[R] restricting pairwise comparisons of interaction effects

Levi Waldron leviwaldron at gmail.com
Mon Apr 28 23:07:29 CEST 2008


I'm interested in restricting the pairwise comparisons of interaction
effects in a multi-way factorial ANOVA, because I find comparisons of
interactions between all different variables different to interpret.
For example (supposing a p<0.10 cutoff just to be able to use this
example):

> summary(fm1 <- aov(breaks ~ wool*tension, data = warpbreaks))
             Df Sum Sq Mean Sq F value    Pr(>F)
wool          1  450.7   450.7  3.7653 0.0582130 .
tension       2 2034.3  1017.1  8.4980 0.0006926 ***
wool:tension  2 1002.8   501.4  4.1891 0.0210442 *
Residuals    48 5745.1   119.7
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

> TukeyHSD(fm1,conf.level=0.90)
  Tukey multiple comparisons of means
    90% family-wise confidence level

Fit: aov(formula = breaks ~ wool * tension, data = warpbreaks)

$wool
         diff       lwr        upr    p adj
B-A -5.777778 -10.77183 -0.7837284 0.058213

$tension
          diff       lwr       upr     p adj
M-L -10.000000 -17.66710 -2.332900 0.0228554
H-L -14.722222 -22.38932 -7.055122 0.0005595
H-M  -4.722222 -12.38932  2.944878 0.4049442

$`wool:tension`
               diff        lwr        upr     p adj
B:L-A:L -16.3333333 -30.112566  -2.554101 0.0302143
A:M-A:L -20.5555556 -34.334788  -6.776323 0.0029580
B:M-A:L -15.7777778 -29.557010  -1.998545 0.0398172
A:H-A:L -20.0000000 -33.779233  -6.220767 0.0040955
B:H-A:L -25.7777778 -39.557010 -11.998545 0.0001136
A:M-B:L  -4.2222222 -18.001455   9.557010 0.9626541
B:M-B:L   0.5555556 -13.223677  14.334788 0.9999978
A:H-B:L  -3.6666667 -17.445899  10.112566 0.9797123
B:H-B:L  -9.4444444 -23.223677   4.334788 0.4560950
B:M-A:M   4.7777778  -9.001455  18.557010 0.9377205
A:H-A:M   0.5555556 -13.223677  14.334788 0.9999978
B:H-A:M  -5.2222222 -19.001455   8.557010 0.9114780
A:H-B:M  -4.2222222 -18.001455   9.557010 0.9626541
B:H-B:M -10.0000000 -23.779233   3.779233 0.3918767
B:H-A:H  -5.7777778 -19.557010   8.001455 0.8705572

It would seem to make sense (and please correct me if I'm wrong) to
restrict the pairwise comparisons of wool:tension to terms like
B:L-A:L, and A:M-A:L, and not calculate or try to interpret
differences like B:M-A:L.  How can I accomplish this (note that there
are actually 5 factors in the experiment I'm analyzing)?



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