Sample size or precision for an intraclass correlation

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

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.

Value

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

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 \(rho \ge 7\). This makes the assumption that there is no interaction between rater and subject.

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

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

# 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)
#> 
#>      sample size for intraclass correlation 
#> 
#>    rho k  n conf.width conf.level
#> 1 0.85 4 20        0.2       0.95
#> 
# 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)
#> 
#>      precision for intraclass correlation 
#> 
#>    rho k  n conf.width conf.level
#> 1 0.85 4 20  0.1954993       0.95
#>