sound.fields {BradleyTerry2} | R Documentation |

## Kousgaard (1984) Data on Pair Comparisons of Sound Fields

### Description

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

### Usage

```
sound.fields
```

### Format

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:

- field1
a factor with levels

`c("000", "001", "010", "011", "100", "101", "110", "111")`

, the first sound field in a comparison- field2
a factor with the same levels as

`field1`

; the second sound field in a comparison- win1
integer, the number of times that

`field1`

was preferred to`field2`

- tie
integer, the number of times that no preference was expressed when comparing

`field1`

and`field2`

- win2
integer, the number of times that

`field2`

was preferred to`field1`

- win1.adj
numeric, equal to

`win1 + tie/2`

- win2.adj
numeric, equal to

`win2 + tie/2`

- instrument
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")
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- b
a factor with levels

`c("0", "1")`

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

`c("0", "1")`

, the*reverberation*factor (0 for*-24dB*, 1 for*-20dB*); contrasts are sum contrasts

### Details

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.

### Author(s)

David Firth

### Source

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.

### References

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.

### Examples

```
##
## 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)))
```

*BradleyTerry2*version 1.1-2 Index]