powerbinom               package:MCPAN               R Documentation

_A_p_p_r_o_x_i_m_a_t_e _p_o_w_e_r _f_o_r _m_u_l_t_i_p_l_e _c_o_n_t_r_a_s_t _t_e_s_t_s _o_f _b_i_n_o_m_i_a_l _p_r_o_p_o_r_t_i_o_n_s

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

     Approximative power calculation for multiple contrast tests of
     binomial proportions, based on probabilities of the multivariate
     standard normal distribution.

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

     powerbinom(p, n, alpha = 0.05, type = "Williams", cmat = NULL, method = "Wald", alternative = "less")

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

       p: a numeric vector, the proportions assumed under the
          alternative 

       n: an integer vector, the number of observations, must be of
          same length as 'p' 

   alpha: a single numeric value, the alpha-level of the test  

    type: if 'cmat' is not specified, the type of multiple contrast
          test to be applied on the proportions 'p'; will be ignored if
          'cmat' is specified

    cmat: a numeric contrast matrix, number of columns must be the same
          as length of 'n', and 'p'; if secified, 'type' will be
          ignored 

  method: a character string, the method for variance estimation in
          test / confidence interval construction: one of "Wald",
          "ADD1", "ADD2"; see 'binomRDtest' 

alternative: a character string, specifying the alternative, options
          are "two.sided", "less", "greater" 

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

     Calls 'powermcp'. 

     Power for an Union-Intersection-Test is calculated, i.e. the power
     that H0 is rejected for at least one of the contrasts specified by
     'cmat' or 'type'.

     Note, that currently only power calculation for
     Union-Intersection-Tests of  type H0: ALL Lm<=0 vs.  HA: ANY Lm>0
     (alternative="greater"), H0: ALL Lm>=0 vs.  HA: ANY Lm<0
     (alternative="less"), or H0: ALL Lm=0 vs.  HA: ANY Lm<or>0
     (alternative="two.sided") are implemented. Power for tests against
     delta>0 or delta<0 is not implemented.

     Calcualtion is based on probabilities of the multivariate standard
     normal distribution, thus will be only appropriate if normal
     approximation for the test statistics holds. Therefore, results
     might be misleading for small sample sizes, such as n < 40, and a
     warning is posted. In this case, simulation is recommended.

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

     A single numeric value, the power.

_N_o_t_e:

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

     Frank Schaarschmidt

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

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

     'powermcp'

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

     # Assume, one wants to perform a test for increasing trend
     #  using Williams type of contrasts among I=5 groups
     #  (e.g. 4 doses and one control).
     #  Proportions are assumed to have values
     #  pi=(0.1,0.12,0.14,0.14,0.2) under the alternative.


     powerbinom(p=c(0.1, 0.12, 0.14, 0.14, 0.2),
      n=c(20,20,20,20,20), type = "Williams",
       method = "ADD1", alternative = "greater")

     powerbinom(p=c(0.1, 0.12, 0.14, 0.14, 0.2),
      n=c(30,30,30,30,30), type = "Williams",
       method = "ADD1", alternative = "greater")

     powerbinom(p=c(0.1, 0.12, 0.14, 0.14, 0.2),
      n=c(60,60,60,60,60), type = "Williams",
       method = "ADD1", alternative = "greater")

     powerbinom(p=c(0.1, 0.12, 0.14, 0.14, 0.2),
      n=c(80,80,80,80,80), type = "Williams",
       method = "ADD1", alternative = "greater")

     powerbinom(p=c(0.1, 0.12, 0.14, 0.14, 0.2),
      n=c(100,100,100,100,100), type = "Williams",
       method = "ADD1", alternative = "greater")

     powerbinom(p=c(0.1, 0.12, 0.14, 0.14, 0.2),
      n=c(150,150,150,150,150), type = "Williams",
       method = "ADD1", alternative = "greater")

     powerbinom(p=c(0.1, 0.12, 0.14, 0.14, 0.2),
      n=c(190,140,140,140,140), type = "Williams",
       method = "ADD1", alternative = "greater")

