gtWidth {binGroup2} R Documentation

## Expected width of confidence intervals in group testing

### Description

Calculation of the expected value of the width of confidence intervals for one proportion in group testing. Calculations are available for the confidence interval methods in `propCI`.

### Usage

```gtWidth(n, s, p, conf.level = 0.95, alternative = "two.sided", method = "CP")
```

### Arguments

 `n` integer specifying the number of groups. A vector of integers is also allowed. `s` integer specifying the common size of groups. A vector of integers is also allowed. `p` the assumed true proportion of individuals showing the trait to be estimated. A vector is also allowed. `conf.level` the required confidence level of the interval. `alternative` character string specifying the alternative hypothesis, either "two.sided", "less", or "greater". `method` character string specifying the confidence interval method. Available options include those in `propCI`.

### Details

The two-sided (method="two.sided") option calculates the expected width between the lower and upper bound of a two-sided conf.level*100 percent confidence interval. See Tebbs & Bilder (2004) for expression. The one-sided (method="less" or method="greater") options calculate the expected distance between the one-sided limit and the assumed true proportion p for a one-sided conf.level*100 percent confidence interval.

### Value

A matrix containing the columns:

 `ns` the resulting total number of units, n*s. `n` the number of groups. `s` the group size. `p` the assumed true proportion. `expCIWidth` the expected value of the confidence interval width as defined under the argument alternative.

### Author(s)

This function was originally written as `bgtWidth` by Frank Schaarschmidt for the `binGroup` package. Minor modifications have been made for inclusion of the function in the `binGroup2` package.

### References

Tebbs, J., Bilder, C. (2004). “Confidence interval procedures for the probability of disease transmission in multiple-vector-transfer designs.” Journal of Agricultural, Biological, and Environmental Statistics, 9, 75–90. doi: 10.1198/1085711043127, https://doi.org/10.1198/1085711043127.

`propCI` for confidence intervals in group testing.

Other estimation functions: `designEst()`, `designPower()`, `gtPower()`, `gtTest()`, `propCI()`, `propDiffCI()`

### Examples

```# Examine different group sizes to determine
#   the shortest expected width.
gtWidth(n = 20, s = seq(from = 1, to = 200, by = 10),
p = 0.01, alternative = "less", method = "CP")

# Calculate the expected width of the confidence
#   interval with a group size of 1 (individual testing).
gtWidth(n = 20, s = 1, p = 0.005, alternative = "less", method = "CP")
```

[Package binGroup2 version 1.1.0 Index]