1. Play it Again and When Your Parameters Aren’t Metric
Statistics

2. Repeated Measures Designs
Each subject acts as his or her own control
Greater statistical power
Fewer subjects needed
Practice/carryover effects
Counterbalancing/matching
Use ANOVA or variations (e.g., ANCOVA, MANOVA, MANCOVA)
Paired Samples t Test

3. How Many Subjects Do I Need? ANCOVA
c+(j-1)/n<0.1
C=n(0.0999)-(j-1)
N=c+(j-1)/0.0999
N = number of subjects
C=number of covariates
J=number of groups

4. How Many Subjects Do I Need?
MANOVA: Minimally 20 subs per treatment
Multiple regression: n>104+K for individual predictors n>50+8K for testing multiple correlations. Calculate both and take the larger (k = number of predictors).
Factor analysis: components with 4 or more loadings about /0.6/ regardless of smaple size. Compenents with 10 or more loadings around /0.4/ if n => Otherwise, n=>300
Meta analysis: Start with 30 and calculate failsafe n

5. How Many Subjects Do I Need?
Discriminant analysis: 20 subs per variable
Chi-square: if one dementianal, all cells ahave an fe > 5. If multidimensional, all cells have an fe>1 and no more than 20% have an fe of <5.
Logisistic regression: all cells have an fe greater than 1 and no more htan 20% have less than 5
Alpha for scale reliability = 0.7 per Nunnelly, J.C. (1978). Psychometric theory, 2nd Ed., NY: McGraw-Hill

6. And Now, Nonparawhatsits: When you Can’t Use an ANOVA
Kruskall-Wallis: One-Way ANOVA
Friedman’s 2-way: Two-Way ANOVA

7. When You Can’t use a t Test
Mann-Whitney U: Independent t test Wilcoxin’s
Wilcoxin’s Rank: Independent t test (added advantage of dimensionality)
Sign test: Independent t (based on medians)

8. Other Nonparametics of Note
Spearman’s Rho: Pearson’s r
Chi-Square: Frequency counts
Fisher’s Exact Probability: When can’t use chi-square

9. Familiar with Chi-Square
Will NOT use SPSS for this…it’s actually more helpful to calculate it by hand, devise an Excel formula, or find a Java script on the web (
Frequency data (e.g., head counts)
Examples?
Assumptions:
If one dementianal, all cells ahave an fe > 5. If multidimensional, all cells have an fe>1 and no more than 20% have an fe of <5.
Each observation only contributes to 1 cell

10. X2 = S[(fo –fe)2/fe]
fo = Frequency Observed
fe = Frequency Expected
One dimensional vs Multidemensional

11. Unidimensional Chi Square
One dimensional: One variable (1 x Whatever cells)
Brand preference of a taste test (1 x 3)
fe = total/#cells
= /3
=150/3 50
Brand A
Brand B
Brand C 45 40 65

12. Calculating Unidimensional X2
X2 = S[(fo –fe)2/fe]
=(45 – 50)2/50 + (40-50)2/50+(65-50)2/50 =
X2obt = 7
df = c – 1 (#cells – 1)
Df = 3 – 1 = 2
X2 crit = 5.991
X2(2) = 7.0, p ≤ 0.05

13. Multidimensional X2 More than one variable
Attitude toward an 18-yo drinking age by political party (2 x 3)
fe = (column total/total) (row total)
For
Undecided
Against
Total
Republican 68 22
110
200
Democrat 92 18 90
160 40
400

14. Calculate Expected Frequencies
fe = (column total x row total) /total
160(200)/400 = 80
40(200)/400 = 20
200(200)/400 = 100

15. Put it in the Table For Undecided Against Total Republican 68 (80)
22 (20)
110 (100)
200
Democrat
92 (80)
18 (20)
90 (100)
160 40
400

16. Now, go Back to the Original Formula
X2 = S[(fo –fe)2/fe]
(68-80)2/80+(22-20)2/20+( )2/100+(92-80)2/80+(18-20)2/20+(90-100)2/100 =
X2obt = 6.0
Df = (r-1)(c-1)
= (2 – 1)(3 – 1) = 1(2) = 2
X2crit= 5.991
X2(2) = 6.0, p ≤ 0.05

17. Kruskall-Wallis Friedman’s 2-way Mann-Whitney U Wilcoxin’s Rank
You planned to conduct a 2-way ANOVA, but need to use a nonparametric test instead: What do you use?
Kruskall-Wallis
Friedman’s 2-way
Mann-Whitney U
Wilcoxin’s Rank
Friedman’s 2-way

18. Which of the following best describes Chi-square?
Best to use with ordinal-level data
Comparison between expected and observed frequencies
Ratio of between group variances by within group variances
Used only when you cannot use an ANOVA
Comparison between expected and observed frequencies

19. Questions? Thoughts?