Correlated-Samples ANOVA

The Multivariate ApproachOne-Way

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

Mus musculus

Peromyscus maniculatus

Rattus norwegicus domestic

Homo sapiens

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.

The ANOVAProc 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

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

nth) with the mean of all other levels.

Mauchly

• Sphericity Assumption Violated

Sphericity TestsVariables DF Mauchly's

CriterionChi-Square Pr > ChiSq

Orthogonal Components

5 0.6433986 14.87119 0.0109

MANOVAMANOVA Test Criteria and Exact F Statistics for the Hypothesis of no scent Effect

Statistic Value F Value Num DF Den DF Pr > FWilks' Lambda

0.58343 7.85 3 33 0.0004

Pillai's Trace 0.41656 7.85 3 33 0.0004Hotelling-Lawley Trace

0.71398 7.85 3 33 0.0004

Roy's Greatest Root

0.71398 7.85 3 33 0.0004

Univariate ApproachSource DF Anova

SSMean Square

F Value

Pr > F Adj Pr > F

G - G H - F

scent 3 1467.267 489.089 7.01 0.0002 0.0009 0.0006

Error(scent) 105 7326.952 69.7804      

Greenhouse-Geisser Epsilon 0.7824Huynh-Feldt Epsilon 0.8422

• 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

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

Untransformed Meansproc means; var T_clean -- T_Rat;

Randomized Blocks Datadata multi; input block1-block3; subj = _N_;B1vsB3 = block1-block3; B1vsB2 = block1-block2; B2vsB3=block2-block3; cards;10 9 78 6 37 6 45 6 3And two more cases

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

Randomized Blocks ResultsSource DF Anova

SSMean Square

F Value

Pr > F Adj Pr > F

G - G H - F

block 2 39.00000 19.50000 39.00 <.0001 0.0004 0.0001

Error(block) 10 5.000000 0.500000        

Greenhouse-Geisser Epsilon 0.6579Huynh-Feldt Epsilon 0.8000

Pairwise Comparisonsproc means t prt; var B1vsB3 B1vsB2 B2vsB3; run;

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.)

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

The Unpacked Datasubj block errors1 1 101 2 91 3 72 1 82 2 62 3 33 1 7

And so on

LSD with Pooled ErrorProc ANOVA; Class subj block; Model errors = subj block; Means block / lsd lines; run;

Means with the same letter are not significantly different.

t Grouping Mean N blockA 9.3333 6 1       B 8.3333 6 2       C 5.8333 6 3

SPSS• Want to use SPSS instead of SAS?• See my documentThe Multivariate Approach to the One-Way Repeated Measures ANOVA