Question 1

Which of the following values for a statistic is clearly incorrect because it is outside the statistic's range?

Accepted Answer

Lambda ranges from -1 to 1, so a value of 1.20 is outside the range and clearly incorrect. The other statistics have legitimate ranges and values that can fall within those ranges.

Question 2

Which of the following measures of association comes in an asymmetric form?

Accepted Answer

Lambda is an asymmetric measure of association, meaning that the direction of the relationship is relevant. It is used when one variable is considered the independent variable and the other is the dependent variable. The other measures listed (Cramer's V, gamma, and Kendall's tau-c) are symmetric measures of association, meaning that the direction of the relationship is not relevant.

Question 3

The value of Cramer's V is .65. This indicates what type of relationship?

Accepted Answer

D

Question 4

Which measures of association indicate the strength of a relationship?

Accepted Answer

Measures of association for nominal, ordinal, and interval/ratio data can all indicate the strength of a relationship, such as Cramer's V for nominal, Spearman's rho for ordinal, and Pearson's correlation for interval/ratio data.

Question 5

If a measure of association is asymmetric,

Accepted Answer

If a measure of association is asymmetric, it means that it matters which variable is considered the independent variable and which is the dependent variable. For example, in some cases, the correlation between X and Y may be different than the correlation between Y and X. Therefore, the direction of causality or the order in which variables are entered into a regression model can affect the measure of association.

Question 6

If two variables are inversely related, cases that have low scores on one variable will tend to have _____ scores on the other variable.

Accepted Answer

Inverse relationship means that as one variable increases, the other variable decreases and vice versa. Therefore, if cases have low scores on one variable, they will tend to have high scores on the other variable.

Question 7

If two variables are positively related, cases that have low scores on one variable will tend to have _____ scores on the other variable.

Accepted Answer

When two variables are positively related, cases with low scores on one variable tend to have low scores on the other variable as well, indicating a direct relationship between the two.

Question 8

Which of the following measures of association indicates the direction of a relationship?

Accepted Answer

Kendall's tau-c indicates the direction of the relationship.

Question 9

Which of the following gamma values indicates the strongest relationship?

Accepted Answer

Out of the given options, gamma value closest to +1 (strongest positive relationship) is 0.85. Therefore, D is the correct answer.

Question 10

Which of the following gamma values indicates the weakest relationship?

Accepted Answer

A gamma value of .05 indicates a very weak relationship or no relationship at all between the two variables. A negative gamma value, such as −.90 or −.45, indicates a negative relationship between the variables, while a positive gamma value, such as .55, indicates a positive relationship between the variables.

Question 11

Which of the following is a nominal measure of association?

Accepted Answer

Coefficient of contingency measures the degree of association between two nominal variables. Kendall's tau-b, Kendall's tau-c, and Somers' d are measures of association for ordinal variables.

Question 12

Which of the following is most appropriate for measuring the relationship between an ordinal variable and an ordinal variable?

Accepted Answer

Kendall's tau-b is the most appropriate measure for the relationship between two ordinal variables because it accounts for tied ranks and provides a measure of association that ranges from -1 to 1, with 0 indicating no association and values closer to -1 or 1 indicating stronger association. Cramer's V, lambda, and phi are measures of association for nominal variables, not ordinal variables.

Question 13

Your hypothesis is that the taller a person is, the more self-confident he or she is. Height is an interval/ratio variable measured in inches; self-confidence is a five category ordinal variable with higher scores indicating greater self-confidence. The value of Somers' d is −.68. Does this measure of association

Accepted Answer

Somers' d is a measure of association for ordinal variables. A negative value of d indicates a negative association, meaning that as one variable increases, the other variable tends to decrease. In this case, a negative value of -.68 indicates that as height increases, self-confidence tends to decrease. Therefore, the result contradicts the hypothesis that taller individuals are more self-confident.

Question 14

Which measures of association indicate the direction of a relationship?

Accepted Answer

Only ordinal and interval/ratio measures of association indicate the direction of a relationship. Nominal measures of association only indicate if there is a relationship, but not the direction. Interval/ratio measures of association also indicate the strength of the relationship, but not just the direction. Therefore, B is the best choice.

Question 15

Which of the following tau-b coefficients indicates the strongest relationship?

Accepted Answer

The tau-b coefficient ranges from -1 to 1. The closer the coefficient is to -1 or 1, the stronger the relationship between the variables. A coefficient of -.90 indicates a very strong negative relationship between the variables. Therefore, option A is the best choice.

Question 16

You want to see what percent of persons in each region say they are very happy with their life. Which type of analysis should you do?

Accepted Answer

Creating a crosstab with appropriate percents will allow you to see the percentage of persons in each region who say they are very happy with their life.

Question 17

If Jim and Mary form a concordant pair on the variables height and weight, then

Accepted Answer

A concordant pair in the context of height and weight means that for both variables, one individual consistently ranks higher than the other. Therefore, if Jim and Mary form a concordant pair, it means one of them is both taller and heavier than the other.

Question 18

Which statistic is modeled after Pearson's r but transforms the scores on both variables to ranks before calculating the measure of association?

Accepted Answer

Spearman's correlation coefficient is modeled after Pearson's r but converts the actual scores on both variables to ranks before calculating the association. This makes it suitable for measuring the relationship between two variables when the data are ordinal or not normally distributed. In contrast, Cramer's V, gamma, and Somers' d are measures of association for categorical data, with different underlying assumptions and calculation methods.

Question 19

The number of years a person has been married and their level of happiness with their marriage have a Kendall's tau-b value of .75. Which of the following is true?

Accepted Answer

Kendall's tau-b value of .75 indicates a moderately strong positive correlation between the number of years married and happiness with the marriage. This means that as the number of years married increases, happiness with the marriage tends to increase as well. Therefore, persons married more years tend to be happier with their marriage.

Question 20

Which of the following measures of association does NOT indicate the direction of a relationship?

Accepted Answer

Cramer's V does not indicate the direction of a relationship; it only measures the strength of association between two nominal variables. Pearson's r, Somers' d, and tau-b all indicate both the strength and direction of a relationship.

Quiz 8: Nominal and Ordinal Measures of Association