2. Why is this important? Requirement Understand research articles
Do research for yourself
Real world

3. The Three Goals of this Course
1) Teach a new way of thinking
2) Teach “factoids”

4. Mean But here is the formula == so what you did was
= 320
320 / 4 = 80

5. r =

6. What you have learned!
Describing and Exploring Data / The Normal Distribution
Scales of measurement
Populations vs. Samples
Learned how to organize scores of one variable using:
frequency distributions
graphs

7. What you have learned! Measures of central tendency Variability Mean
Median
Mode
Variability
Range
IQR
Standard Deviation
Variance

8. What you have learned! Z Scores Find the percentile of a give score
Find the score for a given percentile

9. What you have learned! Sampling Distributions & Hypothesis Testing
Is this quarter fair?
Sampling distribution
CLT
The probability of a given score occurring

10. What you have learned! Basic Concepts of Probability
Joint probabilities
Conditional probabilities
Different ways events can occur
Permutations
Combinations
The probability of winning the lottery
Binomial Distributions
Probability of winning the next 4 out of 10 games of Blingoo

11. What you have learned! Categorical Data and Chi-Square
Chi square as a measure of independence
Phi coefficient
Chi square as a measure of goodness of fit

12. What you have learned! Hypothesis Testing Applied to Means
One Sample t-tests
Two Sample t-tests
Equal N
Unequal N
Dependent samples

13. What you have learned! Correlation and Regression Correlation

14. What you have learned! Alternative Correlational Techniques
Pearson Formulas
Point-Biserial
Phi Coefficent
Spearman’s rho
Non-Pearson Formulas
Kendall’s Tau

15. What you have learned! Multiple Regression Common applications
Causal Models
Standardized vs. unstandarized
Multiple R
Semipartical correlations
Common applications
Mediator Models
Moderator Mordels

16. What you have learned! Simple Analysis of Variance ANOVA
Computation of ANOVA
Logic of ANOVA
Variance
Expected Mean Square
Sum of Squares

17. What you have learned! Multiple Comparisons Among Treatment Means
What to do with an omnibus ANOVA
Multiple t-tests
Linear Contrasts
Orthogonal Contrasts
Trend Analysis
Controlling for Type I errors
Bonferroni t
Fisher Least Significance Difference
Studentized Range Statistic
Dunnett’s Test

18. What you have learned! Factorial Analysis of Variance Factorial ANOVA
Computation and logic of Factorial ANOVA
Interpreting Results
Main Effects
Interactions

19. What you have learned!
Factorial Analysis of Variance and Repeated Measures
Factorial ANOVA
Computation and logic of Factorial ANOVA
Interpreting Results
Main Effects
Interactions
Repeated measures ANOVA

20. The Three Goals of this Course
1) Teach a new way of thinking
2) Teach “factoids”
3) Self-confidence in statistics

22. Remember
You just invented a “magic math pill” that will increase test scores.
On the day of the first test you give the pill to 4 subjects. When these same subjects take the second test they do not get a pill
Did the pill increase their test scores?

23. What if. . .
You just invented a “magic math pill” that will increase test scores.
On the day of the first test you give a full pill to 4 subjects. When these same subjects take the second test they get a placebo. When these same subjects that the third test they get no pill.

24. Note You have more than 2 groups You have a repeated measures design
You need to conduct a Repeated Measures ANOVA

25. Tests to Compare Means Design of experiment
Independent Variables and # of levels
Independent Samples
Related Samples
One IV, 2 levels
Independent t-test
Paired-samples t-test
One IV, 2 or more levels
ANOVA
Repeated measures ANOVA
Tow IVs, each with 2 or more levels
Factorial ANOVA
Repeated measures factorial ANOVA

26. What if. . .
You just invented a “magic math pill” that will increase test scores.
On the day of the first test you give a full pill to 4 subjects. When these same subjects take the second test they get a placebo. When these same subjects that the third test they get no pill.

