1. Schedule for Remainder of Semester  
1. ANOVA: One way, Two way
2. Planned contrasts 
3. Correlation and Regression
4. Moderated Multiple Regression
5. Power Analyses
6. Survey design 
7. Non-experimental designs   IF TIME PERMITS
8. Writing up research
Quiz 2: Nov up to and including one-way ANOVA
Quiz 3: Dec. 5 – What we’ve covered by Dec. 5
Class Assignment: Assigned Nov. 28, Due Dec. 7
Final: Dec. 19

2. HANDS ON STATS PRACTICE
SPSS Demo in Computer Lab (Hill Hall Rm. 124)
Thursday, Nov. 16 5:30 to 7:30
Hill Hall, Room 126
Homework:
Extra Credit: 3 Pts full credit, 1 pt partial credit
Homework corresponds to Computer Lab

3. F Distribution Notation
"F (1, 8)" means:
The F distribution with:
1 df in the numerator (1 df associated with variance between treatment groups (= between-group variation))
and
8 df in the denominator (8 df associated with variance around group means (= within-group variation))

4. F Distribution for (2, 42) df
Empirical Sampling (Monte Carlo Simulations)
Theoretical Sampling

5. F is One Distribution; F‘ is Infinite Distributions
Hello: I’m F. I contain Mean Group 1, Mean Group 2, Mean Group 3, Etc.
Hello: I’m F ' I contain Mean Group 1, Mean Group 2, Mean Group 3, Etc.
Hello: I’m F ' I contain Mean Group 1, Mean Group 2, Mean Group 3, Etc.
Hello: I’m F ' I contain Mean Group 1, Mean Group 2, Mean Group 3, Etc.

6. Percent cases null hypothesis is true
Criterion F and p Value
For F (2, 42) = 3.48
Percent cases null hypothesis is true

7. F and F' Distributions (from Monte Carlo Experiments)
Note how often we reject H1 when true!
And the small proportion of H1 accepted when actually true.

8. Which Distribution Do Data Support: F or F′?
If F is correct, then Ho supported: u1 = u2
(First born = Last born)
If F' is correct, then H1 supported: u1  u2
(First born ≠ Last born)

9. Critical Values for F (1, 8) [Result of Birth Order and Rating of Disclosers]
What must our F be in order to reject null hypothesis?
≥ 5.32

10. Decision Rule Regarding F
Reject null hypothesis when F observed >  (m, n)
Reject null hypothesis when F observed > (1, 8).
F (1,8) = 8.88 >  = 5.32
Decision: Reject or Accept null hypothesis?
Reject or Accept alternative hypothesis?
Have we proved alt. hypothesis?
Format for reporting our result:
F (1,8) = 8.88, p < .05
F (1,8) = 8.88, p < also OK, based on our results.
Conclusion: First Borns regard help-seekers as
less "active" than do Last Borns.
No, we supported it. There's a chance (p < .05), that we are wrong.

11. Summary of One Way ANOVA  
1. Specify null and alt. hypotheses
2. Conduct experiment
3. Calculate F ratio = Between Group Diffs
Within Group Diffs
 4. Does F support the null hypothesis? i.e., is
Observed F > Criterion F, at p < .05?
p > .05, accept null hyp.
p < .05, accept alt. hyp.
BUT:
OK to report p < .10 = “marginal difference”
Sometimes OK to report p < .15 = “non significant trend”

12. TYPE I AND TYPE II ERRORS

13. Errors in Hypothesis Testing
Reality
Null Hyp. True Null Hyp. False
Alt. Hyp. False Alt. Hyp. True
Decision
Reject Null Incorrect Correct
Accept Alt Type I Error
Accept Null Correct Incorrect:
Reject Alt Type II Error
Type I Error
Type II Error

14. Avoiding Type I and Type II Errors
Avoiding Type I error:
1. Reduce the size of the Type I rejection region (i.e., go from p < .05 to p < .01 for example).
Avoiding Type II error (= Expt’l Power)
1. Reduce size of Type II rejection region, BUT
a. Not permitted by basic sci. community b. But, OK in some rare applied contexts
2. Reduce random error (within-groups variance)
a. Increase sample size
b. Improve experimental methods/design
1. Standardized instructions
2. Train experimenters
c. Pilot testing , etc.

