cake                  package:lme4                  R Documentation

_B_r_e_a_k_a_g_e _a_n_g_l_e _o_f _c_h_o_c_o_l_a_t_e _c_a_k_e_s

_D_e_s_c_r_i_p_t_i_o_n:

     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.

_U_s_a_g_e:

     data(cake)

_F_o_r_m_a_t:

     A data frame with 270 observations on the following 5 variables.

     '_r_e_p_l_i_c_a_t_e' a factor with levels '1' to '15'

     '_r_e_c_i_p_e' a factor with levels 'A', 'B' and 'C'

     '_t_e_m_p_e_r_a_t_u_r_e' an ordered factor with levels '175' < '185' < '195'
          < '205' < '215' < '225'

     '_a_n_g_l_e' a numeric vector giving the angle at which the cake broke.

     '_t_e_m_p' numeric value of the baking temperature (degrees F).

_D_e_t_a_i_l_s:

     The 'replicate' factor is nested within the 'recipe' factor, and
     'temperature' is nested within 'replicate'.

_S_o_u_r_c_e:

     Original data were presented in Cook (1938), and reported in
     Cochran and Cox (1957, p. 300).  Also cited in Lee, Nelder and
     Pawitan (2006).

_R_e_f_e_r_e_n_c_e_s:

     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.

_E_x_a_m_p_l_e_s:

     str(cake)
     print(fm1 <- lmer(angle ~ recipe * temperature + (1|recipe:replicate), cake,
                       REML = FALSE), corr = FALSE)
     print(fm2 <- lmer(angle ~ recipe + temperature + (1|recipe:replicate), cake,
                       REML = FALSE), corr = FALSE)
     print(fm3 <- lmer(angle ~ recipe + temp + (1|recipe:replicate), cake,
                       REML = FALSE), corr = FALSE)
     anova(fm3, fm2, fm1)

