Data set up as one observation/subject looks like (with a total of 10 subjects)
Two treatments: shoe type with 3 categories and region with 8 categories ==>
24 "treatment" columns
Subject PHallux PMidToes PLatToe PMTH1 PMidMTH PLatMTH PMidfoot
PRearfoot LHallux LMidToes LLatToe LMTH1 LMidMTH LLatMTH LMidfoot
LRearfoot DHallux DMidToes DLatToe DMTH1 DMidMTH DLatMTH DMidfoot DRearfoot
1 203.230 169.970 75.090 208.420 168.860 129.150
104.840 209.960 200.005 88.880 30.820 315.535 105.445 72.265
88.195 211.280 198.970 113.525 65.640 237.175 148.790
86.105 69.830 222.230
R Code:
library(car)
pressure=read.csv("Shoe_data.csv",header=TRUE,sep=",")
datin.model=cbind(pressure[,2],pressure[,3],pressure[,4],pressure[,5],pressure[,6],pressure[,7],pressure[,8],pressure[,9],pressure[,10],pressure[,11],pressure[,12],pressure[,13],
pressure[,14],pressure[,15],pressure[,16],pressure[,17],pressure[,18],pressure[,19],pressure[,20],pressure[,21],pressure[,22],pressure[,23],pressure[,24],pressure[,25])
multmodel=lm(datin.model ~ 1)
Shoe <- factor(c(rep("P",8),rep("L",8),rep("D",8)))
Region
<-factor(rep(c("Hallux","MidToes","LatToe","MTH1","MidMTH","LatMTH","MidFoot","Rearfoot"),3))
fact.idata <- data.frame(Shoe,Region)
pressure.aov = Anova(multmodel, idata=fact.idata, idesign = ~Shoe + Region,
type="III")
> summary(pressure.aov,multivariate=F)
Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
SS num Df Error SS den Df F Pr(>F)
(Intercept) 6275173 1 192361 9 293.5961 3.535e-08 ***
Shoe 2340 2 11839 18 1.7786 0.1973
Region 748644 7 299408 63 22.5037 6.181e-15 ***
---
Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1
Mauchly Tests for Sphericity
Test statistic p-value
Shoe 0.72437 0.275329
Region 0.00032 0.006714
Greenhouse-Geisser and Huynh-Feldt Corrections
for Departure from Sphericity
GG eps Pr(>F[GG])
Shoe 0.78393 0.2065
Region 0.37482 8.391e-07 ***
---
Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1
HF eps Pr(>F[HF])
Shoe 0.92023 0.2008
Region 0.54302 5.227e-09 ***
---
Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1
Everything runs fine, except that Anova will not allow idesign = ~Shoe*Region
So to look for interaction I set up a long format data set with columns
Subject, Pressure, Shoe, Region--df now has 240 rows
Then I ran:
pressure.alt.df=read.csv("ShoeDataAltFormat.csv",header=TRUE,sep=",")
pressure.aovalt=aov(Pressure~(Shoe*Region)+Error(Subject/(Shoe*Region)),data=pressure.alt.df)
> summary(pressure.aovalt)
Error: Subject
Df Sum Sq Mean Sq F value Pr(>F)
Residuals 1 2346.6 2346.6
Error: Subject:Shoe
Df Sum Sq Mean Sq
Shoe 2 3248 1624.0
Error: Subject:Region
Df Sum Sq Mean Sq
Region 7 606772 86682
Error: Subject:Shoe:Region
Df Sum Sq Mean Sq
Shoe:Region 14 34345 2453.2
Error: Within
Df Sum Sq Mean Sq F value Pr(>F)
Shoe 2 35 17.5 0.0063 0.9937
Region 7 152734 21819.2 7.8272 2.469e-08 ***
Shoe:Region 14 15479 1105.6 0.3966 0.9747
Residuals 192 535219 2787.6
---
Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1
QUESTIONS:
1) Why does the Anova function not allow Shoe*Region?
2) Does the use of aov provide a correct test for Shoe:Region Interaction?
3) The main effect for Shoe from Anova has a denominator df=18; shouldn't that
correspond to one of the error terms from aov?
4) Is the Anova p-value of 0.1973 for the main effect of Shoe the correct test
Any help trying to understand exactly what is happening in Anova versus aov is
greatly appreciated. Looking at interaction plots, there does not appear to be
a lot going on except for two regions with relatively (compared to other
regions) different means for at least one Shoe type within the Region.
Thank you,
Tamre
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