2. Practice • Is there a significant ( = .01) relationship between opinions about the death penalty and opinions about the legalization of marijuana? • 933 Subjects responded yes or no to: • “Do you favor the death penalty for persons convicted of murder?” • “Do you think the use of marijuana should be made legal?”

3. Results Marijuana ? Death Penalty ?

4. Step 1: State the Hypothesis • H1: There is a relationship between opinions about the death penalty and the legalization of marijuana • H0:Opinions about the death penalty and the legalization of marijuana are independent of each other

5. Step 2: Create the Data Table Marijuana ? Death Penalty ?

6. Step 3: Find 2 critical • df = (R - 1)(C - 1) • df = (2 - 1)(2 - 1) = 1 •  = .01 • 2 critical = 6.64

7. Step 4: Calculate the Expected Frequencies Marijuana ? Death Penalty ?

8. Step 5: Calculate 2

9. Step 6: Decision • Thus, if 2 > than 2critical • Reject H0, and accept H1 • If 2 < or = to 2critical • Fail to reject H0

10. Step 6: Decision 2 = 3.91 2 crit = 6.64 • Thus, if 2 > than 2critical • Reject H0, and accept H1 • If 2 < or = to 2critical • Fail to reject H0

11. Step 7: Put it answer into words • H0:Opinions about the death penalty and the legalization of marijuana are independent of each other • A persons opinion about the death penalty is not significantly (p > .01) related with their opinion about the legalization of marijuana

12. Effect Size • Chi-Square tests are null hypothesis tests • Tells you nothing about the “size” of the effect • Phi (Ø) • Can be interpreted as a correlation coefficient.

13. Phi • Use with 2x2 tables N = sample size

14. Practice • Is there a significant ( = .01) relationship between opinions about the death penalty and opinions about the legalization of marijuana? • 933 Subjects responded yes or no to: • “Do you favor the death penalty for persons convicted of murder?” • “Do you think the use of marijuana should be made legal?”

15. Results Marijuana ? Death Penalty ?

16. Step 6: Decision 2 = 3.91 2 crit = 6.64 • Thus, if 2 > than 2critical • Reject H0, and accept H1 • If 2 < or = to 2critical • Fail to reject H0

17. Phi • Use with 2x2 tables

18. Bullied Example Ever Bullied

19. 2

20. Phi • Use with 2x2 tables

21. Practice • Practice • Page 170 #6.10 • How strong is the relationship?

22. Results X2 = 5.38 X2 crit = 3.83 English ADD

23. Phi • Use with 2x2 tables

26. Practice • In the 1930’s 650 boys participated in the Cambridge-Somerville Youth Study. Half of the participants were randomly assigned to a delinquency-prevention pogrom and the other half to a control group. At the end of the study, police records were examined for evidence of delinquency. In the prevention program 114 boys had a police record and in the control group 101 boys had a police record. Analyze the data and write a conclusion.

27. Chi Square = 1.17 • Chi Square observed = 3.84 • Phi = .04 • Note the results go in the opposite direction that was expected!

29. 2 as a test for goodness of fit • But what if: • You have a theory or hypothesis that the frequencies should occur in a particular manner?

30. Example • M&Ms claim that of their candies: • 30% are brown • 20% are red • 20% are yellow • 10% are blue • 10% are orange • 10% are green

31. Example • Based on genetic theory you hypothesize that in the population: • 45% have brown eyes • 35% have blue eyes • 20% have another eye color

32. To solve you use the same basic steps as before (slightly different order) • 1) State the hypothesis • 2) Find 2 critical • 3) Create data table • 4) Calculate the expected frequencies • 5) Calculate 2 • 6) Decision • 7) Put answer into words

33. Example • M&Ms claim that of their candies: • 30% are brown • 20% are red • 20% are yellow • 10% are blue • 10% are orange • 10% are green

34. Example • Four 1-pound bags of plain M&Ms are purchased • Each M&Ms is counted and categorized according to its color • Question: Is M&Ms “theory” about the colors of M&Ms correct?

36. Step 1: State the Hypothesis • H0: The data do fit the model • i.e., the observed data does agree with M&M’s theory • H1: The data do not fit the model • i.e., the observed data does not agree with M&M’s theory • NOTE: These are backwards from what you have done before

37. Step 2: Find 2 critical • df = number of categories - 1

38. Step 2: Find 2 critical • df = number of categories - 1 • df = 6 - 1 = 5 •  = .05 • 2 critical = 11.07

39. Step 3: Create the data table

40. Step 3: Create the data table Add the expected proportion of each category

41. Step 4: Calculate the Expected Frequencies

42. Step 4: Calculate the Expected Frequencies Expected Frequency = (proportion)(N)

43. Step 4: Calculate the Expected Frequencies Expected Frequency = (.30)(2081) = 624.30

44. Step 4: Calculate the Expected Frequencies Expected Frequency = (.20)(2081) = 416.20

45. Step 4: Calculate the Expected Frequencies Expected Frequency = (.20)(2081) = 416.20

46. Step 4: Calculate the Expected Frequencies Expected Frequency = (.10)(2081) = 208.10

47. Step 5: Calculate 2 O = observed frequency E = expected frequency

48. 2

49. 2

50. 2