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.
replicate factor is nested within the
temperature is nested within
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 and Hall/CRC.
str(cake) print(fm1 <- lmer(angle ~ recipe * temperature + (1|recipe:replicate), cake, method = "ML"), corr = FALSE) print(fm2 <- lmer(angle ~ recipe + temperature + (1|recipe:replicate), cake, method = "ML"), corr = FALSE) print(fm3 <- lmer(angle ~ recipe + temp + (1|recipe:replicate), cake, method = "ML"), corr = FALSE) anova(fm3, fm2, fm1)