1. PSY 340 Statistics for the Social Sciences Chi-Squared Test of Independence Statistics for the Social Sciences Psychology 340 Spring 2010

2. PSY 340 Statistics for the Social Sciences A manufacturer of watches takes a sample of 200 people. Each person is classified by age and watch type preference (digital vs. analog). A manufacturer of watches takes a sample of 200 people. Each person is classified by age and watch type preference (digital vs. analog). The question: is there a relationship between age and watch preference? Young (under 30) Old (over 30) Chi-Squared Test for Independence

3. PSY 340 Statistics for the Social Sciences A manufacturer of watches takes a sample of 200 people. Each person is classified by age and watch type preference (digital vs. analog). A manufacturer of watches takes a sample of 200 people. Each person is classified by age and watch type preference (digital vs. analog). The question: is there a relationship between age and watch preference? Young (under 30) Old (over 30) Chi-Squared Test for Independence

4. PSY 340 Statistics for the Social Sciences Statistical analysis follows design

5. PSY 340 Statistics for the Social Sciences A manufacturer of watches takes a sample of 200 people. Each person is classified by age and watch type preference (digital vs. analog). The question: is there a relationship between age and watch preference? A manufacturer of watches takes a sample of 200 people. Each person is classified by age and watch type preference (digital vs. analog). The question: is there a relationship between age and watch preference? Chi-Squared Test for Independence

6. PSY 340 Statistics for the Social Sciences Chi-Squared Test for Independence Step 1 : State the hypotheses – H 0 : Preference is independent of age (“no relationship”) – H A : Preference is related to age (“there is a relationship”) A manufacturer of watches takes a sample of 200 people. Each person is classified by age and watch type preference (digital vs. analog). The question: is there a relationship between age and watch preference? A manufacturer of watches takes a sample of 200 people. Each person is classified by age and watch type preference (digital vs. analog). The question: is there a relationship between age and watch preference? Observed scores Chi-Squared Test for Independence

7. PSY 340 Statistics for the Social Sciences Step 2: Compute your degrees of freedom & get critical value df = (#Columns - 1) * (#Rows - 1) = (3-1) * (2-1) = 2 For this example, with df = 2, and α = 0.05 The critical chi-squared value is 5.99 –Go to Chi-square statistic table and find the critical value Chi-Squared Test for Independence

8. PSY 340 Statistics for the Social Sciences Chi-Squared Test for Independence Step 3: Collect the data. Obtain row and column totals (sometimes called the marginals) and calculate the expected frequencies Observed scores

9. PSY 340 Statistics for the Social Sciences Chi-Squared Test for Independence Spot check: make sure the row totals and column totals add up to the same thing Step 3: Collect the data. Obtain row and column totals (sometimes called the marginals) and calculate the expected frequencies Observed scores

10. PSY 340 Statistics for the Social Sciences Step 3: Collect the data. Obtain row and column totals (sometimes called the marginals) and calculate the expected frequencies Under 30 Over 30 Digital AnalogUndecided 705614 30246 Observed scores Expected scores Chi-Squared Test for Independence

11. PSY 340 Statistics for the Social Sciences Step 3: Collect the data. Obtain row and column totals (sometimes called the marginals) and calculate the expected frequencies Under 30 Over 30 Digital AnalogUndecided 705614 30246 Observed scores Expected scores “expected frequencies” - if the null hypothesis is correct, then these are the frequencies that you would expect Chi-Squared Test for Independence

12. PSY 340 Statistics for the Social Sciences Find the residuals (f o - f e ) for each cell Step 4: compute the  2 Chi-Squared Test for Independence

13. PSY 340 Statistics for the Social Sciences Step 4: compute the  2 Find the residuals (f o - f e ) for each cell Chi-Squared Test for Independence

14. PSY 340 Statistics for the Social Sciences Square these differences Find the residuals (f o - f e ) for each cell Step 4: compute the χ 2 Chi-Squared Test for Independence

15. PSY 340 Statistics for the Social Sciences Square these differences Find the residuals (f o - f e ) for each cell Divide the squared differences by f e Step 4: compute the χ 2 Chi-Squared Test for Independence

16. PSY 340 Statistics for the Social Sciences Square these differences Find the residuals (f o - f e ) for each cell Divide the squared differences by f e Sum the results Step 4: compute the χ 2 Chi-Squared Test for Independence

17. PSY 340 Statistics for the Social Sciences Chi-Squared, the final step Step 5 : Compare this computed statistic (38.09) against the critical value (5.99) and make a decision about your hypotheses A manufacturer of watches takes a sample of 200 people. Each person is classified by age and watch type preference (digital vs. analog). The question: is there a relationship between age and watch preference? A manufacturer of watches takes a sample of 200 people. Each person is classified by age and watch type preference (digital vs. analog). The question: is there a relationship between age and watch preference? here we reject the H 0 and conclude that there is a relationship between age and watch preference

18. PSY 340 Statistics for the Social Sciences In SPSS Each person gets a row Each person has data about the variables – age & watch preference

19. PSY 340 Statistics for the Social Sciences In SPSS Analyze => Descriptives => Crosstabs Select the two variables (usually they are nominal or ordinal) you want to examine and click the arrow to move one into the “rows” and one into the “columns” box. Click on “statistics” button, and check the “Chi-square” box. Click “continue.” Click “OK.”

20. PSY 340 Statistics for the Social Sciences SPSS Output Look at the “Chi-square tests” box. The top row of this box gives results for “Pearson’s Chi- Square” “Value” is the value of the χ 2 statistic, “df” is the degrees of freedom for the test “Asymp. Sig. (2-sided)” is the probability (p-value) associated with the test. The chi-squared distribution, like the F-distribution, is “squared” so 1-tailed test is not possible.