Question 1

Lambda compares the number of errors of prediction under two separate rules. In the first rule, the independent variable is________.

Accepted Answer

In the first rule, Lambda ignores the independent variable, meaning it does not take it into account when comparing the number of errors of prediction.

Question 2

A study was made of marital satisfaction experienced by men and women. A phi of .07 was calculated for the relationship between gender and satisfaction. This result shows that________.

Accepted Answer

A phi coefficient ranges from -1 to 1, with values close to 0 indicating a weak relationship. In this case, a phi of .07 suggests a weak relationship between gender and marital satisfaction. The result does not indicate which gender experiences greater satisfaction or whether there is a positive or negative relationship.

Question 3

For a relationship involving education and library use, gamma was +0.37. This relationship is________.

Accepted Answer

Gamma of +0.37 indicates a moderate positive relationship between education and library use.

Question 4

Lambda is asymmetric, which means that________.

Accepted Answer

Lambda is asymmetric and its value may vary depending on which variable is taken as independent.

Question 5

A bivariate table has 1843 pairs of cases ranked the same (Ns) and 345 pairs of cases ranked differently (Nd). This is________.

Accepted Answer

Since there are more pairs of cases ranked the same than ranked differently (Ns > Nd), it indicates that there is a tendency for the variables to be positively related.

Question 6

Measures of association provide the researcher with information that________.

Accepted Answer

Measures of association can provide information about the strength of a relationship between variables, assist in making predictions from one variable to another, and aid in understanding causal relationships between variables. Therefore, all answer choices are correct.

Question 7

For a 3 x 3 table, the appropriate chi square based measure of association would be________.

Accepted Answer

Cramer's V is the appropriate chi-square based measure of association for a table larger than 2x2, such as a 3x3 table.

Question 8

In the formula for gamma, Nd represents the number of pairs of cases________.

Accepted Answer

Gamma measures the strength of association between two variables, based on the number of pairs of cases that are ranked differently on both variables. Therefore, Nd in the formula for gamma represents the number of pairs of cases ranked differently on both variables.

Question 9

If we cannot reduce our errors of prediction for the order of pairs of cases on one variable by predicting from the order of pairs of cases on the other variable,________.

Accepted Answer

If we cannot reduce our errors of prediction for the order of pairs of cases on one variable by predicting from the order of pairs of cases on the other variable, it means that there is no association between the two variables. In this case, gamma (a measure of association between two ordinal variables) will be zero, indicating no relationship between the variables.

Question 10

For ordinal level variables with only a few categories or values, an appropriate measure of association would be________.

Accepted Answer

Gamma is specifically designed for measuring the association between ordinal variables, especially when they have a limited number of categories. It is a non-parametric measure that can capture the strength and direction of the association between two ranked variables.

Question 11

While ignoring the independent variable, we make 78 errors when predicting the dependent variable. When taking the independent variable into account, we reduce the number of errors to 43. Therefore________.

Accepted Answer

The decrease in errors when taking the independent variable into account suggests that the variables are associated. However, we cannot conclude that the independent variable is definitely a cause of the dependent variable without further information or analysis. Phi, a measure of association, cannot be determined with only the given information.

Question 12

A researcher can demonstrate a strong association between gender and income. Which variable is independent?

Accepted Answer

Gender is the independent variable because it is the variable being studied to see its impact on income. Income, on the other hand, is the dependent variable because it is affected by the variable being studied (gender).

Question 13

Which is the correct expression for finding E1?

Accepted Answer

The expression for finding E1 is typically N minus the largest row total, where N is the total number of observations or elements.

Question 14

Unlike lambda, phi________.

Accepted Answer

The answer of Unlike lambda, phi________.
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Question 15

To prove that one variable causes another, we use________.

Accepted Answer

Causal relationships require experimental designs or longitudinal studies that can control for other variables and establish a time order of events. Measures of association and tests of significance can indicate correlation but not causation.

Question 16

A researcher has computed a gamma of -0.45 between marital happiness and number of children. What can she conclude?

Accepted Answer

A gamma of -0.45 suggests a moderate negative relationship between number of children and marital happiness. Therefore, families with more children tend to have lower levels of happiness.

Question 17

A researcher tested the relationship between occupational prestige and level of approval of a proposal to ban handguns in the state, and found a gamma of -0.17. This means that________.

Accepted Answer

A gamma of -0.17 indicates a negative relationship between occupational prestige and level of approval of the proposal to ban handguns. This means that as occupational prestige increases, support for the ban decreases. Therefore, choice A is the best answer. Choices B, C, and D are not supported by the gamma value.

Question 18

Lambda is a PRE measure that is used when variables are measured at the________.

Accepted Answer

Lambda is only applicable for nominal level variables, which are categorical variables that are not ordered in any particular way.

Question 19

Gamma and lambda are based on the logic of________.

Accepted Answer

Gamma and lambda are measures of association used in categorical data analysis. Both of them are based on the logic of proportional reduction in error, which means they estimate the proportion of errors in predicting one variable based on knowledge of the other variable. Therefore, the correct answer is D – proportional reduction in error. Options A, B, and C are not relevant to the logic behind gamma and lambda.

Question 20

A problem with both Cramer's V and phi is that values between 0.00 and 1.00________.

Accepted Answer

Values between 0.00 and 1.00 can be interpreted only as an index of the relative strength of the association. Both Cramer's V and phi can take on values between 0.00 and 1.00, and these values represent the strength of the relationship between two categorical variables. However, these values do not indicate the direction of the relationship (i.e. positive or negative), so it is possible for a value between 0.00 and 1.00 to indicate either a positive or negative relationship. Therefore, it is important to look at the context of the data and the research question to determine the nature of the relationship.

Quiz 12: Bivariate Association for Nominal and Ordinal Level Variables