binWidth {binGroup} R Documentation

## Expected Confidence Interval Width for One Binomial Proportion

### Description

Calculation of expected value of the width of confidence intervals in a binomial experiment, in dependence of the number of trials (number of individuals under observation), confidence level and an assumed true proportion. Available for the confidence interval methods in binCI(binGroup).

### Usage

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

### Arguments

 `n` integer, giving the number of trials (i.e. number of individuals under observation) `p` assumed true proportion of individuals showing the trait to be estimated `conf.level` required confidence level of the interval `alternative` character string, defining the alternative hypothesis, either 'two.sided', 'less' or 'greater' where 'less' calculates the expected width between the assumed true proportion p and the upper conf.level*100 percent-bound of a one-sided CI, 'greater' calculates the expected width between the assumed true proportion p and the lower conf.level*100 percent-bound of a one-sided CI, 'two.sided' calculates the expected width between the lower and the upper bound of a two-sided conf.level*100 percent-CI. `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 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 simple Wald-type interval.

### Details

For calculation of expected interval width in the standard binomial estimation see Brown et al. (2001).

### Value

A list containing:

 `expCIWidth` the expected value of the width of the confidence interval for the specified arguments

and the alternative, p and n which are specified in the function call.

### Author(s)

Frank Schaarschmidt

### See Also

`binDesign` for experimental design for hypothesis testing

### Examples

```

# methods differ slightly in length when sample sizes are large:

binWidth(n=200,p=0.02,alternative="two.sided",
method="CP")\$expCIWidth

binWidth(n=200,p=0.02,alternative="two.sided",
method="Blaker")\$expCIWidth

binWidth(n=200,p=0.02,alternative="two.sided",
method="Score")\$expCIWidth

# but do more for small sample sizes and intermediate p:

binWidth(n=20,p=0.2,alternative="two.sided",
method="CP")\$expCIWidth

binWidth(n=20,p=0.2,alternative="two.sided",
method="Blaker")\$expCIWidth

binWidth(n=20,p=0.2,alternative="two.sided",
method="Score")\$expCIWidth

```

[Package binGroup version 2.2-1 Index]