On this Picostat.com statistics page, you will find information about the cake data set which pertains to Breakage Angle of Chocolate Cakes. The cake data set is found in the lme4 R package. You can load the cake data set in R by issuing the following command at the console data("cake"). This will load the data into a variable called cake. If R says the cake data set is not found, you can try installing the package by issuing this command install.packages("lme4") and then attempt to reload the data. If you need to download R, you can go to the R project website. You can download a CSV (comma separated values) version of the cake R data set. The size of this file is about 5,828 bytes.
Breakage Angle of Chocolate Cakes
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.
A data frame with 270 observations on the following 5 variables.
a factor with levels
a factor with levels
an ordered factor with levels
a numeric vector giving the angle at which the
numeric value of the baking temperature (degrees F).
replicate factor is nested within the
recipe factor, and
temperature is nested
Original data were presented in Cook (1938), and reported
in Cochran and Cox (1957, p. 300). Also cited in Lee,
Nelder and Pawitan (2006).
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
## '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)
Dataset imported from https://www.r-project.org.