Hypothesis test for equality of two correlation coefficients {corrfuns} | R Documentation |

## Hypothesis test for equality of two correlation coefficients

### Description

Hypothesis test for equality of two correlation coefficients.

### Usage

```
correls2.test(r1, r2, n1, n2, type = "pearson")
```

### Arguments

`r1` |
The value of the first correlation coefficient. |

`r2` |
The value of the second correlation coefficient. |

`n1` |
The sample size of the first sample from which the first correlation coefficient was computed. |

`n2` |
The sample size of the second sample from which the first correlation coefficient was computed. |

`type` |
The type of correlation coefficients, "pearson" or "spearman". |

### Details

The test statistic for the hypothesis of equality of two correlation coefficients is the following:

```
Z=\frac{\hat{z}_1-\hat{z}_2}{\sqrt{1/\left(n1-3\right)+1/\left(n2-3\right)}},
```

where `\hat{z}_1`

and `\hat{z}_2`

denote the Fisher's transformation (see `correl`

applied to the two correlation coefficients and `n_1`

and `n_2`

denote the sample sizes of the two correlation coefficients. The denominator is the sum of the variances of the two coefficients and as you can see we used a different variance estimator than the one we used before. This function performs hypothesis testing for the equality of two correlation coefficients. The result is the calculated p-value from the standard normal distribution.

### Value

The test statistic and its associated p-value for the test of equal correlations.

### Author(s)

Michail Tsagris

R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.

### See Also

### Examples

```
y <- rnorm(40)
x <- matrix(rnorm(40 * 1000), ncol = 1000)
a <- correls(y, x )
```

*corrfuns*version 1.0 Index]