Question 1: What is the difference between the chi-square test for goodness-of-fit and the chi-square test for independence? The chi-square test for goodness-of-fit is a nonparametric hypothesis test used with one nominal variable. The chi-square test for independence is a nonparametric test used with two nominal variables.
Question 2: What are the hypotheses when conducting the chi-square test for goodness-of-fit?
Question 3: How are the degrees of freedom for the chi-square hypothesis tests different from those of most other hypothesis tests? In most previous hypothesis tests, the degrees of freedom have been based on sample size. For the chi-square hypothesis tests, however, the degrees of freedom are based on the numbers of categories, or cells, in which participants can be counted. For example, the degrees of freedom for the chi-square test for goodness-of-fit is the number of categories minus 1: dfx2=k-1. Here, k is the symbol for the number of categories.
Question 4: For each of the following, identify the independent variable(s), dependent variable(s), and the level of measurement (nominal, ordinal, scale).
a. The number of loads of laundry washed per month was tracked for women and men living in college dorms.
b. A researcher interested in people's need to maintain social image collected data on the number of miles on someone's car and his/her rank for "need for approval" out of the 183 people studied.
c. A professor of social science was interested in whether involvement in campus life is significantly impacted by whether a student lives on or off campus. Thirty-seven students living on campus and 37 students living off campus were asked whether they were an active member of a club.
Question 5: Use this calculation table for the chi-square test for goodness-of-fit to complete this exercise.
|
Category
|
Observed
(O)
|
Expected
(E)
|
O-E
|
(O-E)2
|
(O-E)2
E
|
|
1
|
750
|
625
|
125
|
15625
|
25
|
|
2
|
650
|
625
|
25
|
625
|
1
|
|
3
|
600
|
625
|
25
|
625
|
1
|
|
4
|
700
|
625
|
75
|
5625
|
9
|
a. Calculate degrees of freedom for this chi-square test for goodness-of-fit.
Dfx2 =K-1 = 2-1 =1
b. Perform all of the calculations to complete this table.
c. Compute the chi-square statistic.
X2 = ∑ [ (O-E)2 ] = 25+1+1+9 = 36
E
Question 6: In a classic prisoner's dilemma game with money for prizes, players who cooperate with each other both earn good prizes. If, however, your opposing player cooperates but you do not (the term used is defect), you receive an even bigger payout and your opponent receives nothing. If you cooperate but your opposing player defects, he or she receives that bigger payout and you receive nothing. If you both defect, you each get a small prize. Because of this, most players of such games choose to defect, knowing that if they cooperate but their partners don't, they won't win anything. The strategies of U.S. and Chinese students were compared. The researchers hypothesized that those from the market economy (United States) would cooperate less (i.e., would defect more often) than would those from the nonmarket economy (China).
|
|
Defect
|
Cooperate
|
|
China
|
31
|
36
|
|
United States
|
41
|
14
|
a. How many variables are there in this study? What are the levels of any variables you identified?
b. What hypothesis test would be used to analyze these data? Justify your answer.
c. Conduct the six steps of hypothesis testing for this example, using the above data.