# prec_icc: Sample size or precision for an intraclass correlation In presize: Precision Based Sample Size Calculation

## Description

`prec_icc` returns the sample size or the precision for the given intraclass correlation.

## Usage

 `1` ```prec_icc(rho, k, n = NULL, conf.width = NULL, conf.level = 0.95) ```

## Arguments

 `rho` desired intraclass correlation. `k` number of observations per n (subject). `n` number of subjects. `conf.width` precision (the full width of the confidence interval). `conf.level` confidence level.

## Details

Exactly one of the parameters `n` or `conf.width` must be passed as NULL, and that parameter is determined from the others.

Sample size or precision is calculated according to formula 3 in Bonett (2002), which is an approximation. Whether ICC is calculated for a one-way or a two-way ANOVA does not matter in the approximation. As suggested by the author, 5*rho is added to n, if k = 2 and rho ≥ 7.

n is rounded up to the next whole number using `ceiling`.

## Value

Object of class "presize", a list of arguments (including the computed one) augmented with method and note elements.

## References

Bonett DG (2002). Sample size requirements for estimating intraclass correlations with desired precision. Statistics in Medicine, 21:1331-1335. doi: 10.1002/sim.1108

## Examples

 ```1 2 3 4 5 6 7 8 9``` ```# Bonett (2002) gives an example using 4 raters, with an ICC of 0.85 and want # a confidence width of 0.2. Bonett calculated that a sample size of 19.2 was # required. This can be done via prec_icc(0.85, 4, conf.width = 0.2) # note that \code{presamp} rounds up to the nearist integer. # Bonett then goes on to estimate the width given the sample size, finding a # value 'close to 0.2': prec_icc(0.85, 4, 20) ```

### Example output

```     sample size for intraclass correlation

rho k  n conf.width conf.level
1 0.85 4 20        0.2       0.95

precision for intraclass correlation

rho k  n conf.width conf.level
1 0.85 4 20  0.1954993       0.95
```

presize documentation built on April 9, 2021, 1:05 a.m.