1. Reasoning in Psychology Using Statistics Psychology 138 2015

2. Reasoning in Psychology Using Statistics Annoucements Don’t forget quiz 8 due this Friday

3. Reasoning in Psychology Using Statistics Chi-Square Test for Independence 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)

4. Reasoning in Psychology Using Statistics Chi-Square Test for Independence 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)

5. Reasoning in Psychology Using Statistics Decision tree Chi-square test of independence (χ 2 lower-case chi ) –Describing the relationship between two categorical variables or YoungOld or

6. Reasoning in Psychology Using Statistics 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

7. Reasoning in Psychology Using Statistics Chi-Squared Test for Independence Step 1 : State the hypotheses and select an alpha level –H 0 : Preference is independent of age ( “ no relationship ” ) –H A : Preference is related to age ( “ there is a relationship ” ) –We ’ ll set α = 0.05 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

8. Reasoning in Psychology Using Statistics 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 Chi-Squared Test for Independence The critical chi-squared value is 5.99 –Go to Chi-square statistic table and find the critical value

9. Reasoning in Psychology Using Statistics Chi-Squared Test for Independence X 2 α =.05 5.99 7.81 11.07 14.07 As df gets larger, need larger X 2 value for significance. Number of cells get larger.

10. Reasoning in Psychology Using Statistics Step 3: Collect the data. Obtain row and column totals (sometimes called the marginals) and calculate the expected frequencies Chi-Squared Test for Independence Observed scores

11. Reasoning in Psychology Using Statistics Step 3: Collect the data. Obtain row and column totals (sometimes called the marginals) and calculate the expected frequencies Chi-Squared Test for Independence Observed scores Spot check: make sure the row totals and column totals add up to the same thing

12. Reasoning in Psychology Using Statistics Chi-Squared Test for Independence Under 30 Over 30 Digital AnalogUndecided 705614 30246 Observed scores Expected scores Step 3: Collect the data. Obtain row and column totals (sometimes called the marginals) and calculate the expected frequencies (in each cell)

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

14. Reasoning in Psychology Using Statistics Find the residuals (f o - f e ) for each cell Step 4: compute the χ 2 Chi-Squared Test for Independence

15. Reasoning in Psychology Using Statistics Computing the Chi-square Find the residuals (f o - f e ) for each cell Step 4: compute the χ 2

16. Reasoning in Psychology Using Statistics Computing the Chi-square Square these differences Find the residuals (f o - f e ) for each cell Step 4: compute the χ 2

17. Reasoning in Psychology Using Statistics Computing the Chi-square Find the residuals (f o - f e ) for each cell Divide the squared differences by f e Step 4: compute the χ 2 Square these differences

18. Reasoning in Psychology Using Statistics Computing the Chi-square 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

19. Reasoning in Psychology Using Statistics 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

20. Reasoning in Psychology Using Statistics Chi square as a statistical test each cell = observed difference. difference expected by chance

21. Reasoning in Psychology Using Statistics Chi-Square Test in SPSS Analyze  Descriptives  Crosstabs

22. Reasoning in Psychology Using Statistics Chi-Square Test in SPSS Analyze  Descriptives  Crosstabs Click this to get the expected frequencies and residuals Click this to get bar chart of the results

23. Reasoning in Psychology Using Statistics Chi-Square Test in SPSS

24. Reasoning in Psychology Using Statistics Wrap up In lab: Gain experience using and interpreting Chi-square procedures Questions?