springall {BradleyTerry2}

Springall (1973) Data on Subjective Evaluation of Flavour Strength

Description

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.

Usage

springall

Format

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

Details

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.

Author(s)

David Firth

Source

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

References

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.

Examples

##
## 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))