + 13 + 22)/66 = 71%.

Question 32

The formula for Cramer's phi statistic is

A)√(χ²/N/df_Smaller).
B)√(χ²/df).
C)√(χ²/N).
D)√[χ²/(N)(df_Smaller)] .

Question 33

A school psychologist surveyed 75 students (both boys and girls) who had been reported as "bullies" and asked them which bullying method they used most often: physical, verbal, psychological, or cyber-bullying. The results and an excerpt from this fictitious study follow:
Excerpt: "Based on a chi-square test for independence, there was a significant association between gender and bullying method, χ² (3, N = 75) = 11.85, p < .05."
The phi coefficient for this study is

A)√(11.85²/75)= 1.37
B)√(11.85/75²)= .05
C)√[11.85²/(75-1)] = 1.38
D)√(11.85/75)= .40

Question 34

In a study with 100 participants,an analysis results in a χ² of 3.15.What is the phi coefficient?

A)√(3.15/100²)= .02
B)√(3.15²/100)= .32
C)√[(3.15/(100-1)] = .18
D)√(3.15/100)= .18

Question 35

based on the following scenario.
In a third world country, 100 randomly selected people were surveyed about their socioeconomic class and religious affiliation. The results and an excerpt from this fictitious study follow:

Excerpt: "Based on a chi-square test for independence, the working class differed from the middle class in the distribution of religious identification, χ² (4, N = 100) = 11.73, p < .05."
One finding of the study was that

A)being working class caused subjects to be Catholic.
B)working class subjects tended to be Protestant,Catholic,or other,whereas middle class subjects were most likely to be Protestant.
C)middle class subjects valued religion more than working class subjects.
D)being Catholic caused subjects to be working class.

Question 36

A school psychologist surveyed 75 students (both boys and girls) who had been reported as "bullies" and asked them which bullying method they used most often: physical, verbal, psychological, or cyber-bullying. The results and an excerpt from this fictitious study follow:
Excerpt: "Based on a chi-square test for independence, there was a significant association between gender and bullying method, χ² (3, N = 75) = 11.85, p < .05."
What proportion of boys indicated that verbal or cyber bullying was their primary method?

A)(8+6)/30 = .47
B)(7+5)/30 = .40
C)(8+6)/75 = .19
D)(7+5)/75 = .16

Question 37

The phi coefficient is

A)always less than 0.
B)√(χ²/N).
C)always greater than 1.
D)always less than 1.

Question 38

The reporting of chi-square tests in research articles

A)almost always includes the information needed to repeat the calculation.
B)has been downplayed until recently.
C)relies exclusively on tables.
D)was not emphasized in research articles until recently.

Question 39

In a study with a 3 × 2 design,φ and Cramer's φ

A)are equivalent.
B)are equivalent if φ is divided by 2.
C)are equivalent if φ is divided by √2.
D)are unrelated.

Question 40

A school psychologist surveyed 75 students (both boys and girls) who had been reported as "bullies" and asked them which bullying method they used most often: physical, verbal, psychological, or cyber-bullying. The results and an excerpt from this fictitious study follow:
Excerpt: "Based on a chi-square test for independence, there was a significant association between gender and bullying method, χ² (3, N = 75) = 11.85, p < .05."
Which cutoff chi-square value is appropriate for testing the null hypothesis?

A)3.841
B)5.992
C)7.815
D)9.488

Question 41

"(N_Columns-1)(N_Rows-1)" is the formula for the degrees of freedom for the chi-square test for __________.

Question 42

A controversy in the use of chi-square tests involves the potential problem of __________.

Question 43

The chi-square test was invented by __________.

Question 44

A researcher planned to examine the relationship between gender (male or female)and number of times having fallen in love (never,once,twice,or 3+ times)using 100 participants.If a medium effect size is predicted,the approximate power for a chi-square test for interdependence (using the .05 significance level)would be __________.(Give a number.)

Question 45

Effect size,sample size,and the degrees of freedom of a chi-square test are necessary for determining the test's __________.

Question 46

A lack of relationship between two nominal variables is __________.

Question 47

A chart showing the frequencies in each combination of categories of two nominal variables is a(n)__________.

Question 48

Chi-square tests involving cells with very small expected frequencies may be acceptable,but such studies may still be unwise because of the study's decreased __________.

Question 49

Contingency table information is typically included in research articles describing chi-square tests for __________.

