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

Description

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)

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Dataset imported from https://www.r-project.org.