achisq               package:DCluster               R Documentation

_A_n_o_t_h_e_r _i_m_p_l_e_m_e_n_t_a_t_i_o_n _o_f _P_e_a_r_s_o_n'_s _C_h_i-_s_q_u_a_r_e _s_t_a_t_i_s_t_i_c

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

     Another implementation of Pearson's Chi-square has been written to
     fit the needs in package _DCLuster_.

     _achisq.stat_ is the function that calculates the value of the
     statistic for the data.

     _achisq.boot_ is used when performing a non-parametric bootstrap.

     _achisq.pboot_ is used when performing a parametric bootstrap.

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

     This statistic can be used to detect whether observed data depart
     (over or above) expected number of cases significantly. The test
     considered stands for relative risks among areas to be equal to an
     (unknown) constant lambda, while the alternative hypotheses is
     that not all relative risks are equal.

     The actual value of the statistic depends on null hypotheses. If
     we consider that all the relative risks are equal to 1, the  value
     is

     T=

                      sum_i ( (O_i-E_i)^2/E_i )


     and the degrees of freedom are equal to the number of regions.

     On the other hand, if we just consider relative risks to be equal,
     without specifying their value (i.e., lambda is unknown), E_i must
     be substituted by E_i*(O_+/E_+) and the number of degrees of
     freedom is the number of regions minus one.

     When internal standardization is used, null hypotheses must  be
     all relative risks equal to 1 and the number of degrees of freedom
     is the number of regions minus one. This is due to the fact that,
     in this case, O_+=E_+.

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

     Potthoff, R. F. and Whittinghill, M.(1966). Testing for
     Homogeneity: I. The Binomial and Multinomial Distributions.
     Biometrika 53, 167-182.

     Potthoff, R. F. and Whittinghill, M.(1966). Testing for
     Homogeneity: The Poisson Distribution. Biometrika 53, 183-190.

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

     DCluster, achiq.stat, achisq.boot, achisq.pboot

