approx.hotelling.diff.test {ergm}

Approximate Hotelling T^2-Test for One or Two Population Means

Description

A multivariate hypothesis test for a single population mean or a difference between them. This version attempts to adjust for multivariate autocorrelation in the samples.

Usage

approx.hotelling.diff.test(
  x,
  y = NULL,
  mu0 = 0,
  assume.indep = FALSE,
  var.equal = FALSE,
  ...
)

Arguments

x

a numeric matrix of data values with cases in rows and variables in columns.

y

an optinal matrix of data values with cases in rows and variables in columns for a 2-sample test.

mu0

an optional numeric vector: for a 1-sample test, the poulation mean under the null hypothesis; and for a 2-sample test, the difference between population means under the null hypothesis; defaults to a vector of 0s.

assume.indep

if TRUE, performs an ordinary Hotelling's test without attempting to account for autocorrelation.

var.equal

for a 2-sample test, perform the pooled test: assume population variance-covariance matrices of the two variables are equal.

...

additional arguments, passed on to spectrum0.mvar(), etc.; in particular, ⁠order.max=⁠ can be used to limit the order of the AR model used to estimate the effective sample size.

Value

An object of class htest with the following information:

statistic

The T^2 statistic.

parameter

Degrees of freedom.

p.value

P-value.

method

Method specifics.

null.value

Null hypothesis mean or mean difference.

alternative

Always "two.sided".

estimate

Sample difference.

covariance

Estimated variance-covariance matrix of the estimate of the difference.

covariance.x

Estimated variance-covariance matrix of the estimate of the mean of x.

covariance.y

Estimated variance-covariance matrix of the estimate of the mean of y.

It has a print method print.htest().

Note

For mcmc.list input, the variance for this test is estimated with unpooled means. This is not strictly correct.

References

Hotelling, H. (1947). Multivariate Quality Control. In C. Eisenhart, M. W. Hastay, and W. A. Wallis, eds. Techniques of Statistical Analysis. New York: McGraw-Hill.

See Also

t.test()