CorrDiff: 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

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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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  # Example:
  ens <- matrix(rnorm(100),20,5)
  ens.ref <- ens[, 1:3] + 0.2
  obs <- rnorm(20)
  CorrDiff(ens, ens.ref, obs, sign.level=0.1)

Questions? Problems? Suggestions? or email at ian@mutexlabs.com.

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