Question 1

Cell frequencies are the sum of the frequencies in the corresponding row or column.

Accepted Answer

Cell frequencies are the frequencies in each individual cell of a table or matrix, not the sum of frequencies in the row or column they belong to.

Question 2

The chi-square test is typically used to analyze the relationship between two variables when both variables are qualitative in nature (that is,measured on a nominal level).

Accepted Answer

The chi-square test is commonly used for analyzing the association between two categorical variables that are measured on a nominal or ordinal scale. Therefore, the statement is true.

Question 3

If people in a gender and political party identification study were selected so that it consisted of a specified number of individuals of each gender (for instance,100 males and 100 females)who were then classified according to political party identification,the marginal frequencies for the party identification variable would still be random,but the marginal frequencies for the gender variable would be fixed.

Accepted Answer

Since the study has a fixed number of individuals for each gender, the marginal frequencies for gender would be fixed. However, the political party identification variable would still have random marginal frequencies as the individuals in the study may choose to identify with any political party.

Question 4

Because the relationship between two variables can take a number of different forms,the alternative hypothesis for the chi-square test,as with the F test in analysis of variance,is directional in nature.

Accepted Answer

The statement is false. The alternative hypothesis for the chi-square test, like the F test, is not necessarily directional in nature. It simply indicates that there is a difference or association between the variables being studied, without specifying the direction of that difference or association.

Question 5

The chi-square test is a parametric statistical test.

Accepted Answer

The chi-square test is a non-parametric statistical test. It does not make assumptions about the underlying distribution of the data, unlike parametric tests such as t-tests or ANOVAs.

Question 6

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

Accepted Answer

The statement is incorrect. The chi-square test is designed for use with qualitative variables, and means can be computed for quantitative variables.

Question 7

The assignment of one variable as the row variable and the other variable as the column variable in a contingency table is arbitrary.

Accepted Answer

The assignment of row and column variables in a contingency table is interchangeable, so it is arbitrary which variable is assigned to which dimension.

Question 8

A 2x5 contingency table indicates that the column variable has two levels and the row variable has 5 levels.

Accepted Answer

The answer of A 2x5 contingency table indicates that the...

Question 9

The null hypothesis for a chi-square test states that the variables of interest are unrelated
in the population,while the alternative hypothesis states that there is a relationship between the two variables in the population.

Accepted Answer

This is the correct definition of the null and alternative hypotheses for a chi-square test. The null hypothesis assumes that there is no relationship between the variables, while the alternative hypothesis assumes that there is a relationship.

Question 10

Unlike the previous tests we have considered,the chi-square test analyzes the relationship between variables using frequency information.

Accepted Answer

The chi-square test is used to analyze the relationship between variables using frequency information.

Question 11

When scores on quantitative variables are collapsed into intervals,the power of the chi-square test is reduced relative to that of a parametric test.

Accepted Answer

When scores on quantitative variables are collapsed into intervals, information is lost and the data are transformed into categorical variables. This reduces the power of the chi-square test which is designed for categorical data. Parametric tests, on the other hand, make use of the original quantitative data and may have greater power depending on the circumstances.

Question 12

The entries within cells represent the number of individuals in the sample who are characterized by the corresponding levels of the variables and are referred to as marginal frequencies.

Accepted Answer

Marginal frequencies refer to the totals of rows or columns in a contingency table, not the individual cell entries.

Question 13

If people in a study on gender and political party identification were selected for participation without regard to gender or political party identification,the marginal frequencies for both of these variables would be free to vary,or random.

Accepted Answer

If people in a study were selected without regard to gender or political party identification, the sample would be representative of the population and therefore the marginal frequencies for both variables would be free to vary, or random.

Question 14

The logic underlying the chi-square test focuses on the concept of expected frequencies and how they compare to observed frequencies.

Accepted Answer

The chi-square test is based on comparing the expected frequencies (the frequencies that would be expected if there was no relationship between the variables being studied) to the observed frequencies (the actual frequencies that were observed in the sample).

Question 15

A modified Bonferroni procedure can be applied to pairwise comparisons between the proportions of observations in various cells of the contingency table to analyze the nature of the relationship between two qualitative variables.

Accepted Answer

A modified Bonferroni procedure can indeed be applied to pairwise comparisons between the proportions of observations in various cells of a contingency table for analyzing the relationship between two qualitative variables.

Question 16

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

Accepted Answer

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

Question 17

Application of the chi-square test requires computation of an expected frequency for each cell under the assumption of no relationship between the two variables.

Accepted Answer

Application of chi-square test involves determining the expected frequency for each cell assuming no relationship between the two variables. The computed expected frequency is then compared with the observed frequency to determine if there is a statistically significant relationship between the variables.

Question 18

When the marginal frequencies are random for one variable and fixed for the other,the analytical procedures are identical but the test is referred to as the chi-square test of heterogeneity.

Accepted Answer

When the marginal frequencies are random for one variable and fixed for the other, the analytical procedures are not identical and the test is referred to as the chi-square test of independence. The chi-square test of heterogeneity is used when comparing the distribution of a categorical variable across different groups or categories.

Question 19

Each unique combination of variables in a contingency table is referred to as a cell.

Accepted Answer

This statement is true. A contingency table is often used to display the distribution of two categorical variables and the unique combination of each variable is presented as a cell in the table.

Question 20

In order to calculate an expected frequency for a given cell,you divide the total of the column (the column marginal frequency)in which it appears by the total number of observations and then multiply this by the total of the row (the row marginal frequency)in which the cell appears.

Accepted Answer

This is the correct formula for calculating expected frequency in contingency table analysis.

Quiz 14: Chi-Square Test