## 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)