Question 1

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

Collapsing scores into intervals reduces the level of information and precision in the data. As a result, the chi-square test, which relies on categorical data, may not capture all the variability and provide less power than a parametric test that uses more precise data. Therefore, the statement is true.

Question 2

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 alternative hypothesis for the chi-square test is non-directional, as it typically tests for the presence of any association between variables rather than a specific direction of association.

Question 3

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

This statement is incorrect. The chi-square test is designed for use with categorical variables, which can be expressed as frequencies. Quantitative variables can be used in other types of statistical tests such as t-tests or ANOVA, and means can be calculated for these variables.

Question 4

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 compares observed frequencies to expected frequencies, with the logic based on the assumption that the observed frequencies should match the expected frequencies if there is no significant difference between the groups being compared.

Question 5

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

This is correct. The expected frequency for each cell is calculated based on the assumption of no relationship between the two variables being studied.

Question 6

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

Accepted Answer

Cell frequencies refer to the individual counts or observations in each cell of a contingency table, not the sum of frequencies in a row or column. Row or column totals are the sums of cell frequencies within that row or column.

Question 7

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

Accepted Answer

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

Question 8

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 method for calculating expected frequency.

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 a correct description of the null and alternative hypothesis for a chi-square test.

Question 10

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 11

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 individuals were selected based on a fixed number of individuals of each gender, the marginal frequencies for the gender variable would be fixed, while the marginal frequencies for the party identification variable would still be randomly distributed among the selected individuals.

Question 12

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

This statement is true. The modified Bonferroni procedure is a statistical method to control for Type I error rate in multiple comparisons. By applying it to pairwise comparisons of proportions in a contingency table, analysts can test the independence or association between two categorical variables.

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 participants were selected without regard to gender or political party identification, the marginal frequencies for both variables would be free to vary since they were not controlled or manipulated in any way. This would result in a more representative and diverse sample, but could also lead to potentially skewed or biased results depending on the population being studied.

Question 14

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 variables as row or column variables is based on preference and convenience, and does not affect the results or analysis of the contingency table.

Question 15

The chi-square test is a parametric statistical test.

Accepted Answer

The chi-square test is a non-parametric statistical test, which means it does not require any assumptions about the distribution of the population being tested.

Question 16

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

Accepted Answer

This is true. A cell in a contingency table represents a unique combination of values for the variables being analyzed.

Question 17

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

This is correct as the chi-square test is used to analyze the relationship between two categorical variables, which are qualitative in nature and measured on a nominal level.

Question 18

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

Accepted Answer

The given statement is true. The chi-square test analyzes the association between categorical variables using frequency data.

Question 19

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

The entries within cells represent the number of individuals characterized by the corresponding levels of the variables and are referred to as cell frequencies, not marginal frequencies. Marginal frequencies are the totals found in the margins (rows and columns) of the table, summarizing either the row or column totals.

Question 20

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, it is known as the chi-square test of independence, not dependence.

Quiz 15: Chi-Square Test