# Robust correlation coefficients.

### Description

The `pcbor`

function computes the percentage bend correlation coefficient, `wincor`

the Winsorized correlation,
`pball`

the percentage bend correlation matrix, `winall`

the Winsorized correlation matrix.

### Usage

1 2 3 4 |

### Arguments

`x` |
a numeric vector, a matrix or a data frame. |

`y` |
a second numeric vector (for correlation functions). |

`beta` |
bending constant. |

`tr` |
amount of Winsorization. |

### Details

It tested is whether the correlation coefficient equals 0 (null hypothesis) or not. Missing values are deleted pairwise. The tests are sensitive to heteroscedasticity. The test statistic H in `pball`

tests the hypothesis that all correlations are equal to zero.

### Value

`pbcor`

and `wincor`

return an object of class `"pbcor"`

containing:

`cor` |
robust correlation coefficient |

`test` |
value of the test statistic |

`p.value` |
p-value |

`n` |
number of effective observations |

`call` |
function call |

`pball`

and `winall`

return an object of class `"pball"`

containing:

`pbcorm` |
robust correlation matrix |

`p.values` |
p-values |

`H` |
H-statistic |

`H.p.value` |
p-value H-statistic |

`cov` |
variance-covariance matrix |

### References

Wilcox, R. (2012). Introduction to Robust Estimation and Hypothesis Testing (3rd ed.). Elsevier.

### See Also

`twocor`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
x1 <- subset(hangover, subset = (group == "control" & time == 1))$symptoms
x2 <- subset(hangover, subset = (group == "control" & time == 2))$symptoms
pbcor(x1, x2)
pbcor(x1, x2, beta = 0.1)
wincor(x1, x2)
wincor(x1, x2, tr = 0.1)
require(reshape)
hanglong <- subset(hangover, subset = group == "control")
hangwide <- cast(hanglong, id ~ time, value = "symptoms")[,-1]
pball(hangwide)
winall(hangwide)
``` |