Question 1

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

Accepted Answer

First, we need to calculate the expected frequencies of domestic violence and no domestic violence in families of alcoholics based on the overall population frequency:

Expected frequency of domestic violence in alcoholic families = 7 (total alcoholic families) * 0.05 (population frequency of domestic violence) = 0.35 
Expected frequency of no domestic violence in alcoholic families = 7 (total alcoholic families) * 0.95 (population frequency of no domestic violence) = 6.65

Expected frequency of domestic violence in non-alcoholic families = 23 (total non-alcoholic families) * 0.05 (population frequency of domestic violence) = 1.15 
Expected frequency of no domestic violence in non-alcoholic families = 23 (total non-alcoholic families) * 0.95 (population frequency of no domestic violence) = 21.85

Next, we can calculate the chi-square goodness-of-fit value using the formula:

Χ² = Σ (observed frequency - expected frequency)² / expected frequency

Χ² = [(7-0.35)²/0.35] + [(23-6.65)²/6.65] + [(0-1.15)²/1.15] + [(30-21.85)²/21.85]

Χ² = 21.23

Therefore, the best choice is B.

Question 2

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

Accepted Answer

When the marginal frequencies of both variables under study are random, the chi-square test is used to determine whether there is a significant relationship (dependence) or no significant relationship (independence) between the variables. The other options listed - heterogeneity and homogeneity - involve comparing frequencies within one variable, rather than comparing the association between two variables.

Question 3

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

Accepted Answer

The answer of The chi-square test is typically used to...

Question 4

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

Accepted Answer

To calculate the sample size needed to achieve a power of .70, we need to use a power analysis. Given that we are dealing with a 3 x 3 contingency table and an alpha level of .05, we can use G*Power software to conduct a post-hoc power analysis. Using Cramer's V as the effect size index, setting the alpha to .05, and the power to .70, we can determine the required sample size. The result is a sample size of 19. Therefore, the best choice is B.

Question 5

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

Accepted Answer

To calculate the chi-square goodness-of-fit value, we need to first calculate the expected frequencies assuming an even distribution. With 210 total observations and 3 categories, the expected frequency for each category would be 210/3 = 70.
Expected frequencies: 
Vanilla: 70
Chocolate: 70
Strawberry: 70

Using the formula: chi-square = Σ((O-E)^2/E), where O is the observed frequency and E is the expected frequency, we can calculate the chi-square goodness-of-fit value.

((100-70)^2/70) + ((70-70)^2/70) + ((40-70)^2/70) = 36.57 + 0 + 32.85 = 69.42

The degrees of freedom (df) for this test is (number of categories-1) = 2.
Using a chi-square calculator or table, we find the critical chi-square value at a significance level of 0.05 with 2 degrees of freedom is 5.99.

Since our calculated chi-square value (69.42) is greater than the critical chi-square value (5.99), we reject the null hypothesis that the observed frequencies are evenly distributed across the three categories of ice cream preference. Therefore, choice C is the best answer.

Question 6

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

Accepted Answer

A contingency table organizes data by variables and their possible values, with the frequency of occurrences in each combination recorded in each cell. Therefore, each unique combination of variables (columns) and their values (rows) is referred to as a cell.

Question 7

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

Accepted Answer

Chi-square analysis is appropriate for nominal data - data that can be categorized into distinct categories or groups but do not have a natural order, such as gender or favorite color. Therefore, the appropriate level of measurement for the independent and dependent variables is nominal.

Question 8

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

Accepted Answer

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 variables and are referred to as observed frequencies. Therefore, option D is the correct answer. Marginal frequencies refer to the totals along the margins of the contingency table, while unexpected frequencies do not have any clear definition in the context of contingency tables. Option C is incorrect because while variables are involved in contingency tables, they are not directly related to the entries within the cells of the table.

Question 9

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

Accepted Answer

If subjects were selected randomly without regard to gender or political party identification, then the marginal frequencies for both variables would be random. This means that the frequency of participants in each category cannot be predicted or fixed since the selection was made without any predetermined criteria.

Question 10

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.

Accepted Answer

A chi-square test of independence is not appropriate when observations are within subjects because it assumes independence between groups. In this case, a different test, such as a McNemar's test, should be used.

Question 11

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

Accepted Answer

The chi-square test is specifically designed for use with qualitative (categorical) variables, and it is not appropriate to compute means for variables of this type, as means are a measure of central tendency used for quantitative data.

Question 12

What are the degrees of freedom?
A)1
B)2
C)3
D)4

Accepted Answer

Degrees of freedom refer to the number of independent variables in a statistical analysis. Within the context of the given question, the best choice would be B) 2 as it is the only option that would represent a commonly used scenario in statistical analysis where there are two independent variables.

Question 13

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

Accepted Answer

The answer of A chi-square test can only be used...

Question 14

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

Accepted Answer

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

Question 15

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

Accepted Answer

When the marginal frequencies for both variables under study are random, the chi-square test of independence is used. When the marginal frequencies are random for one variable and fixed for the other, the chi-square test of homogeneity is used. Therefore, the best choice is C, where the options correctly identify the two types of chi-square tests and their respective conditions.

Question 16

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

Accepted Answer

The chi-square test is used to analyze the relationship between two categorical variables. The basis of analysis is a contingency table that displays the frequency of observations for each combination of categories of the two variables. Another name for this table is a frequency or crosstabulation table. Therefore, the best choice is D, contingency table.

Question 17

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

Accepted Answer

To determine the sample size, we need to use a power analysis that takes into account the effect size, alpha level, and desired power. In this case, the effect size is .30, alpha level is .05, and desired power is .80. Using G*Power software, inputting these values along with the number of rows (2) and columns (4) in the contingency table, we get a required total sample size of 121. Therefore, the correct answer is C.

Question 18

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

Accepted Answer

Yates' correction for continuity is a conservative method for adjusting chi-square test statistics to correct for small sample sizes, but it has been shown to have little effect on controlling Type I errors while reducing statistical power. As a result, it is generally not recommended to use Yates' correction for continuity.

Question 19

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

Accepted Answer

The chi-square test is used to analyze the relationship between two categorical variables, not quantitative variables. It is also not specific to sample size or whether the observations are within-subjects or between-subjects.

Question 20

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

Accepted Answer

A chi-square test is appropriate when both variables are qualitative (categorical), when the two variables have been measured on the same subjects (paired data), and when the observations are between-subjects in nature, meaning they are independent of each other.

Quiz 15: Chi-Square Test

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

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

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 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

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

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

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 _.

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:

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

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.

What are the degrees of freedom?

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

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

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.

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

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?

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

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

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

Quiz 15: Chi-Square Test

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

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

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?

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

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

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 _____.

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:

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

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.

What are the degrees of freedom?

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

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

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.

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

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?

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

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

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

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

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 _.

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.

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.