Question 50

The power of a study testing hypotheses using the chi-square test of independence is determined by significance level,degrees of freedom,sample size,and __________.

Question 51

The hypothesis testing procedure that examines how well an observed frequency distribution of a nominal variable fits some expected pattern is a chi-square test for __________.

Question 52

One difference between a chi-square test and an analysis of variance is that in a chi-square test,all variables are __________.

Question 53

Complete the following formula: φ = __________.(Use symbols.)

Question 54

The effect size for the chi-square test for independence is measured by __________.

Question 55

Chi-square distributions are __________ skewed.

Question 56

In the chi-square test for goodness of fit,the degrees of freedom are __________ minus 1.

Question 57

The main assumption of a chi-square test is that __________.

Question 58

A researcher wants to examine the relationship between gender (male or female)and number of times having fallen in love (never,once,twice,or 3+ times).If a large effect size is predicted,then __________ participants would be needed for a chi-square test for interdependence (tested at the .05 level)to have 80% power.(Give a number.)

Question 59

The formula for chi-square is __________.(Answer with a formula in symbols.)

Question 60

The formula for the degrees of freedom for a chi-square test for independence is the number of columns minus one,__________ the number of rows minus one.

Question 61

A clinical psychologist conducted a study in which women rated their sense of humor as high,medium,or low,and then stated whether they believed they were generally disliked or liked.The results and an excerpt from this fictitious study follow: Observed (and Expected)Frequencies Excerpt: "A chi-square test for independence was conducted to see if the extent to which participants found themselves to be funny was related to whether they thought others liked or disliked them.The result was significant,χ² (2,N = 68)= 8.94,p < .05."
Of the women who rated themselves as highly humorous,__________% also thought they were liked.

Question 62

Fifty students at a small high school were randomly surveyed regarding the upcoming senior trip in terms of their preferred trip length (3,5,or 7 days)and their preferred trip destination (Miami,Dallas,or Reno).The results are displayed in the following table.Using the .05 significance level,are length and destination related? a.Use the five steps of hypothesis testing.
b.Sketch the chi-square distribution.Be sure your sketch gives a rough indication of its shape and shows the cutoff score and the sample's score.
c.Explain the logic of what you have done to a person who is familiar with the logic and steps of hypothesis testing for the t test and analysis of variance,but who knows nothing about chi-square tests.Be sure your explanation includes the logic of figuring the chi-square statistic,determining the degrees of freedom,describing the shape of the chi-square distribution,and using the chi-square table.
d.Figure a measure of effect size and indicate whether it is small,medium,or large.

Question 63

A health psychologist was interested in women's weight-reduction strategies.Of the 56 participants surveyed,22 preferred running,8 preferred swimming,15 preferred dancing,and 11 preferred some other activity.Using the .05 significance level,do the results suggest that people prefer different weight-reduction strategies in general?
a.Use the five steps of hypothesis testing.
b.Sketch the chi-square distribution.Be sure your sketch gives a rough indication of its shape and shows the cutoff score and the sample's score.
c.Explain the logic of what you have done to a person who is familiar with the logic and steps of hypothesis testing for the t test and analysis of variance,but who knows nothing about chi-square tests.Be sure your explanation includes the logic of figuring the chi-square statistic,determining the degrees of freedom,describing the shape of the chi-square distribution,and using the chi-square table.

Question 64

A clinical psychologist conducted a study in which women rated their sense of humor as high,medium,or low,and then stated whether they believed they were generally disliked or liked.The results and an excerpt from this fictitious study follow: Observed (and Expected)Frequencies Excerpt: "A chi-square test for independence was conducted to see if the extent to which participants found themselves to be funny was related to whether they thought others liked or disliked them.The result was significant,χ² (2,N = 68)= 8.94,p < .05."
Of the women who reported that they were liked,__________% also reported that they had either a low or medium sense of humor.

Question 65

A clinical psychologist conducted a study in which women rated their sense of humor as high,medium,or low,and then stated whether they believed they were generally disliked or liked.The results and an excerpt from this fictitious study follow: Observed (and Expected)Frequencies Excerpt: "A chi-square test for independence was conducted to see if the extent to which participants found themselves to be funny was related to whether they thought others liked or disliked them.The result was significant,χ² (2,N = 68)= 8.94,p < .05."
The effect size for this study is __________,which is a(n)__________ effect size.

