# Calculate and evaluate the difference of correlation of two ensemble forecasts.

### Description

Calculate the difference of the correlation coefficients of two competing ensemble forecasts for the same observation. Confidence intervals and a p value of a one-sided test for equality are calculated to evaluate the difference.

### Usage

1 | ```
CorrDiff(ens, ens.ref, obs, sign.level=0.05)
``` |

### Arguments

`ens` |
N*K matrix. A collection of N ensemble forecasts, each with K members. |

`ens.ref` |
A N*L matrix. A collection of N ensemble forecasts, each with L members, which predict the same observation as 'ens'. |

`obs` |
vector of length N. The verifying observations that 'ens' and 'ens.ref' try to predict. |

`sign.level` |
The significance level of the confidence interval of the correlation difference. |

### Value

The function returns a vector of length 4. The first element is the difference of the correlation coefficients 'cor(ens, obs) - cor(ens.ref, obs)'. The second and third element are the lower and upper confidence limits corresponding to 'sign.level', calculated using results from Zou (2007). The 4th element is a p-value of a one-sided t-test for zero difference, calculated using the result from Steiger (1980).

### References

Steiger, JH (1980). Tests for Comparing Elements of a Correlation Matrix. Psychological Bulletin Vol. 87, No. 2, pp 245-251

Zou, GY (2007). Toward Using Confidence Intervals to Compare Correlation. Psychological Methods Vol. 12, No. 4, pp 399-413

### Examples

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