testmeanshapes {shapes} | R Documentation |
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.
testmeanshapes(A, B, Hotelling = TRUE, tol1 = 1e-05, tol2 = 1e-05)
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 |
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) |
Ian Dryden
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.
procGPA
#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)