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

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

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

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 => 150. Otherwise, n=>300 Meta analysis: Start with 30 and calculate failsafe n

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

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

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)

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

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 (http://people.ku.edu/~preacher/chisq/chisq.htm) 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

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

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

Calculating Unidimensional X2 X2 = S[(fo –fe)2/fe] =(45 – 50)2/50 + (40-50)2/50+(65-50)2/50 = 0.5 + 2 + 4.5 X2obt = 7 df = c – 1 (#cells – 1) Df = 3 – 1 = 2 X2 crit = 5.991 X2(2) = 7.0, p ≤ 0.05

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

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

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

Now, go Back to the Original Formula X2 = S[(fo –fe)2/fe] (68-80)2/80+(22-20)2/20+(110+100)2/100+(92-80)2/80+(18-20)2/20+(90-100)2/100 = 1.80 + 0.2 + 1.0 + 1.8 + 0.2 + 1.0 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

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

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

Questions? Thoughts?