testmeanshapes            package:shapes            R Documentation

_T_e_s_t_s _f_o_r _m_e_a_n _s_h_a_p_e _d_i_f_f_e_r_e_n_c_e

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

     Carries out Hotelling's $T^2$ or Goodall's $F$ test to examine
     differences in mean shape between two independent populations, for
     $m>=2$ dimensional data.  The procedure uses complex eigenanalysis
     for $m=2$ and iterative  Generalised Procrustes Analysis for $m>2$
     dimensions.

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

     testmeanshapes(A, B, Hotelling = TRUE, tol1 = 1e-05, tol2 = 1e-05)

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

       A: The random sample for group 1: k x m x n1 array of data,
          where  k is the number of landmarks, m is dimension and n1 is
          the sample size

       B: The random sample for group 2: k x m x n2 array of data,
          where  k is the number of landmarks, m is dimension and n2 is
          the sample size

Hotelling: Logical. If TRUE then carry out Hotelling's $T^2$ test,  if
          FALSE carry out Goodall's $F$ test

    tol1: Tolerance for optimal rotation for the iterative  algorithm
          ($m>2$): tolerance on the mean sum of squares between
          successive iterations  (depends on scale of objects)

    tol2: tolerance for rescale/rotation step for the iterative 
          algorithm ($m>2$): tolerance on the Riemannian shape distance
           between successive mean shapes

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

     A list with components  

       F: the F statistic

df1 and df2: degrees of freedom of the F statistic

    pval: p-value for the test

     Tsq: the $T^2$ statistic (if Hotelling)

T.df1 and T.df2: degrees of freedom of the $T^2$ statistic (if
          Hotelling)

Tsq.partition: the $T^2$ statistic partitioned into  contributions from
          each of the pooled principal components (if Hotelling)

F.partition: the F statistic partitioned into  contributions from each
          of the pooled principal components (if Hotelling)

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

     Ian Dryden

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

     Dryden, I.L. and Mardia, K.V. (1998) Statistical Shape Analysis, 
     Wiley, Chichester. Chapter 7. 

     Dryden and Mardia (1993) Multivariate shape analysis. Sankhya A,
     55:460-480.

     Goodall, C. R. (1991). Procrustes methods in the statistical
     analysis  of shape (with discussion). Journal of the Royal
     Statistical Society,  Series B, 53: 285-339.

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

     procGPA

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

     #2D example : female and male Gorillas (cf. Dryden and Mardia, 1998)

     data(gorf.dat)
     data(gorm.dat)

     #Hotelling's Tsq test
     test1<-testmeanshapes(gorf.dat,gorm.dat)

     #Goodall's isotropic test
     test2<-testmeanshapes(gorf.dat,gorm.dat,Hotelling=FALSE)

