2. Is a persons’ size related to if they were bullied
You gathered data from 209 children at Springfield Elementary School.
Assessed:
Height (short vs. not short)
Bullied (yes vs. no)

3. Results
Ever Bullied

4. Results
Ever Bullied

5. Results
Ever Bullied

6. Results
Ever Bullied

7. Results
Ever Bullied

8. Results
Ever Bullied

9. Is this difference in proportion due to chance?
To test this you use a Chi-Square (2)
Notice how this is different than a t-test or an ANOVA
t-tests and ANOVAs use quantitative variables
Chi-squares use frequency counts of categories

10. Hypothesis H1: There is a relationship between the two variables
i.e., a persons size is related to if they were bullied
H0:The two variables are independent of each other
i.e., there is no relationship between a persons size and if they were bullied

11. Logic Is the same as t-tests and ANOVAs
1) calculate an observed Chi-square
2) Find a critical value
3) See if the the observed Chi-square falls in the critical area

12. Chi-Square
O = observed frequency
E = expected frequency

13. Results
Ever Bullied

14. Observed Frequencies
Ever Bullied

15. Expected frequencies
Are how many observations you would expect in each cell if the null hypothesis was true
i.e., there there was no relationship between a persons size and if they were bullied

16. Expected frequencies To calculate a cells expected frequency:
For each cell you do this formula

17. Expected Frequencies
Ever Bullied

18. Expected Frequencies
Ever Bullied

19. Expected Frequencies
Row total = 92
Ever Bullied

20. Expected Frequencies
Row total = 92
Column total = 72
Ever Bullied

21. Expected Frequencies Ever Bullied Row total = 92 N = 209
Column total = 72
Ever Bullied

22. Expected Frequencies
E = (92 * 72) /209 = 31.69
Ever Bullied

23. Expected Frequencies
Ever Bullied

24. Expected Frequencies
Ever Bullied

25. Expected Frequencies
E = (92 * 137) /209 = 60.30
Ever Bullied

26. Expected Frequencies Ever Bullied E = (117 * 72) / 209 = 40.30

27. Expected Frequencies Ever Bullied
The expected frequencies are what you would expect if there was no relationship between the two variables!
Ever Bullied

28. How do the expected frequencies work?
Looking only at:
Ever Bullied

29. How do the expected frequencies work?
If you randomly selected a person from these 209 people what is the probability you would select a person who is short?
Ever Bullied

30. How do the expected frequencies work?
If you randomly selected a person from these 209 people what is the probability you would select a person who is short? 92 / 209 = .44
Ever Bullied

31. How do the expected frequencies work?
If you randomly selected a person from these 209 people what is the probability you would select a person who was bullied?
Ever Bullied

32. How do the expected frequencies work?
If you randomly selected a person from these 209 people what is the probability you would select a person who was bullied? 72 / 209 = .34
Ever Bullied

33. How do the expected frequencies work?
If you randomly selected a person from these 209 people what is the probability you would select a person who was bullied and is short?
Ever Bullied

34. How do the expected frequencies work?
If you randomly selected a person from these 209 people what is the probability you would select a person who was bullied and is short? (.44) (.34) = .15
Ever Bullied

35. How do the expected frequencies work?
How many people do you expect to have been bullied and short?
Ever Bullied

36. How do the expected frequencies work?
How many people would you expect to have been bullied and short? (.15 * 209) = (difference due to rounding)
Ever Bullied

37. Back to Chi-Square
O = observed frequency
E = expected frequency

38. 2

39. 2

40. 2

41. 2

42. 2

43. 2

44. 2

45. Significance Is a 2 of 9.13 significant at the .05 level?
To find out you need to know df

46. Degrees of Freedom
To determine the degrees of freedom you use the number of rows (R) and the number of columns (C)
DF = (R - 1)(C - 1)

47. Degrees of Freedom
Rows = 2
Ever Bullied

48. Degrees of Freedom
Rows = 2
Columns = 2
Ever Bullied

49. Degrees of Freedom
To determine the degrees of freedom you use the number of rows (R) and the number of columns (C)
df = (R - 1)(C - 1)
df = (2 - 1)(2 - 1) = 1

50. Significance Look on Table E -- page 389 df = 1  = .05
2critical = 3.84

51. Decision Thus, if 2 > than 2critical
Reject H0, and accept H1
If 2 < or = to 2critical
Fail to reject H0

52. Current Example 2 = 9.13 2critical = 3.84
Thus, reject H0, and accept H1

53. Current Example
H1: There is a relationship between the the two variables
A persons size is significantly (alpha = .05) related to if they were bullied

55. Seven Steps for Doing 2 1) State the hypothesis 2) Create data table
3) Find 2 critical
4) Calculate the expected frequencies
5) Calculate 2
6) Decision
7) Put answer into words

56. Example With whom do you find it easiest to make friends?
Subjects were either male and female.
Possible responses were: “opposite sex”, “same sex”, or “no difference”
Is there a significant (.05) relationship between the gender of the subject and their response?

57. Results

58. Step 1: State the Hypothesis
H1: There is a relationship between gender and with whom a person finds it easiest to make friends
H0:Gender and with whom a person finds it easiest to make friends are independent of each other

59. Step 2: Create the Data Table

60. Step 2: Create the Data Table
Add “total” columns and rows

61. Step 3: Find 2 critical
df = (R - 1)(C - 1)

62. Step 3: Find 2 critical df = (R - 1)(C - 1) df = (2 - 1)(3 - 1) = 2
 = .05
2 critical = 5.99

63. Step 4: Calculate the Expected Frequencies
Two steps:
4.1) Calculate values
4.2) Put values in your data table

64. Step 4: Calculate the Expected Frequencies

65. Step 4: Calculate the Expected Frequencies

66. Step 4: Calculate the Expected Frequencies

67. Step 4: Calculate the Expected Frequencies