Extraction of the Expectation, Variance and Covariance of the Linear Statistic

Description

Methods for extraction of the expectation, variance and covariance of the linear statistic.

Usage

## S4 method for signature 'IndependenceLinearStatistic'
expectation(object, ...)
## S4 method for signature 'IndependenceTest'
expectation(object, ...)

## S4 method for signature 'CovarianceMatrix'
variance(object, ...)
## S4 method for signature 'IndependenceLinearStatistic'
variance(object, ...)
## S4 method for signature 'IndependenceTest'
variance(object, ...)
## S4 method for signature 'Variance'
variance(object, ...)

## S4 method for signature 'CovarianceMatrix'
covariance(object, ...)
## S4 method for signature 'IndependenceLinearStatistic'
covariance(object, ...)
## S4 method for signature 'IndependenceTest'
covariance(object, ...)

Arguments

Details

The methods expectation, variance and covariance extract the expectation, variance and covariance, respectively, of the linear statistic.

Value

The expectation, variance or covariance of the linear statistic extracted from object. A numeric vector or matrix.

Examples

## Example data
dta <- data.frame(
    y = gl(3, 2),
    x = sample(gl(3, 2))
)

## Asymptotic Cochran-Mantel-Haenszel Test
ct <- cmh_test(y ~ x, data = dta)

## The linear statistic, i.e., the contingency table...
(l <- statistic(ct, type = "linear"))

## ...and its expectation...
(El <- expectation(ct))

## ...and covariance
(Vl <- covariance(ct))

## The standardized contingency table...
(l - El) / sqrt(variance(ct))

## ...is identical to the standardized linear statistic
statistic(ct, type = "standardized")