Description Usage Arguments Details Value References See Also Examples

Robust one-sample test and confidence interval for the correlation coefficient.

1 2 | ```
sscor.test(x, y, rho0=0, alternative=c("two.sided","less","greater"),
conf.level=0.95, ...)
``` |

`x,y` |
(required) numeric vectors of observations, must have the same length. |

`rho0` |
(optional) correlation coefficient under the null hypothesis. The default is 0. |

`alternative` |
(optional) character string indicating the type of alternative to be tested. Must be one of |

`conf.level` |
(optional) confidence level. The default is 0.95. |

`...` |
optional arguments passed to sscor (such as location and scale estimates to be used). |

The test is based on the spatial sign correlation (Dürre et al. 2015), which is a highly robust correlation estimator, consistent for the generalized correlation coefficient under ellipticity. The confidence interval and the p-value are based on the asymptotic distribution after a variance-stabilizing transformation similar to Fisher's z-transform. They provide accurate approximations also for very small samples (Dürre and Vogel, 2015). The test is furthermore distribution-free within the elliptical model. It has, e.g., the same power at the elliptical Cauchy distribution as at the multivariate Gaussian distribution.

A list with class `"htest"`

containing the following values (similar to the output of `cor.test`

):

`statistic` |
the value of the test statistic. Under the null, the test statistic is (asymptotically) standard normal. |

`p.value` |
the p-value of the test. |

`estimate` |
the estimated spatial sign correlation. |

`null.value` |
the true correlation under the null hypothesis. |

`alternative` |
a character string describing the alternative hypothesis. |

`method` |
a characters string indicating the choosen correlation estimator. Currently only the spatial sign correlation is implemented. |

`data.name` |
a character giving the names of the data. |

`conf.int` |
confidence interval for the correlation coefficient. |

Dürre, A., Vogel, D., Fried, R. (2015): Spatial sign correlation, *Journal of Multivariate Analyis*, vol. 135, 89–105.
arvix 1403.7635

Dürre, A., Vogel, D. (2015): Asymptotics of the two-stage spatial sign correlation, preprint. arxiv 1506.02578

Classical correlation testing: `cor.test`

.

For more information on the spatial sign correlation: `sscor`

.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | ```
set.seed(5)
require(mvtnorm)
# create bivariate shape matrix with correlation 0.5
sigma <- matrix(c(1,0.5,0.5,1),ncol=2)
# under normality, both tests behave similarly
data <- rmvnorm(100,c(0,0),sigma)
x <- data[,1]
y <- data[,2]
sscor.test(x,y)
cor.test(x,y)
# sscor.test also works at a Cauchy distribution
data <- rmvt(100,diag(1,2), df=1)
x <- data[,1]
y <- data[,2]
sscor.test(x,y)
cor.test(x,y)
``` |

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