# Calculates various confidence intervals for the difference of two dependent proportions

### Description

This function gives 12 different two-sided confidence intervals. Data are assumed to be of a fourfold table, which contains the numbers of concordance and the numbers of discordance of two dependent methods. The following intervals are listed: Wald, Wald with continuity correction, Agresti, Tango, Exact (Clopper Pearson and mid-p), Profile Likelihood, Wilson (without and with continuity corrections) and nonparametric approaches using rank methods (with normal and t-approximation).

### Usage

1 |

### Arguments

`a` |
first number of concordant paires as described above |

`b` |
first number of discordant paires as described above |

`c` |
second number of discordant paires as described above |

`d` |
second number of concordant paires as described above |

`n` |
number of observed objects |

`alpha` |
type I error; between zero and one |

### Details

Details are given for each function separately.

### Value

A matrix containing the method, the difference estimator and the corresponding confidence limits.

### Author(s)

Daniela Wenzel, Antonia Zapf

### References

Newcombe, R.G. (1998). Improved confidence intervals for the difference between binomial proportions based on paired data. Statistics in Medicine 17. 2635-2650.

Clopper, C. and Pearson, E.S. (1934). The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika 26, 404-413.

Vollset, S.E. (1993). Confidence intervals for a binomial proportion. Statistics in Medicine 12. 809-824.

Lange, K. and Brunner, E. (2012). Sensitivity, Specificity and ROC-curves in multiple reader diagnostic trials-A unified, nonparametric approach. Statistical Methodology 9, 490-500.

Fleiss, Joseph L. et al. (2003). Statistical Methods for Rates and Proportions. Wiley.

### Examples

1 2 | ```
# a=59, b=23, c=3, d=37, n=122, type I error is 0.05
diffpci(59,23,3,37,122,0.05)
``` |