glhpwr                package:hpower                R Documentation

_P_o_w_e_r _F_u_n_c_t_i_o_n _f_o_r _T_e_s_t_s _o_f _t_h_e _G_e_n_e_r_a_l _L_i_n_e_a_r _H_y_p_o_t_h_e_s_i_s

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

     Use a noncentral F approximation to compute the power of a test of
     the general linear hypothesis.

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

     glhpwr(alpha, x, bt1, sigma, cc, u, th0, test=1, tol=1e-08)

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

   alpha: type I error probability of the test. 

       x: N-by-q design matrix. 

     bt1: q-by-p alternative hypothesis value of the regression
          coefficient. 

   sigma: p-by-p variance matrix of a single observation. 

      cc: a-by-q between-rows contrast matrix. 

       u: p-by-b between-columns contrast matrix. 

     th0: a-by-b null value of cc%*%beta%*%u. 

    test: test for which power is desired.  test=1 (the default) is the
          Wilks lambda test; test=2 is the Hotelling-Lawley trace test;
          test=3 is the Pillai-Bartlett trace test.  See Muller and
          Peterson (1984) for details. 

     tol: tolerance for computing the rank of x (using qr()).  The
          default is 1.e-8. 

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

     the approximate power of a test of the general linear hypothesis
     cc%*%beta%*%u=th0 under the alternative beta=bt1. The model is
     y(Nxp)=x(Nxq)%*%beta(qxp)+e(Nxp), where x is the design, beta is
     the matrix of multivariate regression parameters, and e is the
     error matrix, whose rows are assumed to be independent draws from
     a multivariate normal with mean 0 and p-by-p variance matrix
     sigma.

_N_O_T_E:

     If the computed approximate degrees of freedom are negative, a
     power of 0 is returned; this may mean that the proposed design has
     no degrees of freedom for error.

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

     Daniel F. Heitjan <dheitjan@peter.cpmc.columbia.edu>,   R-port by
     Stefan Funke <funke@attglobal.net>

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

     Muller, K.E. and Peterson, B.L. (1984).  Practical methods for
     computing power in testing the multivariate general linear
     hypothesis.  Computational Statistics and Data Analysis 2,
     143-158.

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

     `pfnc', `sscomp'

