cake: Breakage Angle of Chocolate Cakes

In lme4: Linear Mixed-Effects Models using 'Eigen' and S4

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

• \insertRef

  cook1938chocolatelme4

• \insertRef

  cochran1957experimentallme4

• \insertRef

  lee2006generalizedlme4

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)

lme4 documentation built on March 6, 2026, 1:07 a.m.