Question 1

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 used with qualitative (categorical) variables, and it is not appropriate to compute means for these types of variables because means are a measure of central tendency for quantitative data.

Question 2

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

Accepted Answer

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

Question 3

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?

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

Accepted Answer

We can use the chi-square goodness-of-fit formula:

χ^2 = Σ[(Observed frequency - Expected frequency)^2 / Expected frequency]

We can calculate the expected frequency for domestic violence as:

Expected frequency = Total sample size * Relative frequency of domestic violence in the population
Expected frequency = 100 * 0.05
Expected frequency = 5

We can calculate the expected frequency for no domestic violence as:

Expected frequency = Total sample size * Relative frequency of no domestic violence in the population
Expected frequency = 100 * 0.95
Expected frequency = 95

We can then calculate the chi-square goodness-of-fit value:

χ^2 = [(10-5)^2/5] + [(90-95)^2/95]
χ^2 = 5 + 0.263
χ^2 = 5.263

Looking at the answer choices, the closest value to 5.263 is B) 21.23, so that is our answer.

Question 4

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 cells in a contingency table represent the number of individuals who are characterized by the corresponding levels of the variables, so the correct option is D. The entries in these cells are referred to as observed frequencies, which represent the frequencies of the data that are actually observed in the sample. Marginal frequencies represent the total frequencies of each category in each variable, while expected frequencies are those that would be expected if there was no association between the variables.

Question 5

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 typically used to analyze the relationship between two categorical variables. It is not suited for use with quantitative variables, nor is it the best choice when dealing with an extremely small sample size. Additionally, the within-subjects design is better suited for repeated measures analysis of variance (ANOVA) rather than the chi-square test.

Question 6

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

Chi-square test of independence is used when the observations are independent. Therefore, if the observations are within subjects (repeated measures), a different test, such as McNemar's test or Cochran's Q test would be more appropriate.

Question 7

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

All of these are conditions for using a chi-square test to analyze the relationship between two variables.

Question 8

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 test is known as the chi-square test of independence. This test checks whether two categorical variables are independent or not. The null hypothesis is that there is no relationship between the two variables, and the alternative hypothesis is that there is a relationship between the two variables.

Question 9

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 consists of rows and columns that represent variables. Each cell in the table represents a unique combination of values for the variables being studied. Therefore, each unique combination of variables in a contingency table is referred to as a cell.

Question 10

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 analyzing categorical data, and categorical data is mostly measured at the nominal level of measurement. Nominal variables have categories that cannot be ranked or ordered, hence making them appropriate for chi-square analysis. This type of analysis is used to determine whether there is a significant association between two categorical variables.

Question 11

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 compare the observed frequencies in a contingency table to the expected frequencies, based on the assumption of independence between the variables. Therefore, the basis of analysis for the chi-square test is a contingency table, which shows the frequencies of the different categories or levels of two or more variables. A contingency table is also called a frequency or crosstabulation table, and it organizes the counts of a categorical variable in rows and another categorical variable in columns. The cells of the table represent the frequency or count for the combination of the levels of the two variables. Therefore, the correct answer is D, contingency table, as it is the most appropriate and specific term to describe the type of table that is required for the chi-square test. The other options, expected frequency, cellular, and summary, could be related to specific aspects or components of the contingency table, but they do not represent the overall or essential characteristic of the table.

Question 12

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 the frequencies in the corresponding row or column are referred to as marginal frequencies. This is because they are the frequencies that appear in the margins of the table, rather than in the cells themselves. Observed frequencies refer to the actual frequencies that were observed or measured in a particular study, while expected frequencies refer to the frequencies that would be expected if a particular hypothesis or model were true. Total frequencies is not a commonly used term in statistical analysis.

Question 13

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?

A)0
B)5.99
C)25.71

Accepted Answer

To calculate the chi-square goodness-of-fit value for this data, we need to compare the observed frequencies (7 for vanilla, 10 for chocolate, and 9 for strawberry) with the expected frequencies if preferences were evenly distributed (8 for each flavor).

The formula for chi-square is Σ(observed-expected)^2/expected.

Plugging in the values, we get:
(7-8)^2/8 + (10-8)^2/8 + (9-8)^2/8 = 0.125 + 0.5 + 0.125 = 0.75

This value is then compared to a chi-square distribution table with 2 degrees of freedom (3 categories - 1 for the expected value). The closest value in the table is 5.99 for a p-value of 0.05.

Since our calculated value (0.75) is smaller than the critical value (5.99), we fail to reject the null hypothesis that the preferences are evenly distributed. Therefore, the best choice is C, and we can conclude that there is no significant difference between the observed frequencies and the expected frequencies if preferences were evenly distributed.

Question 14

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 15

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 small adjustment made to chi-squared tests to account for the fact that the test assumes continuous values, while the data is usually in the form of discrete categories. However, studies have shown that this correction tends to reduce statistical power without providing much control over Type I errors. Therefore, it is often recommended to not use this correction unless the sample size is very small (less than 20).

Question 16

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

The answer of If the researcher suspects that the strength...

Question 17

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 18

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 19

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 the subjects were selected randomly, then the marginal frequencies for gender and political party identification would also be random.

Question 20

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 achieve a power of 0.80 with an alpha level of 0.05 for a 2 x 4 contingency table and an expected Cramer's V of 0.30, a sample size of 121 is required.

Quiz 14: Chi-Square Test

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

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

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

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

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

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

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

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?

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.

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

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?

What are the degrees of freedom?

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

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:

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?

Quiz 14: Chi-Square Test

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

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

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

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

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

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

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

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?

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.

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

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?

What are the degrees of freedom?

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

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:

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?

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.

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 _.

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

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.