Question 66

An experimenter planned a study in which a crucial step was offering participants a food reward,and having three food rewards that were equal in appeal was important.Thus,participants in a pilot study were asked which of three rewards they preferred.Of the 60 participants,16 preferred cupcakes,26 preferred candy bars,and 18 favored dried apricots.Using the .05 significance level,do the results suggest that people prefer different foods in general?
a.Use the five steps of hypothesis testing.
b.Sketch the chi-square distribution.Be sure your sketch gives a rough indication of its shape and shows the cutoff score and the sample's score.
c.Explain the logic of what you have done to a person who is familiar with the logic and steps of hypothesis testing for the t test and analysis of variance,but who knows nothing about chi-square tests.Be sure your explanation includes the logic of figuring the chi-square statistic,determining the degrees of freedom,describing the shape of the chi-square distribution,and using the chi-square table.

Question 67

A study was conducted in which unemployed workers were randomly assigned either to participate in a special job-finding training program or to a control program.After the program,the workers were followed to see whether they obtained a job in the next year.The results included the following statement: "Those in the job-finding program were significantly more likely to have found a job in the following year,χ² (1,N = 380)= 4.21,p < .05."
a.Figure a measure of association and indicate whether it represents a small,medium,or large effect size.
b.Explain the results of the study,including the effect size result,to a person who is familiar with hypothesis testing in general,such as with the t test for independent means,but who knows nothing about chi-square tests.

Question 68

Sandy was interested in whether her friends' responses to a Facebook event invitation (definite yes,definite no,maybe,no response)would differ depending on their primary method of travel (car or train).The results are displayed in the following table.Using the .05 significance level,is type of response related to type of travel? a.Use the five steps of hypothesis testing.
b.Sketch the chi-square distribution.Be sure your sketch gives a rough indication of its shape and shows the cutoff score and the sample's score.
c.Explain the logic of what you have done to a person who is familiar with the logic and steps of hypothesis testing for the t test and analysis of variance,but who knows nothing about chi-square tests.Be sure your explanation includes the logic of figuring the chi-square statistic,determining the degrees of freedom,describing the shape of the chi-square distribution,and using the chi-square table.
d.Figure a measure of effect size and indicate whether it is small,medium,or large.

Question 69

A clinical psychologist conducted a study in which women rated their sense of humor as high,medium,or low,and then stated whether they believed they were generally disliked or liked.The results and an excerpt from this fictitious study follow: Observed (and Expected)Frequencies Excerpt: "A chi-square test for independence was conducted to see if the extent to which participants found themselves to be funny was related to whether they thought others liked or disliked them.The result was significant,χ² (2,N = 68)= 8.94,p < .05."
Of the women who rated their humor as medium,__________% also thought they were disliked.

Question 70

An advertising firm wanting to target people with strong desires for success conducted a study to see if such people differed in the types of television shows they watched.Randomly selected participants recorded the shows they watched for a week,then their desire for success was assessed,and finally they were divided into two groups.Low Success seekers watched 8 comedies,15 romances,6 documentaries,13 dramas,and 3 news shows.High Success seekers watched 3 comedies,3 romances,9 documentaries,7 dramas,and 8 news shows.Using the .05 significance level,is the distribution of type of shows watched different for participants having high and low desires for success?
a.Use the five steps of hypothesis testing.
b.Sketch the chi-square distribution.Be sure your sketch gives a rough indication of its shape and shows the cutoff score and the sample's score.
c.Explain the logic of what you have done to a person who is familiar with the logic and steps of hypothesis testing for the t test and analysis of variance,but who knows nothing about chi-square tests.Be sure your explanation includes the logic of figuring the chi-square statistic,determining the degrees of freedom,describing the shape of the chi-square distribution,and using the chi-square table.
d.Figure a measure of effect size and indicate whether it is small,medium,or large.

Question 71

A clinical psychologist conducted a study in which women rated their sense of humor as high,medium,or low,and then stated whether they believed they were generally disliked or liked.The results and an excerpt from this fictitious study follow: Observed (and Expected)Frequencies Excerpt: "A chi-square test for independence was conducted to see if the extent to which participants found themselves to be funny was related to whether they thought others liked or disliked them.The result was significant,χ² (2,N = 68)= 8.94,p < .05."
Of the women who reported that they were disliked,__________% also reported that they had a low sense of humor.