Lab #10 Preview
Chi-Square Tests
Purpose
- Chi-Square Test for Independence – determine whether there is a relationship between two categorical variables; like a correlation, but for frequency data
- Chi-Square Goodness of Fit Test – compare a sample frequency distribution to a specific population distribution
Chi-Square Test for Independence
Scenario: a training experiment where two training methods are being compared – do participants find one training method more boring than the other?
Null Hypothesis: There is no relationship between training method and boringness
Alternative Hypothesis: There is a relationship between training method and boringness
Chi-Square Goodness of Fit Test
Scenario: distribution of grades after change of textbook – do current grades differ from historical grade distribution in the percentage of A, B, C, D, and F grades?
Null Hypothesis: There is no difference between the distributions
Alternative Hypothesis: There is a difference between the distributions
For both tests, the Chi-square test is a test of the null hypothesis. Based on test results, we either:
- Reject the null hypothesis (and conclude the alternative is supported), or
- Fail to reject the null hypothesis (and conclude there is no relationship or no difference)
APA Style
Chi-square results are reported similarly to our other tests with a chi-square statement attached to the end of sentences about the findings. The sentences should report the categorical data (the frequencies or percentages or both) and whether the variables are related (for a test of independence) or whether the variables follow the expected pattern (for a test of goodness of fit). The statement reports the Χ2 symbol, followed by degrees of freedom AND sample size in parentheses (as shown in the examples below), followed by the value of the chi-square statistic, followed by the p-value. SPSS doesn’t allow you to insert Greek letters so you can spell out “chi-square” instead of typing the Χ2 symbol in your annotations.
Test of Independence:
- 62.5% of females were married and 67.2% of males were married. The percentage of participants that were married did not differ by gender, Χ2 (1, N = 90) = 0.89, p > .05.
- Catholic teens (75.4%) were less likely to show an interest in attending college than were Protestant teens (88.2%). The relation between these variables was significant with more Protestant than Catholic teens interested in college, Χ2 (2, N = 170) = 14.14, p < .01.
Test of Goodness of Fit:
- The rural sample included 30 respondents (23.8%) who had never married, 54 (42.9%) who were married, 26 (20.6%) who reported being separated or divorced, and 16 (12.7%) who were widowed. These rural frequencies did not fit the expected pattern from the larger state population, Χ2 (3, N = 126) = 10.15, p = .017.
- In the blind taste test, 16 students preferred Sam’s Choice cola, 18 preferred Coke, and 19 preferred Pepsi. Preference for the three sodas was distributed equally across the three brands of cola, Χ2 (2, N = 53) = 1.53, p > .05.