Test Bank

Chapter 10: Introduction: Hypothesis Testing With Two Categorical Variables: Chi-Square

Multiple Choice

1. The χ² is a ______.

A. multinomial hypothesis test

B. binomial hypothesis test

C. univariate hypothesis test

D. bivariate hypothesis test

2. The χ² test of independence is ______.

A. the hypothesis test appropriate when the independent variable and dependent variable are categorical

B. the hypothesis test appropriate when the independent variable and dependent variable are continuous

C. the hypothesis test appropriate when the independent variable is categorical, but the dependent variable is continuous

D. the hypothesis test appropriate for continuous data

3. When two variables are statistically dependent, ______.

A. the independent variable has predictive power over the dependent variable

B. the independent variable does not have predictive power over the dependent variable

C. the dependent variable has predictive power over the independent variable

D. the dependent variable does not have predictive power over the independent variable

4. The first step in completing a χ² procedure is ______.

A. the creation of the H₀ and H₁

B. the selection of the appropriate critical value to help make a determination about the null hypothesis

C. the selection of an appropriate critical value to help make a determination about the alternative hypothesis

D. the selection of an appropriate alpha level to help make sense of any observed outcomes

5. What is the formula for degrees of freedom in the χ²?

A. χ² does not make use of degrees of freedom

B. df = N – 1

C. df = (r – 1)(c – 1)

D. df = N + 1

6. In the χ², the row and column totals are referred to as ______.

A. marginals

B. minimals

C. meniscus

D. mummations

7. In χ² analyses, it is common practice among researchers to establish an α level equal to ______.

A. 0.09

B. 0.10

C. 1.0

D. 0.05

8. In the χ² test, what is meant by the term obtained value?

A. It is the value of the critical region used to reject the H_1.

B. It is the value of the critical region used to reject the H_0.

C. It is the value of the test statistics calculated using the mathematical formulas specific to a particular test.

D. It is the final value of the α level as established by a research scientist.

9. A researcher has established α = .05. If , then the probability of obtaining this particular X²_obt value by chance alone is . . .

A. less than .95

B. less than .05

C. greater than .95

D. greater than .05

10. What does a researcher do when the results of a hypothesis test reveal that ?

A. retains the H₀

B. retains the H₁

C. rejects the H₁

D. rejects the H₀

11. Expected frequencies in a χ² analysis are symbolized by ______.

A. N

B. f_x

C. f_e

D. f_o

12. The λ measure of association test is ______.

A. a test of association appropriate for use with any level of data

B. a test of association appropriate for use with nominal data

C. a test of association appropriate for use with continuous data

D. a test of association appropriate for use with ordinal data

13. What is the range of λ?

A. −1.00 to 1.00

B. 0.00 to ± 1.00

C. 0.00 to 1.00

D. 0.00 to −1.00

14. Goodman and Kruskal’s γ has a range of ______.

A. −1.00 to 1.00

B. 0.00 to 1.00

C. 0.00 to ± 1.00

D. 0.00 to −1.00

15. In Somers’ d, a negative relationship means ______.

A. that as the independent variable increases, so does the dependent variable

B. that as the independent variable decreases, so does the dependent variable

C. that as the independent variable increases, the dependent variable decreases

D. that as the independent variable remains unchanged, so does the dependent variable

16. In Cramer’s V, a positive relationship means ______.

A. that as the independent variable increases, so does the dependent variable

B. that as the independent variable decreases, the dependent variable remains static

C. that as the independent variable increases, the dependent variable decreases

D. that as the independent variable remains unchanged, so does the dependent variable

17. In SPSS, what is the probability associated with the obtained value of the test statistic called?

A. the confidence level

B. the alpha level

C. the p value

D. the

18. When viewing SPSS output, how does one know what decision to make with regard to the H₀?

A. if the confidence level lies between the p value and , the H₀ can be rejected

B. if p > α, the H₀ can be rejected

C. if p < α, the H₀ can be rejected

D. if the is greater than the critical value, the H₀ can be retained

19. If a professor calculated a λ value of .70, what would that indicate?

A. The λ of .70 would mean that knowing a person’s or object’s classification on the independent variable reduces dependent variable prediction errors by about 70%.

B. The λ of .70 would mean that knowing a person’s or object’s classification on the independent variable reduces dependent variable prediction errors by about .70%.

C. The λ of .70 would mean that knowing a person’s or object’s classification on the independent variable reduces dependent variable prediction errors by about 30%.

D. The λ of .70 would mean that knowing a person’s or object’s classification on the independent variable reduces dependent variable prediction errors by about .30%.

