springall {BradleyTerry2} | R Documentation |

Data from Section 7 of the paper by Springall (1973) on Bradley-Terry response surface modelling. An experiment to assess the effects of gel and flavour concentrations on the subjective assessment of flavour strength by pair comparisons.

```
springall
```

A list containing two data frames, `springall$contests`

and
`springall$predictors`

.

The `springall$contests`

data frame has 36 observations (one for each
possible pairwise comparison of the 9 treatments) on the following 7
variables:

- row
a factor with levels

`1:9`

, the row number in Springall's dataset

#

- col
a factor with levels

`1:9`

, the column number in Springall's dataset- win
integer, the number of wins for column treatment over row treatment

- loss
integer, the number of wins for row treatment over column treatment

- tie
integer, the number of ties between row and column treatments

- win.adj
numeric, equal to

`win + tie/2`

- loss.adj
numeric, equal to

`loss + tie/2`

The `predictors`

data frame has 9 observations (one for each treatment)
on the following 5 variables:

- flav
numeric, the flavour concentration

- gel
numeric, the gel concentration

- flav.2
numeric, equal to

`flav^2`

- gel.2
numeric, equal to

`gel^2`

- flav.gel
numeric, equal to

`flav * gel`

The variables `win.adj`

and `loss.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 Rao and
Kupper (1967) model that Springall (1973) uses.

David Firth

Springall, A (1973) Response surface fitting using a generalization
of the Bradley-Terry paired comparison method. *Applied Statistics*
**22**, 59–68.

Rao, P. V. and Kupper, L. L. (1967) Ties in paired-comparison
experiments: a generalization of the Bradley-Terry model. *Journal of
the American Statistical Association*, **63**, 194–204.

```
##
## Fit the same response-surface model as in section 7 of
## Springall (1973).
##
## Differences from Springall's fit are minor, arising from the
## different treatment of ties.
##
## Springall's model in the paper does not include the random effect.
## In this instance, however, that makes no difference: the random-effect
## variance is estimated as zero.
##
summary(springall.model <- BTm(cbind(win.adj, loss.adj), col, row,
~ flav[..] + gel[..] +
flav.2[..] + gel.2[..] + flav.gel[..] +
(1 | ..),
data = springall))
```

[Package *BradleyTerry2* version 1.1-2 Index]