Deck 9: Testing Hypotheses With Categorical Data

Question 1

A contingency table shows the joint distribution of two ______.

A) interval-level variables
B) ratio-level variables
C) categorical variables
D) dependent variables

Answer 1

C

Question 2

The Chi-square test investigates the null hypothesis that two ______.

A) nominal- or ordinal-level variables are independent
B) ordinal- interval-level variables are independent
C) nominal- interval-level variables are independent
D) nominal- ratio-level variables are independent

Answer 2

A

Question 3

The Chi-square test ______.

A) tells us if there is a significant relationship between two variables AND the strength of that relationship
B) tells us if there is a significant relationship between two variables ONLY
C) tells us if there is a significant relationship between two variables AND the direction of the difference
D) produces negative values for especially strong negative relationships

Answer 3

B

Question 4

The expected frequencies of a contingency table is ______.

A) the joint frequency distribution we would expect to see if the two variables were dependent on each other
B) the joint frequency distribution we would expect to see if the two variables caused each other
C) the joint frequency distribution we would expect to see if the independent variable influenced the dependent variable
D) the joint frequency distribution we would expect to see if the two variables were independent on each other

Question 5

Which of the following is the correct equation to calculate the degrees of freedom in a Chi-square test?

A) $(\# \text { of rows - 2) } *(\text { \#of columns - 2) }$
B) $(\# o f \text { rows }-1) *(\# \text { of columns - 1) }$
C) $(\# o f \text { rows - 2) }+(\# \text { of columns }-2)$
D) $(\# \text { of rows }-1)+(\# \text { of columns }-1)$

Question 6

For results that included four groups with a total number of 250 participants, what would the appropriate degrees of freedom be?

A) 3
B) 4
C) 249
D) 250

Question 7

The researcher calculated the $\chi$ ² comparing people's feelings of safety and whether they or not they felt the police did a good job. If the null hypotheses are not rejected, which of the following would be the most appropriate conclusion?

A) There is no difference between people who are afraid and if they are satisfied with police.
B) The expected frequencies differed significantly from the observed frequencies.
C) The was a small effect between the expected and observed frequencies.
D) The groups are not all equal to each other.

Question 8

The alternative computational formula for a Chi-square test ______.

A) produces results that are slightly higher than the definitional formula
B) produces results that are slightly lower than the definitional formula
C) produces results that are identical to the definitional formula
D) produces results that are much different than the definitional formula

Question 9

In the definitional formula, $x^{2}=\sum_{i=1}^{k} \frac{\left(f_{0}-f_{e}\right)^{2}}{f_{e}}$ , and the computational formula, $x^{2}=\sum_{i=1}^{k} \frac{\left(f_{o}^{2}\right)}{f_{e}}-n$ , squaring the numerator ensures that ______.

A) a Chi-square statistic is never zero
B) a Chi-square statistic is never less than zero
C) only severely variables that are dependent on each other will be negative
D) it is easier to reject the null hypothesis because exponentiating a value increases its size

Question 10

______ is a summary measure that captures the magnitude or strength of the relationship between two variables.

A) Chi-square test
B) Joint frequency distribution
C) Alpha level
D) Measure of association

Question 11

The phi-coefficient as a measure of association is appropriate for ______.

A) nominal-level variables in a 2x2 table
B) nominal-level variables in any kind of table
C) ratio-level variables in a 2x2 table
D) ratio-level variables in any kind of table

Question 12

The contingency coefficient as a measure of association is appropriate for ______.

A) nominal-level variables in any kind of table
B) ratio-level variables in a 2x2 table
C) ratio-level variables in any kind of table
D) nominal-level variables in a 2x2 table only

Question 13

One disadvantage of the contingency coefficient is that ______.

A) a perfect relationship may be greater than 1.0
B) a perfect relationship may be lower than 1.0
C) a perfect relationship may be twice as large as 1.0
D) it cannot estimate a perfect relationship

Question 14

A measure of association for nominal-level variables that does not have the disadvantage of the contingency coefficient is ______.

A) Goodman's gamma
B) Kruskal's gamma
C) Cramer's V
D) Yule's Q

Question 15

The Goodman and Kruskal's gamma measure of association is appropriate for ______.

A) ordinal-level variables
B) ratio-level variables
C) interval-level variables
D) nominal-level variables

Question 16

Which of the following measure of association is best used for a Chi-square table that is 3 by 4 with ordinal-level variables?

A) φ
B) contingency coefficient
C) Yule's Q
D) Goodman and Kruskal's gamma

Question 17

For a Chi-square test the researcher has to compare percentage differences found in the categories for the independent variable at the same category of the dependent variable.

Question 18

For a Chi-square table examining an independent variable with four groups and a dependent variable with three groups, the degrees of freedom to find the critical value would be 5.

Question 19

Chi-square allows for the rejection of a null hypothesis of independence but does not tell the researcher the magnitude or strength of that relationship.

Question 20

Since the Chi-square does not indicate the strength of the association, a researcher must then conduct a separate test for the measure of association.

Question 21

A Chi-square statistic can never be less than zero.

Question 22

A significant Chi-square test suggests that the observed frequencies are different from the expected frequencies.

Question 23

If the observed frequencies are significantly different from the expected frequencies then the values of the variables are dependent on one another.

Question 24

The Chi-square test is able to test the independence of two ratio-level variables.

Question 25

What does it mean if a Chi-square test reveals a significant association between gender and crime type (violent or property)?