eff.aovlist              package:stats              R Documentation

_C_o_m_p_u_t_e _E_f_f_i_c_i_e_n_c_i_e_s _o_f _M_u_l_t_i_s_t_r_a_t_u_m _A_n_a_l_y_s_i_s _o_f _V_a_r_i_a_n_c_e

_D_e_s_c_r_i_p_t_i_o_n:

     Computes the efficiencies of fixed-effect terms in an analysis of
     variance model with multiple strata.

_U_s_a_g_e:

     eff.aovlist(aovlist)

_A_r_g_u_m_e_n_t_s:

 aovlist: The result of a call to 'aov' with an 'Error' term. 

_D_e_t_a_i_l_s:

     Fixed-effect terms in an analysis of variance model with multiple
     strata may be estimable in more than one stratum, in which case
     there is less than complete information in each.  The efficiency
     for a term is the fraction of the maximum possible precision
     (inverse variance) obtainable by estimating in just that stratum. 
     Under the assumption of balance, this is the same for all
     contrasts involving that term.

     This function is used to pick strata in which to estimate terms in
     'model.tables.aovlist' and 'se.contrast.aovlist'.

     In many cases terms will only occur in one stratum, when all the
     efficiencies will be one: this is detected and no further
     calculations are done.

     The calculation used requires orthogonal contrasts for each term,
     and will throw an error if non-orthogonal contrasts (e.g.
     treatment contrasts or an unbalanced design) are detected.

_V_a_l_u_e:

     A matrix giving for each non-pure-error stratum (row) the
     efficiencies for each fixed-effect term in the model.

_R_e_f_e_r_e_n_c_e_s:

     Heiberger, R. M. (1989) _Computation for the Analysis of Designed
     Experiments_.  Wiley.

_S_e_e _A_l_s_o:

     'aov', 'model.tables.aovlist', 'se.contrast.aovlist'

_E_x_a_m_p_l_e_s:

     ## An example from Yates (1932),
     ## a 2^3 design in 2 blocks replicated 4 times

     Block <- gl(8, 4)
     A <- factor(c(0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,
                   0,1,0,1,0,1,0,1,0,1,0,1))
     B <- factor(c(0,0,1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0,1,1,
                   0,0,1,1,0,0,1,1,0,0,1,1))
     C <- factor(c(0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,1,
                   1,0,1,0,0,0,1,1,1,1,0,0))
     Yield <- c(101, 373, 398, 291, 312, 106, 265, 450, 106, 306, 324, 449,
                272, 89, 407, 338, 87, 324, 279, 471, 323, 128, 423, 334,
                131, 103, 445, 437, 324, 361, 302, 272)
     aovdat <- data.frame(Block, A, B, C, Yield)

     old <- getOption("contrasts")
     options(contrasts=c("contr.helmert", "contr.poly"))
     (fit <- aov(Yield ~ A*B*C + Error(Block), data = aovdat))
     eff.aovlist(fit)
     options(contrasts = old)

