raoscott                 package:aod                 R Documentation

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

     Tests the homogeneity of proportions between I groups (H0: p_1 =
     p_2 = ... = p_I ) from clustered binomial  data (n, y) using the
     adjusted chi-squared statistic proposed by Rao and Scott (1993).

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

     raoscott(formula = NULL, response = NULL, weights = NULL, 
                   group = NULL, data, pooled = FALSE, deff = NULL)

_A_r_g_u_m_e_n_t_s:

 formula: An optional formula where the left-hand side is either a
          matrix of the form 'cbind(y, n-y)', where the modelled
          probability is 'y/n', or a vector of proportions to be
          modelled ('y/n').  In both cases, the right-hand side must
          specify a single grouping variable. When the left-hand side
          of the formula  is a vector of proportions, the argument
          'weight' must be used to indicate the denominators of the 
          proportions.

response: An optional argument: either a matrix of the form 'cbind(y,
          n-y)', where the modelled probability  is 'y/n', or a vector
          of proportions to be modelled ('y/n').

 weights: An optional argument used when the left-hand side of
          'formula' or 'response' is a vector of proportions: 'weight'
          is the denominator of the proportions.

   group: An optional argument only used when 'response' is used. In
          this case, this argument is a factor  indicating a grouping
          variable.

    data: A data frame containing the response ('n' and 'y') and the
          grouping variable.

  pooled: Logical indicating if a pooled design effect is estimated
          over the I groups.

    deff: A numerical vector of I design effects.

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

     The method is based on the concepts of design effect and effective
     sample size.

      The design effect in each group i is estimated by deff_i =
     vratio_i / vbin_i, where vratio_i is  the variance of the ratio
     estimate of the probability in group i (Cochran, 1999, p. 32 and
     p. 66) and vbin_i is the standard binomial variance. A pooled
     design effect (i.e., over the I groups) is estimated if argument
     'pooled = TRUE' (see Rao and Scott, 1993, Eq. 6). Fixed design
     effects can be specified with the argument 'deff'.
      The deff_i are used  to compute the effective sample sizes nadj_i
     = n_i / deff_i, the effective numbers of successes yadj_i = y_i /
     deff_i in each group i, and the overall effective proportion  padj
     = sum(yadj_i) / sum(deff_i). The test statistic is obtained by
     substituting these quantities in the usual chi-squared statistic,
     yielding:

 X^2 = sum( (yadj_i - nadj_i * padj)^2 / (nadj_i * padj * (1 - padj)) )

     which is compared to a chi-squared distribution with I - 1 degrees
     of freedom.

_V_a_l_u_e:

     An object of formal class "drs": see 'drs-class' for details. The
     slot 'tab' provides the proportion of successes, the variances of
     the proportion and the design effect for each group.

_A_u_t_h_o_r(_s):

     Matthieu Lesnoff matthieu.lesnoff@cirad.fr, Renaud Lancelot
     renaud.lancelot@cirad.fr

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

     Cochran, W.G., 1999, 2nd ed. _Sampling techniques_. John Wiley &
     Sons, New York.
      Rao, J.N.K., Scott, A.J., 1992. _A simple method for the analysis
     of clustered binary data_. Biometrics 48, 577-585.

_S_e_e _A_l_s_o:

     'chisq.test', 'donner', 'icc', 'drs-class'

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

       data(rats)
       # deff by group
       raoscott(cbind(y, n - y) ~ group, data = rats)
       raoscott(y/n ~ group, weights = n, data = rats)
       raoscott(response = cbind(y, n - y), group = group, data = rats)
       raoscott(response = y/n, weights = n, group = group, data = rats)
       # pooled deff
       raoscott(cbind(y, n - y) ~ group, data = rats, pooled = TRUE)
       # standard test
       raoscott(cbind(y, n - y) ~ group, data = rats, deff = c(1, 1))
       data(antibio)
       raoscott(cbind(y, n - y) ~ treatment, data = antibio)
       