27. Results Pill Placebo No Pill Sub 1 57 60 64 Sub 2 71 72 74 Sub 3 75 7678
Sub 4 93 92 96
Mean

28. For now . . . Ignore that it is a repeated design
Pill
Placebo
No Pill
Sub 1 57 60 64
Sub 2 71 72 74
Sub 3 75 76 78
Sub 4 93 92 96
Mean

29. Pill Placebo No Pill Sub 1 57 60 64 Sub 2 71 72 74 Sub 3 75 76 7893 92 96
Mean
Between Variability = low

30. Pill Placebo No Pill Sub 1 57 60 64 Sub 2 71 72 74 Sub 3 75 76 7893 92 96
Mean
Within Variability = high

32. Pill Placebo No Pill Sub 1 57 60 64 Sub 2 71 72 74 Sub 3 75 76 78
Notice – the within variability of a group can be predicted by the other groups
Pill
Placebo
No Pill
Sub 1 57 60 64
Sub 2 71 72 74
Sub 3 75 76 78
Sub 4 93 92 96
Mean

33. Pill Placebo No Pill Sub 1 57 60 64 Sub 2 71 72 74 Sub 3 75 76 78
Notice – the within variability of a group can be predicted by the other groups
Pill
Placebo
No Pill
Sub 1 57 60 64
Sub 2 71 72 74
Sub 3 75 76 78
Sub 4 93 92 96
Mean
Pill and Placebo r = .99; Pill and No Pill r = .99; Placebo and No Pill r = .99

34. Pill Placebo No Pill Mean Sub 1 57 60 64 60.33 Sub 2 71 72 74 72.3375 76 78
76.33
Sub 4 93 92 96
93.66
These scores are correlated because, in general, some subjects tend to do very well and others tended to do very poorly

35. Repeated ANOVA
Some of the variability of the scores within a group occurs due to the mean differences between subjects.
Want to calculate and then discard the variability that comes from the differences between the subjects.

36. Example Pill Placebo No Pill Mean Sub 1 57 60 64 60.33 Sub 2 71 72 74
72.33
Sub 3 75 76 78
76.33
Sub 4 93 92 96
93.66
75.66

37. Sum of Squares SS Total Computed the same way as before
The total deviation in the observed scores
Computed the same way as before

38. Pill Placebo No Pill Mean Sub 1 57 60 64 60.33 Sub 2 71 72 74 72.3375 76 78
76.33
Sub 4 93 92 96
93.66
75.66
SStotal = ( )2+ ( ) ( )2 = 908
*What makes this value get larger?

39. Pill Placebo No Pill Mean Sub 1 57 60 64 60.33 Sub 2 71 72 74 72.3375 76 78
76.33
Sub 4 93 92 96
93.66
75.66
SStotal = ( )2+ ( ) ( )2 = 908
*What makes this value get larger?
*The variability of the scores!

40. Sum of Squares SS Subjects
Represents the SS deviations of the subject means around the grand mean
Its multiplied by k to give an estimate of the population variance (Central limit theorem)

41. Pill Placebo No Pill Mean Sub 1 57 60 64 60.33 Sub 2 71 72 74 72.3375 76 78
76.33
Sub 4 93 92 96
93.66
75.66
SSSubjects = 3(( )2+ ( ) ( )2) = 1712
*What makes this value get larger?

42. Pill Placebo No Pill Mean Sub 1 57 60 64 60.33 Sub 2 71 72 74 72.3375 76 78
76.33
Sub 4 93 92 96
93.66
75.66
SSSubjects = 3(( )2+ ( ) ( )2) = 1712
*What makes this value get larger?
*Differences between subjects

43. Sum of Squares SS Treatment
Represents the SS deviations of the treatment means around the grand mean
Its multiplied by n to give an estimate of the population variance (Central limit theorem)

44. Pill Placebo No Pill Mean Sub 1 57 60 64 60.33 Sub 2 71 72 74 72.3375 76 78
76.33
Sub 4 93 92 96
93.66
75.66
SSTreatment = 4(( )2+ ( )2+( )2) = 34.66
*What makes this value get larger?

45. Pill Placebo No Pill Mean Sub 1 57 60 64 60.33 Sub 2 71 72 74 72.3375 76 78
76.33
Sub 4 93 92 96
93.66
75.66
SSTreatment = 4(( )2+ ( )2+( )2) = 34.66
*What makes this value get larger?
*Differences between treatment groups

46. Sum of Squares Have a measure of how much all scores differ
SSTotal
Have a measure of how much this difference is due to subjects
SSSubjects
Have a measure of how much this difference is due to the treatment condition
SSTreatment
To compute error simply subtract!

