resampletest {shapes}R Documentation

Tests for 2D mean shape difference, including bootstrap and permutation tests

Description

Carries out tests to examine differences in mean shape between two independent populations, for $m=2$ dimensional data. Four test statistics are calculated:

lambda : the asymptotically pivotal statistic $lambda_{min}$ from Amaral et al. (2006), equ.(16)

H : Hotelling $T^2$ statistic (see Amaral et al., 2006, equ.(26), Dryden and Mardia, 1998, equ.(7.4))

J : James' statistic (see Amaral et al., 2006, equ.(27) )

G : Goodall's F statistic (see Amaral et al., 2006, equ.(28), Dryden and Mardia, 1998, equ.(7.9))

p-values are given based on resampling (either a bootstrap test or a permutation test) as well as the usual table based p-values.

Usage

resampletest(A, B, resamples = 200, permutation = FALSE)

Arguments

A The random sample for group 1: k x 2 x n1 array of data, where k is the number of landmarks and n1 is the sample size. (Alternatively a k x n1 complex matrix)
B The random sample for group 3: k x 2 x n2 array of data, where k is the number of landmarks and n2 is the sample size. (Alternatively a k x n2 complex matrix)
resamples Integer. The number of resampling iterations.
permutation Logical. If permutation = TRUE then permutation resampling is carried without replacement from the pooled samples. If permutation = FALSE then bootstrap resampling is carried out in each group (sampling with replacement).

Value

A list with components

lambda $λ_{min}$ statistic
lambda.pvalue p-value for $λ_{min}$ test based on resampling
lambda.table.pvalue p-value for $λ_{min}$ test based on the asymptotic chi-squared distribution (large n1,n2)
H The Hotelling $T^2$ statistic
H.pvalue p-value for the Hotelling $T^2$ test based on resampling
H.table.pvalue p-value for the Hotelling $T^2$ test based on the null F distribution, assuming normality and equal covariance matrices
J The Hotelling $T^2$ statistic
J.pvalue p-value for the Hotelling $T^2$ test based on resampling
J.table.pvalue p-value for the Hotelling $T^2$ test based on the null F distribution, assuming normality and unequal covariance matrices
G The Goodall $F$ statistic
G.pvalue p-value for the Goodall test based on resampling
G.table.pvalue p-value for the Goodall test based on the null F distribution, assuming normality and equal isotropic covariance matrices)

Author(s)

Ian Dryden

References

Amaral, G.J.A., Dryden, I.L. and Wood, A.T.A (2006). Pivotal bootstrap methods for $k$-sample problems in directional statistics and shape analysis. Journal of the American Statistical Association. To appear.

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

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.

See Also

testmeanshapes

Examples


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

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

#just select 3 landmarks and the first 10 observations in each group
select<-c(1,2,3)
A<-gorf.dat[select,,1:10]
B<-gorm.dat[select,,1:10]
resampletest(A,B,resamples=100)


[Package shapes version 1.1-1 Index]