20. A Cramer’s V of .90 would be indicative of what type of relationship?

A. strong statistical significance

B. a perfect positive relationship

C. a strong relationship

D. a weak relationship

21. Somers’ d is which type of measure?

A. asymmetrical

B. symmetrical

C. normal

D. modal

22. Which of the following are characteristic of Somers’ d?

A. It takes on different values depending on which variable is called the independent variable and which variable is called the dependent variable.

B. It takes on the same value regardless of which variable is called the independent variable and which variable is called the dependent variable.

C. It is a measure appropriate for use with nominal data.

D. It has a range of 0.00–1.00.

23. What factor in a study dictates the measure of association that can be used?

A. the α level

B. the sample size

C. the level of measurement of the independent variable and dependent variable

D. the needs of the researcher

24. Somers’ d is a measure of association for ______-level variables.

A. nominal

B. categorical

C. ordinal

D. interval

25. Goodman and Kruskal’s γ is a measure of association for ______-level variables.

A. nominal

B. categorical

C. ordinal

D. interval

26. The null hypothesis is rejected if the obtained value of the χ² test statistic is ______ the critical value.

A. greater than

B. less than

C. the same as

D. none of these

27. Observed frequencies in a χ² analysis are symbolized as ______.

A. f_e

B. f_o

C. f_x

D. none of these

28. The theoretical results that would be seen if the H₀ were true are known as ______ frequencies.

A. observed

B. raw

C. expected

D. robust

29. A procedure for determining the strength or magnitude of a relationship between an independent variable and a dependent variable is referred to as a ______.

A. measure of association

B. measure of disassociation

C. measure of diversity

D. none of these

30. 46. If _, then a researcher should ______ the H₀.

A. confirm

B. accept

C. reject

D. none of these

31. Which of the following is a nonparametric test?

A. t test

B. ANOVA

C. χ² test

D. none of these

32. ______ means that knowing which category an object falls into on the IV does not help predict its placement on the DV.

A. Statistical analysis

B. Statistical independence

C. Statistical dependence

D. none of these

33. Which of the following represents the statistic on an SPSS output?

A. pearson Correlation

B. cramer’s V

C. pearson χ²

D. none of these

34. The ______ tells you the exact probability of the obtained value of the test statistic.

A. df value

B. p value

C. χ² value

D. none of these

35. ______ frequencies are the empirical results seen in the sample.

A. Relative

B. Conditional

C. Observed

D. Expected

1. Statistical independence means that knowing which category a person or object falls into on the independent variable does not aid in the prediction of their placement on the dependent variable.

2. In the χ² distribution, the shape of the curve is dependent upon the degrees of freedom.

3. In a χ² analysis, df is not based on sample size but on the size of the crosstabs table.

4. The symbol is used to indicate the χ² critical value that is set in advance of the analysis and is used to make decisions about the null hypothesis.

5. The empirical values that appear in the crosstabs table produced from sample-derived data are known as expected frequencies.

6. While the χ² test indicates whether a statistically significant relationship between two variables exists, it does not allude to the strength or magnitude of that relationship.

7. Cramer’s V is a test of association appropriate for use with nominal-level data only.

8. Cramer’s V can range from –1.00 to 1.00.

9. λ is a proportion.

10. In Cramer’s V, lower values represent stronger relationships.

11. In a Goodman and Kruskal’s γ test, a zero indicates no relationship between the variables of interest.

12. The range of Somers’ d is from –1.00 to 1.00

13. While statistical significance is important, it is the magnitude of the relationship that tells how meaningful the association is in practical terms.

14. It is possible to have a statistically significant relationship but a corresponding measure of association that is very low.

15. λ is a proportionate reduction in error (PRE) measure, which refers to the extent to which knowing a person’s or object’s placement on an independent variable helps predict that person’s or object’s classification on the dependent variable.

16. Two variables that are not related to one another are said to be statistically independent.

17. When two variables are related to one another, they are said to be statistically dependent.

18. The χ² statistic is symbolized as X².

19. In the χ² distribution, as the df increases, the shape of the distribution becomes more skewed.

20. The χ² crosstabs tables are also known as contingency tables.

1. λ is an asymmetrical measure. Briefly explain what this means.

2. Cramer’s V is a symmetrical measure. What does this mean?

3. When should a researcher use a Cramer’s V instead of a lambda measure of association?

4. Take the formula for the χ² statistic itself and identify its components.

: the obtained χ² statistic

f_oi: the observed frequencies of each individual cell

f_ei: the expected frequencies of each individual cell

Cognitive Domain: Application

Answer Location: The Chi-Square Test of Independence

Difficulty Level: Medium

5. The contingency table below contains neighborhood-level homicide data broken down by victim race. Using an σ of .05, conduct a five-step hypothesis test to determine whether there is a relationship between neighborhood and victim race.

Number of Homicides Occurring Yearly in Individual Neighborhoods

Neighborhood