15. ANOVA II (Part 1)
Class 17

16. Assumptions of Methods Class
Kent is not inventing facts
2. Kent is actually a psychology professor
3. Readings are accurate
4. Statistics isn’t voodoo
5. This class is real, not a bad dream

17. Assumptions of ANOVA 2. Homogeneity of error variance
1. Normally distributed error variance
2. Homogeneity of error variance
3. Independence of error components
4. Additivity of components
5. Equal sample sizes

18. Opera Appreciation as a Function of Substance Sampling
Opera Enjoyment Score
Equal Variance
Normal Variance
Equal n’s
Random assign’d
Soda Group:
n = 30, X = σ = 2.6
Vodka Group:
n = 30, X = σ = 2.6
Ss randomly assigned to Soda Group or Vodka Group

19. Non-Normal Distributions Distort 2%-3%
(Platykurtotic)

20. Effect of Different Variances on ANOVA:
Violation of Homogeneity Assumption

21. Additivity of Components
ASij =  + (j - ) + (ASij - j)
Individual Score
Total
Mean
Group Mean minus
Total Mean
Individ. Score
minus
Total Mean

22. UNEQUAL SAMPLE SIZES Not a problem if sizes unequal and:
a. Differences in sample sizes is small, or
b. Size of smallest sample is relatively large (n > 30, e.g.)
Is a problem if sizes unequal AND:
a. Differences in sample sizes is large
b. Samples differ in their variances

23. Unplanned and Unequal Subject Loss
1. Subject loss due to "real world" circumstances
2. Subjects fail to meet inclusion criterion
Subjects fail to meet response-level criterion
Problem occurs if unplanned loss is systematic, not random

24. Unequal Subject Loss and Compromised RandomnessN
Total Subjects Quit
Motivated Subjects Quit
Unmotivated Subjects Quit
Vodka Condition 30 5
(.17) 3
(.10) 2
(.07)
Soda Condition 9
(.30) 8
(.27) 1
(.03)

25. ANOVA is Robust to Which Kinds
of Violations?
1. Normally distributed error variance
2. Homogeneity of error variance
3. Independence of error components
4. Additivity of components
5. Equal sample sizes
Yes
Yes No No
But not a worry
Diffs are small, or smallest sample large AND Diffs not due to systematic attrition
Yes, if:

26. Variance as a Descriptive Statistic
How much do groups differ in their within groups variance?
One-Way ANOVA Levene Test for Homogeneity of Variance
μ1 = μ2 = μ3 = μx σ1 = σ2 = σ3 = σx
SPSS Conducts Levene Test for Homogeneity of Variance

27. Appreciate Friends if Suppress or Express Scary Movie Thoughts and Feelings
Suppress Cond
Express Cond
Friend Appreciation Score
How do conditions differ?
Suppress Group:
n = 10, σ = 0.69
Confide Group:
n = 10, σ = 1.51
Does variability of suppress group differ from
variability of confide group?

28. Levene's Test of Homogeneity of Variance
Is a sig. Levene's Test a big problem?
No. Recall ANOVA robust to violation of equal var.
Levene's Test output
How fix this problem?
Data transformations.
Run more subs.
But, again ANOVA is robust!

29. Multiple Factor ANOVA

30. Multiple Factor Tests
Birth Order Means

31. Anatomy of Factorial Design
"FX" = "Effects"

32. Limitations of Main Effects
Show “what” but not “why”
Fail to account for the “what ifs”
Cannot show moderation
Cannot account for underlying causes

33. X X

34. Gender Main Effect X X

35. Birth Order Main EffectX X

36. Verbal Definitions of Interaction Effects
(Keppel, 178)
1. "Two variables interact when the effect of (at least) one variable changes at different levels of the other variable".  
2. "An interaction is present when the simple main effects of one variable are not the same at different levels of the second variable". 

37. Implications of Interaction
1. Main effects, alone, will not fully describe the results.
2. Each factor (or IV) must be interpreted in terms of the factor(s) with which it interacts.
3. Analysis of findings, when an interaction is present, will focus on individual treatment means rather than on overall factor (IV) means.
4. Interaction indicates moderation.

38. Interactions are Non-Additive Relationships Between Factors
1. Additive: When presence of one factor changes the expression of another factor consistently, across all levels.
2. Non-Additive: When the presence of one factor changes the expression of another factor differently, at different levels.

39. Ordinal and Disordinal Interactions

40. Eyeballing Interactions and Main Effects*
Dem
GOP * * X X X
North
South X
Dem
GOP * * * X X
North
South

41. Birth Order Main Effect:
Gender Main Effect:
Interaction: NO NO NO

42. Birth Order Main Effect:
Gender Main Effect:
Interaction:
YES NO NO

43. Birth Order Main Effect:
Gender Main Effect:
Interaction: NO
YES NO

44. Birth Order Main Effect:
Gender Main Effect:
Interaction:
YES
YES NO

45. Birth Order Main Effect:
Gender Main Effect:
Interaction: NO NO
YES

46. Birth Order Main Effect:
Gender Main Effect:
Interaction:
YES NO
YES

47. Birth Order Main Effect:
Gender Main Effect:
Interaction: NO
YES
YES

48. Birth Order Main Effect:
Gender Main Effect:
Interaction:
YES
YES
YES