shapes (version 1.0-2)

testmeanshapes: Tests for mean shape difference

Description

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.

Usage

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

Arguments

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

Value

• 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)

References

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.

See Also

procGPA

Examples

#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)