expectation-methods | R Documentation |

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

```
## S4 method for signature 'IndependenceLinearStatistic'
expectation(object, partial = FALSE, ...)
## S4 method for signature 'IndependenceTest'
expectation(object, partial = FALSE, ...)
## S4 method for signature 'Variance'
variance(object, ...)
## S4 method for signature 'CovarianceMatrix'
variance(object, ...)
## S4 method for signature 'IndependenceLinearStatistic'
variance(object, partial = FALSE, ...)
## S4 method for signature 'IndependenceTest'
variance(object, partial = FALSE, ...)
## S4 method for signature 'CovarianceMatrix'
covariance(object, ...)
## S4 method for signature 'IndependenceLinearStatistic'
covariance(object, invert = FALSE, partial = FALSE, ...)
## S4 method for signature 'QuadTypeIndependenceTestStatistic'
covariance(object, invert = FALSE, partial = FALSE, ...)
## S4 method for signature 'IndependenceTest'
covariance(object, invert = FALSE, partial = FALSE, ...)
```

`object` |
an object from which the expectation, variance or covariance of the linear statistic can be extracted. |

`partial` |
a logical indicating that the partial result for each block should be
extracted. Defaults to |

`invert` |
a logical indicating that the Moore-Penrose inverse of the covariance should
be extracted. Defaults to |

`...` |
further arguments (currently ignored). |

The methods `expectation`

, `variance`

and `covariance`

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

For tests of conditional independence within blocks, the partial result for
each block is obtained by setting `partial = TRUE`

.

The expectation, variance or covariance of the linear statistic extracted from
`object`

. A matrix or array.

```
## 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...
(T <- statistic(ct, type = "linear"))
## ...and its expectation...
(mu <- expectation(ct))
## ...and variance...
(sigma <- variance(ct))
## ...and covariance...
(Sigma <- covariance(ct))
## ...and its inverse
(SigmaPlus <- covariance(ct, invert = TRUE))
## The standardized contingency table...
(T - mu) / sqrt(sigma)
## ...is identical to the standardized linear statistic
statistic(ct, type = "standardized")
## The quadratic form...
U <- as.vector(T - mu)
U %*% SigmaPlus %*% U
## ...is identical to the test statistic
statistic(ct, type = "test")
```

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