R: Approximate Hotelling T^2-Test for One or Two Population...

approx.hotelling.diff.test {ergm} | R Documentation

## 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()`

[Package ergm version 4.1.2 Index]