# bgtCI: Confidence Intervals for One Proportion in Binomial Group... In binGroup: Evaluation and Experimental Design for Binomial Group Testing

## Description

Calculates the point estimate, the exact Clopper-Pearson and Blaker CI, the Score test derived Wilson and Agresti-Coull CI, the asymptotic second-order corrected interval fo Cai and the Wald CI for a single binomial proportion estimated from a binomial group testing trial. Assumes equal group sizes, an assay method classifying a group as positive if at least one unit in the group is positive, individuals units randomly assigned to the groups.

## Usage

 1 2 bgtCI(n, s, y, conf.level = 0.95, alternative = "two.sided", method = "CP")

## Arguments

 n integer, specifying the number of groups (i.e. assays i.e. observations) s integer, specifying the common size of groups i.e. the number of individual units in each group y integer, specifying the number of positive groups conf.level nominal confidence level of the interval alternative character string defining the alternative hypothesis, either 'two.sided', 'less' or 'greater' where 'less' gives the only an upper bound with confidence level=conf.level 'greater' gives the only a lower bound with confidence level=conf.level and 'two.sided' gives a two-sided confidence interval with confidence level=conf.level method character string defining the method for CI calculation, where: "CP" is Clopper-Pearson, an exact tail interval showing symmetric coverage probability (inversion of two one-sided tests), "Blaker" is the Blaker interval, an exact interval, inversion of one two.sided test, therefore defined only two.sided, but shorter than the two-sided Clopper-Pearson CI. Both guarantee to contain the true parameter with at least conf.level*100 percent probability, "AC" is the Agresti-Coull (generalized Agresti-Coull) interval, asymptotic method, "Score" is Wilson Score, asymptotic method derived from inversion of the Score test, "SOC" is the second order corrected interval, asymptotic method for one-sided problems (for details see Cai, 2005), and "Wald" the Wald interval, which cannot be recommended.

## Details

This function allows the computation of confidence intervals for binomial group testing as described in Tebbs & Bilder (2004) and Schaarschmidt (2007). If an actual confidence level greater or equal to that specified in the conf.level argument shall always be guaranteed, the exact method of Clopper-Pearson (method="CP") can be recommended for one-sided and the improved method of Blaker (2000) (method="Blaker") can be recommended for two-sided hypotheses. If a mean confidence level close to that specified in the argument conf.level is required, but moderate violation of this level is acceptable, the Second-Order corrected (method="SOC"), Wilson Score (method="Score") or Agresti-Coull (method="AC") might be used (Brown, Cai, DasGupta, 2001; Cai 2005).

## Value

A list containing:

 conf.int a confidence interval for the proportion estimate the point estimator of the proportion

## Author(s)

Frank Schaarschmidt

## References

Blaker H (2000). Confidence curves and improved exact confidence intervals for discrete distributions. The Canadian Journal of Statistics 28 (4), 783-798.

Brown LD, Cai TT, DasGupta A (2001). Interval estimation for a binomial proportion. Statistical Science 16 (2), 101-133.

Cai TT (2005). One-sided confidence intervals in discrete distributions. Journal of Statistical Planning and Inference 131, 63-88.

Schaarschmidt F (2007). Experimental design for one-sided confidence intervals or hypothesis tests in binomial group testing. Communications in Biometry and Crop Science 2 (1), 32-40. http://agrobiol.sggw.waw.pl/cbcs/

Tebbs JM & Bilder CR (2004). Confidence interval procedures for the probability of disease transmission in multiple-vector-transfer designs. Journal of Agricultural, Biological and Environmental Statistics, 9 (1), 75-90.