1. Correlated-Samples ANOVA The Multivariate Approach One-Way

2. Cross-Species-Fostering House mice onto house mice, prairie deer mice, or domestic Norway rats. After weaning, tested in apparatus with access to tunnels scented like clean pine shavings, house mouse, deer mouse, or rat. House mice and deer mice were descendants of recently wild-trapped mice. Reversed light cycle, red lighting

3. Mus musculus

4. Peromyscus maniculatus

5. Rattus norwegicus domestic

6. Homo sapiens

7. data Mus; infile 'C:\... \tunnel4b.dat'; INPUT NURS V_clean V_Mus V_Pero V_Rat VT_clean VT_Mus VT_Pero VT_Rat T_clean T_Mus T_Pero T_Rat TT_clean TT_Mus TT_Pero TT_Rat L_clean L_Mus L_Pero L_Rat LT_clean LT_Mus LT_Pero LT_Rat; Format NURS rodent. ; The TT_ variables have been transformed to normal.

8. The ANOVA Proc ANOVA; Model TT_clean TT_mus TT_pero TT_rat = / nouni; Repeated scent 4 Contrast(1) / summary printe; run; “nouni” suppresses irrelevant output “summary” and “printe” gives us ANOVA tables for contrasts and “printe” tests sphericity

9. Contrasts Contrast(1) – compare the first condition with all other conditions. Profile – compare each condition with the next condition Polynomial – trend analysis Helmert – contrast each condition with the mean of the following conditions Mean(n) -- contrast each level (except the n th ) with the mean of all other levels.

10. Mauchly Sphericity Assumption Violated Sphericity Tests VariablesDFMauchly's Criterion Chi-SquarePr > ChiSq Orthogonal Components 50.643398614.871190.0109

11. MANOVA MANOVA Test Criteria and Exact F Statistics for the Hypothesis of no scent Effect StatisticValueF ValueNum DFDen DFPr > F Wilks' Lambda 0.583437.853330.0004 Pillai's Trace0.416567.853330.0004 Hotelling- Lawley Trace 0.713987.853330.0004 Roy's Greatest Root 0.713987.853330.0004

12. Univariate Approach SourceDFAnova SS Mean Square F Value Pr > FAdj Pr > F G - GH - F scent31467.267489.0897.010.00020.00090.0006 Error(scent)1057326.95269.7804 Greenhouse-Geisser Epsilon0.7824 Huynh-Feldt Epsilon0.8422 Both the G-G and the H-F are near or above.75, it is probably best to use the H-F df = 3(.8422), 105(.8422) = 2.53, 88.43

13. Contrasts: Clean Scent vs. Mus musculus: p =.008 Peromyscus maniculatus: p =.29 Rattus norvegicus: p =.14

14. Untransformed Means proc means; var T_clean -- T_Rat;

15. Randomized Blocks Data data multi; input block1-block3; subj = _N_; B1vsB3 = block1-block3; B1vsB2 = block1-block2; B2vsB3=block2-block3; cards; 10 9 7 8 6 3 7 6 4 5 6 3 And two more cases

16. Randomized Blocks ANOVA Proc ANOVA; Model block1-block3 = / nouni; Repeated block 3 / nom;

17. Randomized Blocks Results SourceDFAnova SS Mean Square F Value Pr > FAdj Pr > F G - GH - F block239.0000019.5000039.00<.00010.00040.0001 Error(block)105.0000000.500000 Greenhouse-Geisser Epsilon0.6579 Huynh-Feldt Epsilon0.8000

18. Pairwise Comparisons proc means t prt; var B1vsB3 B1vsB2 B2vsB3; run;

19. Want Pooled Error? The comparisons on previous slide use individual error terms. Get more power with pooled error. First, unpack data from multivariate setup to univariate setup. Then use ANOVA with desired procedure (LSD, Tukey, REGWQ, etc.)

20. Unpack the Data data univ; set multi; array b[3] block1-block3; do block = 1 to 3; errors = b[block]; output; end; drop block1- block3;

21. The Unpacked Data subjblockerrors 1110 129 137 218 226 233 317 And so on

22. LSD with Pooled Error Proc ANOVA; Class subj block; Model errors = subj block; Means block / lsd lines; run; Means with the same letter are not significantly different. t GroupingMeanNblock A9.333361 B8.333362 C5.833363

23. SPSS Want to use SPSS instead of SAS? See my document The Multivariate Approach to the One-Way Repeated Measures ANOVA