sound.fields {BradleyTerry2}R Documentation

Kousgaard (1984) Data on Pair Comparisons of Sound Fields


The results of a series of factorial subjective room acoustic experiments carried out at the Technical University of Denmark by A C Gade.




A list containing two data frames, sound.fields$comparisons, and sound.fields$design.

The sound.fields$comparisons data frame has 84 observations on the following 8 variables:


a factor with levels c("000", "001", "010", "011", "100", "101", "110", "111"), the first sound field in a comparison


a factor with the same levels as field1; the second sound field in a comparison


integer, the number of times that field1 was preferred to field2


integer, the number of times that no preference was expressed when comparing field1 and field2


integer, the number of times that field2 was preferred to field1


numeric, equal to win1 + tie/2


numeric, equal to win2 + tie/2


a factor with 3 levels, c("cello", "flute", "violin")

The sound.fields$design data frame has 8 observations (one for each of the sound fields compared in the experiment) on the following 3 variables:


a factor with levels c("0", "1"), the direct sound factor (0 for obstructed sight line, 1 for free sight line); contrasts are sum contrasts


a factor with levels c("0", "1"), the reflection factor (0 for -26dB, 1 for -20dB); contrasts are sum contrasts


a factor with levels c("0", "1"), the reverberation factor (0 for -24dB, 1 for -20dB); contrasts are sum contrasts


The variables win1.adj and win2.adj are provided in order to allow a simple way of handling ties (in which a tie counts as half a win and half a loss), which is slightly different numerically from the Davidson (1970) method that is used by Kousgaard (1984): see the examples.


David Firth


Kousgaard, N. (1984) Analysis of a Sound Field Experiment by a Model for Paired Comparisons with Explanatory Variables. Scandinavian Journal of Statistics 11, 51–57.


Davidson, R. R. (1970) Extending the Bradley-Terry model to accommodate ties in paired comparison experiments. Journal of the American Statistical Association 65, 317–328.


##  Fit the Bradley-Terry model to data for flutes, using the simple 
##  'add 0.5' method to handle ties:
flutes.model <- BTm(cbind(win1.adj, win2.adj), field1, field2, ~ field,
                    id = "field",
                    subset = (instrument == "flute"),
                    data = sound.fields)
##  This agrees (after re-scaling) quite closely with the estimates given
##  in Table 3 of Kousgaard (1984):
table3.flutes <- c(-0.581, -1.039, 0.347, 0.205, 0.276, 0.347, 0.311, 0.135)
plot(c(0, coef(flutes.model)), table3.flutes)
abline(lm(table3.flutes ~ c(0, coef(flutes.model))))
##  Now re-parameterise that model in terms of the factorial effects, as
##  in Table 5 of Kousgaard (1984):
flutes.model.reparam <- update(flutes.model,
                               formula = ~ a[field] * b[field] * c[field]
table5.flutes <- c(.267, .250, -.088, -.294, .062, .009, -0.070)
plot(coef(flutes.model.reparam), table5.flutes)
abline(lm(table5.flutes ~ coef(flutes.model.reparam)))

[Package BradleyTerry2 version 1.1-2 Index]