1. Reasoning in Psychology Using Statistics
2017

2. Don’t forget quiz 8 due this Friday
Annoucements

3. Exam(s) 3 Lecture Exam 3 Lab Exam 3 Combined Exam 3
Mean 55.1 (55.1/75 = 73.5%)
Lab Exam 3
Mean 61.3 (61.3/75 = 81.7%)
Combined Exam 3
Mean 77.6%
Exam(s) 3

4. 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).
Young (under 30)
Old (over 30)
The question: Is there a relationship between age and watch preference?
Chi-Square Test for Independence

5. 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).
Young (under 30)
Old (over 30)
The question: Is there a relationship between age and watch preference?
Chi-Square Test for Independence

6. Decision tree Chi-square test of independence (χ2 lower-case chi )
Describing the relationship between two categorical variables or
Young
Old or
Decision tree

7. Chi-Squared 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). The
question: is there a relationship between age and watch preference?
Chi-Squared Test for Independence

8. Chi-Squared 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). The
question: is there a relationship between age and watch preference?
Step 1: State the hypotheses and select an alpha level
H0: Preference is independent of age (“no relationship”)
HA: Preference is related to age (“there is a relationship”)
We’ll set α = 0.05
Observed scores
Chi-Squared Test for Independence

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

10. Chi-Squared Test for Independence
As df gets larger, need larger X2 value for significance. Number of cells get larger.
X2 α = .05
5.99
7.81
11.07
14.07
Chi-Squared Test for Independence

11. 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
Chi-Squared Test for Independence

12. 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
Spot check: make sure the row totals and column totals add up to the same thing
Chi-Squared Test for Independence

13. Chi-Squared Test for Independence
Step 3: Collect the data. Obtain row and column totals (sometimes called the marginals) and calculate the expected frequencies (in each cell)
Observed scores
Expected scores 70 56 14 30 24 6
Under 30
Over 30
Digital
Analog
Undecided
Chi-Squared Test for Independence

14. Chi-Squared Test for Independence
Step 3: Collect the data. Obtain row and column totals (sometimes called the marginals) and calculate the expected frequencies (in each cell)
Observed scores
Expected scores 70 56 14
“expected frequencies” - if the null hypothesis is correct, then these are the frequencies that you would expect 30 24 6
Under 30
Over 30
Digital
Analog
Undecided
Chi-Squared Test for Independence

15. Chi-Squared Test for Independence
Step 4: compute the χ2
Find the residuals (fo - fe) for each cell
Chi-Squared Test for Independence

16. Computing the Chi-square
Step 4: compute the χ2
Find the residuals (fo - fe) for each cell
Computing the Chi-square

17. Computing the Chi-square
Step 4: compute the χ2
Find the residuals (fo - fe) for each cell
Square these differences
Computing the Chi-square

18. Computing the Chi-square
Step 4: compute the χ2
Find the residuals (fo - fe) for each cell
Square these differences
Divide the squared differences by fe
Computing the Chi-square

19. Computing the Chi-square
Step 4: compute the χ2
Find the residuals (fo - fe) for each cell
Square these differences
Divide the squared differences by fe
Sum the results
Computing the Chi-square

20. Chi-Squared, the final step
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?
Step 5: Compare this computed statistic (38.09) against the critical value (5.99) and make a decision about your hypotheses
here we reject the H0 and conclude that there is a relationship between age and watch preference
Chi-Squared, the final step

21. Chi square as a statistical test
each cell = observed difference
difference expected by chance
Chi square as a statistical test

22. Chi-Square Test in SPSS
Analyze  Descriptives  Crosstabs
Chi-Square Test in SPSS

23. 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
Chi-Square Test in SPSS

24. Chi-Square Test in SPSS

25. In lab: Gain experience using and interpreting Chi-square procedures
Questions?
Chi-squared test: (~12 mins)
Chi-squared test: (~38 mins)
Chi-squared in SPSS:
Chi-squared distribution:
Wrap up