Computes a matrix of Hoeffding's (1948)
D statistics for all
possible pairs of columns of a matrix.
D is a measure of the
is the joint CDF of
marginal CDFs. Missing values are deleted in pairs rather than deleting
all rows of
x having any missing variables. The
statistic is robust against a wide variety of alternatives to
independence, such as non-monotonic relationships. The larger the value
D, the more dependent are
Y (for many
types of dependencies).
D used here is 30 times Hoeffding's
D, and ranges from -0.5 to 1.0 if there are no ties in
print.hoeffd prints the information derived by
hoeffd. The higher the value of
D, the more dependent are
hoeffd also computes the mean and maximum
absolute values of the difference between the joint empirical CDF and
the product of the marginal empirical CDFs.
1 2 3
a numeric matrix with at least 5 rows and at least 2 columns (if
a numeric vector or matrix which will be concatenated to
Uses midranks in case of ties, as described by Hollander and Wolfe.
P-values are approximated by linear interpolation on the table
in Hollander and Wolfe, which uses the asymptotically equivalent
Blum-Kiefer-Rosenblatt statistic. For
P values are
computed using a well-fitting linear regression function in
log P vs.
the test statistic.
Ranks (but not bivariate ranks) are computed using efficient
algorithms (see reference 3).
a list with elements
matrix of D statistics,
matrix of number of observations used in analyzing each pair of variables,
P, the asymptotic P-values.
Pairs with fewer than 5 non-missing values have the D statistic set to NA.
The diagonals of
n are the number of non-NAs for the single variable
corresponding to that row and column.
Department of Biostatistics
Hoeffding W. (1948): A non-parametric test of independence. Ann Math Stat 19:546–57.
Hollander M. and Wolfe D.A. (1973). Nonparametric Statistical Methods, pp. 228–235, 423. New York: Wiley.
Press WH, Flannery BP, Teukolsky SA, Vetterling, WT (1988): Numerical Recipes in C. Cambridge: Cambridge University Press.
1 2 3 4 5 6 7 8 9 10 11 12 13
Loading required package: lattice Loading required package: survival Loading required package: Formula Loading required package: ggplot2 Attaching package: 'Hmisc' The following objects are masked from 'package:base': format.pval, round.POSIXt, trunc.POSIXt, units D x y z q x 1 0 NA 1 y 0 1 NA 0 z NA NA 1 NA q 1 0 NA 1 avg|F(x,y)-G(x)H(y)| x y z q x 0.00 0.04 0 0.16 y 0.04 0.00 0 0.04 z 0.00 0.00 0 0.00 q 0.16 0.04 0 0.00 max|F(x,y)-G(x)H(y)| x y z q x 0.00 0.1 0 0.24 y 0.10 0.0 0 0.10 z 0.00 0.0 0 0.00 q 0.24 0.1 0 0.00 n x y z q x 5 5 4 5 y 5 5 4 5 z 4 4 4 4 q 5 5 4 5 P x y z q x 0.3633 0.0000 y 0.3633 0.3633 z q 0.0000 0.3633 D x y x 1.00 0.06 y 0.06 1.00 avg|F(x,y)-G(x)H(y)| x y x 0.0000 0.0407 y 0.0407 0.0000 max|F(x,y)-G(x)H(y)| x y x 0.0000 0.0763 y 0.0763 0.0000 n= 200 P x y x 0 y 0
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.