Data on the breakage angle of chocolate cakes made with
three different recipes and baked at six different
temperatures. This is a split-plot design with the
recipes being whole-units and the different temperatures
being applied to sub-units (within replicates). The
experimental notes suggest that the replicate numbering
represents temporal ordering.
Format
A data frame with 270 observations on the following 5 variables.
replicate
a factor with levels 1 to 15
recipe
a factor with levels A, B and C
temperature
an ordered factor with levels 175
< 185 < 195 < 205 < 215 < 225
angle
a numeric vector giving the angle at which the
cake broke.
temp
numeric value of the baking temperature (degrees F).
Details
The replicate factor is nested within the
recipe factor, and temperature is nested
within replicate.
Source
Original data were presented in Cook (1938), and reported
in Cochran and Cox (1957, p. 300). Also cited in Lee,
Nelder and Pawitan (2006).
References
Cook, F. E. (1938) Chocolate cake, I. Optimum
baking temperature. Master's Thesis, Iowa State College.
Cochran, W. G., and Cox, G. M. (1957) Experimental
designs, 2nd Ed. New York, John Wiley & Sons.
Lee, Y., Nelder, J. A., and Pawitan, Y. (2006)
Generalized linear models with random effects.
Unified analysis via H-likelihood. Boca Raton, Chapman
and Hall/CRC.
Examples
str(cake)
## 'temp' is continuous, 'temperature' an ordered factor with 6 levels
(fm1 <- lmer(angle ~ recipe * temperature + (1|recipe:replicate), cake, REML= FALSE))
(fm2 <- lmer(angle ~ recipe + temperature + (1|recipe:replicate), cake, REML= FALSE))
(fm3 <- lmer(angle ~ recipe + temp + (1|recipe:replicate), cake, REML= FALSE))
## and now "choose" :
anova(fm3, fm2, fm1)