I think I found the solution ! > cc<-factor(cars) > dd<-factor(driver) > MODEL<-y~cc+dd+additive > summary(aov(MODEL,data=DATA))
On 14 Jun, 2010, at 2:52 PM, Andrea Bernasconi DG wrote: > Hi R help, > > Hi R help, > > Which is the easiest (most elegant) way to force "aov" to treat numerical > variables as categorical ? > > Sincerely, Andrea Bernasconi DG > > PROBLEM EXAMPLE > > I consider the latin squares example described at page 157 of the book: > Statistics for Experimenters: Design, Innovation, and Discovery by George E. > P. Box, J. Stuart Hunter, William G. Hunter. > > This example use the data-file /BHH2-Data/tab0408.dat from > ftp://ftp.wiley.com/ in /sci_tech_med/statistics_experimenters/BHH2-Data.zip. > > The file tab0408.dat contains following DATA: > > DATA > driver cars additive y > 1 1 1 A 19 > 2 2 1 D 23 > 3 3 1 B 15 > 4 4 1 C 19 > 5 1 2 B 24 > 6 2 2 C 24 > 7 3 2 D 14 > 8 4 2 A 18 > 9 1 3 D 23 > 10 2 3 A 19 > 11 3 3 C 15 > 12 4 3 B 19 > 13 1 4 C 26 > 14 2 4 B 30 > 15 3 4 A 16 > 16 4 4 D 16 > > Now > > summary( aov(MODEL, data=DATA) ) > Df Sum Sq Mean Sq F value Pr(>F) > cars 1 12.8 12.800 0.8889 0.3680 > driver 1 115.2 115.200 8.0000 0.0179 * > additive 3 40.0 13.333 0.9259 0.4634 > Residuals 10 144.0 14.400 > --- > Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1 > > This results differ from book result at p 159, since "cars" and "driver" are > treated as numerical variables by "aov". > > BRUTE FORCE SOLUTION > > Manually transforming "cars" and "driver" into categorical variables, I > obtain the correct result: > > DATA_AB > driver cars additive y > 1 D1 C1 A 19 > 2 D2 C1 D 23 > 3 D3 C1 B 15 > 4 D4 C1 C 19 > 5 D1 C2 B 24 > 6 D2 C2 C 24 > 7 D3 C2 D 14 > 8 D4 C2 A 18 > 9 D1 C3 D 23 > 10 D2 C3 A 19 > 11 D3 C3 C 15 > 12 D4 C3 B 19 > 13 D1 C4 C 26 > 14 D2 C4 B 30 > 15 D3 C4 A 16 > 16 D4 C4 D 16 > > summary( aov(MODEL, data=DATA_AB) ) > Df Sum Sq Mean Sq F value Pr(>F) > cars 3 24 8.000 1.5 0.307174 > driver 3 216 72.000 13.5 0.004466 ** > additive 3 40 13.333 2.5 0.156490 > Residuals 6 32 5.333 > --- > Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1 > > QUESTION > > Which is the easiest (most elegant) way to force "driver" and "cars" from > DATA to be treated as categorical variables by "aov"? > More generally, which is the easiest way to force "aov" to treat numerical > variables as categorical ? > > Sincerely, Andrea Bernasconi DG > > PROBLEM EXAMPLE > > I consider the latin squares example described at page 157 of the book: > Statistics for Experimenters: Design, Innovation, and Discovery by George E. > P. Box, J. Stuart Hunter, William G. Hunter. > > This example use the data-file /BHH2-Data/tab0408.dat from > ftp://ftp.wiley.com/ in /sci_tech_med/statistics_experimenters/BHH2-Data.zip. > > The file tab0408.dat contains following DATA: > > DATA > driver cars additive y > 1 1 1 A 19 > 2 2 1 D 23 > 3 3 1 B 15 > 4 4 1 C 19 > 5 1 2 B 24 > 6 2 2 C 24 > 7 3 2 D 14 > 8 4 2 A 18 > 9 1 3 D 23 > 10 2 3 A 19 > 11 3 3 C 15 > 12 4 3 B 19 > 13 1 4 C 26 > 14 2 4 B 30 > 15 3 4 A 16 > 16 4 4 D 16 > > Now > > summary( aov(MODEL, data=DATA) ) > Df Sum Sq Mean Sq F value Pr(>F) > cars 1 12.8 12.800 0.8889 0.3680 > driver 1 115.2 115.200 8.0000 0.0179 * > additive 3 40.0 13.333 0.9259 0.4634 > Residuals 10 144.0 14.400 > --- > Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1 > > This results differ from book result at p 159, since "cars" and "driver" are > treated as numerical variables by "aov". > > BRUTE FORCE SOLUTION > > Manually transforming "cars" and "driver" into categorical variables, I > obtain the correct result: > > DATA_AB > driver cars additive y > 1 D1 C1 A 19 > 2 D2 C1 D 23 > 3 D3 C1 B 15 > 4 D4 C1 C 19 > 5 D1 C2 B 24 > 6 D2 C2 C 24 > 7 D3 C2 D 14 > 8 D4 C2 A 18 > 9 D1 C3 D 23 > 10 D2 C3 A 19 > 11 D3 C3 C 15 > 12 D4 C3 B 19 > 13 D1 C4 C 26 > 14 D2 C4 B 30 > 15 D3 C4 A 16 > 16 D4 C4 D 16 > > summary( aov(MODEL, data=DATA_AB) ) > Df Sum Sq Mean Sq F value Pr(>F) > cars 3 24 8.000 1.5 0.307174 > driver 3 216 72.000 13.5 0.004466 ** > additive 3 40 13.333 2.5 0.156490 > Residuals 6 32 5.333 > --- > Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1 > > QUESTION > > Which is the easiest (most elegant) way to force "driver" and "cars" from > DATA to be treated as categorical variables by "aov"? > More generally, which is the easiest way to force "aov" to treat numerical > variables as categorical ? > > Mobile +41 79 621 74 07 [[alternative HTML version deleted]]
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