47. Sum of Squares SSError = SSTotal - SSSubjects – SSTreatment
8.0 =

48. Compute df Source df SS Subjects 1712.00 Treatment 34.66 Error 8.00
df total = N -1
Source df SS
Subjects
Treatment
34.66
Error
8.00
Total 11

49. Compute df Source df SS Subjects 3 1712.00 Treatment 34.66 Error 8.00
df total = N -1
df subjects = n – 1
Source df SS
Subjects 3
Treatment
34.66
Error
8.00
Total 11

50. Compute df Source df SS Subjects 3 1712.00 Treatment 2 34.66 Error
df total = N -1
df subjects = n – 1
df treatment = k-1
Source df SS
Subjects 3
Treatment 2
34.66
Error
8.00
Total 11

51. Compute df Source df SS Subjects 3 1712.00 Treatment 2 34.66 Error 6
df total = N -1
df subjects = n – 1
df treatment = k-1
df error = (n-1)(k-1)
Source df SS
Subjects 3
Treatment 2
34.66
Error 6
8.00
Total 11

52. Compute MS Source df SS MS Subjects 3 1712.00 Treatment 2 34.66 17.33
Error 6
8.00
Total 11

53. Compute MS Source df SS MS Subjects 3 1712.00 Treatment 2 34.66 17.33
Error 6
8.00
1.33
Total 11

54. Compute F Source df SS MS F Subjects 3 1712.00 Treatment 2 34.66 17.33
13.00
Error 6
8.00
1.33
Total 11

55. Test F for Significance
Source df SS MS F
Subjects 3
Treatment 2
34.66
17.33
13.00
Error 6
8.00
1.33
Total 11

56. Test F for Significance
Source df SS MS F
Subjects 3
Treatment 2
34.66
17.33
13.00*
Error 6
8.00
1.33
Total 11
F(2,6) critical = 5.14

57. Test F for Significance
Source df SS MS F
Subjects 3
Treatment 2
34.66
17.33
13.00*
Error 6
8.00
1.33
Total 11
F(2,6) critical = 5.14

59. Additional tests Source df SS MS F Subjects 3 1712.00 Treatment 2
34.66
17.33
13.00*
Error 6
8.00
1.33
Total 11
Can investigate the meaning of the F value by computing t-tests and Fisher’s LSD

60. Remember

61. Pill
Placebo
No Pill
Mean 74 75 78
75.66

62. Pill
Placebo
No Pill
Mean 74 75 78
75.66
Pill vs. Placebo

63. Pill
Placebo
No Pill
Mean 74 75 78
75.66
Pill vs. Placebo t=1.23

64. Pill Placebo No Pill Mean 74 75 78 75.66 Pill vs. Placebo t=1.23
t (6) critical = 2.447

65. Pill Placebo No Pill Mean 74 75 78 75.66 Pill vs. Placebo t=1.23
Pill vs. No Pill t =4.98*
t (6) critical = 2.447

66. Pill Placebo No Pill Mean 74 75 78 75.66 Pill vs. Placebo t=1.23
Pill vs. No Pill t =4.98*
Placebo vs. No Pill t =3.70*
t (6) critical = 2.447

67. Practice
You wonder if the statistic tests are of all equal difficulty. To investigate this you examine the scores 4 students got on the three different tests. Examine this question and (if there is a difference) determine which tests are significantly different.

68. Test 1
Test 2
Test 3
Sub 1 60 70 78
Sub 2 76 85
Sub 3 64 90 89
Sub 4 77 81 94

71. SPSS Homework – Bonus
1) Determine if practice had an effect on test scores.
2) Examine if there is a linear trend with practice on test scores.

73. Four Step When Solving a Problem
1) Read the problem
2) Decide what statistical test to use
3) Perform that procedure
4) Write an interpretation of the results

74. Four Step When Solving a Problem
1) Read the problem
2) Decide what statistical test to use
3) Perform that procedure
4) Write an interpretation of the results

75. Four Step When Solving a Problem
1) Read the problem
2) Decide what statistical test to use
3) Perform that procedure
4) Write an interpretation of the results

76. How do you know when to use what?
If you are given a word problem, would you know which statistic you should use?

77. Example
An investigator wants to predict a male adult’s height from his length at birth. He obtains records of both measures from a sample of males.

78. `

79. Example
An investigator wants to predict a male adult’s height from his length at birth. He obtains records of both measures from a sample of males.
Use regression