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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