psych (version 1.0-77)

ICC: Intraclass Correlations (ICC1, ICC2, ICC3 from Shrout and Fleiss)

Description

The Intraclass correlation is used as a measure of association when studying the reliability of raters. Shrout and Fleiss (1979) outline 6 different estimates, that depend upon the particular experimental design. All are implemented and given confidence limits.)

Usage

ICC(x,digits=2,alpha=.05)

Arguments

x

a matrix or dataframe of ratings

digits

Round the output to digits

alpha

The alpha level for significance

Value

• results
  A matrix of 6 rows and 8 columns, including the ICCs, F test, p values, and confidence limits

Details

Shrout and Fleiss (1979) consider six cases of reliability of ratings done by k raters on n targets.

ICC1) Each target is rated by a different judge and the judges are selected at random. (This is a one-way ANOVA random effects model.) 2) A random sample of k judges rate each target. The measure is one of absolute agreement in the ratings. 3) A fixed set of k judges rate each target. There is no generalization to a larger population of judges.

Then, for each of these cases, is reliability to be estimated for a single rating or for the average of k ratings? (The 1 rating case is equivalent to the average intercorrelation, the k rating case to the Spearman Brown adjusted reliability.)

ICC1 is sensitive to differences in means between raters and is a measure of absolute agreement.

ICC2 and ICC3 remove mean differences between judges, but are sensitive to interactions of raters by judges. The difference between ICC2 and ICC3 is whether raters are seen as fixed or random effects.

ICC1k, ICC2k, ICC3K reflect the means of k raters.

References

Shrout, Patrick E. and Fleiss, Joseph L. Intraclass correlations: uses in assessing rater reliability. Psychological Bulletin, 1979, 86, 420-3428.

McGraw, Kenneth O. and Wong, S. P. (1996), Forming inferences about some intraclass correlation coefficients. Psychological Methods, 1, 30-46. + errata on page 390.

Revelle, W. (in prep) An introduction to psychometric theory with applications in R. Springer. (working draft available at http://personality-project.org/r/book/

Examples

sf <- matrix(c(9,    2,   5,    8,
6,    1,   3,    2,
8,    4,   6,    8,
7,    1,   2,    6,
10,   5,   6,    9,
6,   2,   4,    7),ncol=4,byrow=TRUE)
colnames(sf) <- paste("J",1:4,sep="")
rownames(sf) <- paste("S",1:6,sep="")
sf  #example from Shrout and Fleiss (1979)
ICC(sf)