irr (version 0.70)

icc: Intraclass correlation coefficient (ICC) for oneway and twoway models

Description

Computes single score or average score ICCs as an index of interrater reliability of quantitative data. Additionally, F-test and confidence interval are computed.

Usage

icc(ratings, model = c("oneway", "twoway"), 
    type = c("consistency", "agreement"), 
    unit = c("single", "average"), r0 = 0, conf.level = 0.95)

Arguments

ratings

n*m matrix or dataframe, n subjects m raters.

model

a character string specifying if a '"oneway"' model (default) with row effects random, or a '"twoway"' model with column and row effects random should be applied. You can specify just the initial letter.

type

a character string specifying if '"consistency"' (default) or '"agreement"' between raters should be estimated. If a '"oneway"' model is used, only '"consistency"' could be computed. You can specify just the initial letter.

unit

a character string specifying the unit of analysis: Must be one of '"single"' (default) or '"average"'. You can specify just the initial letter.

r0

specification of the null hypothesis r = r0.

conf.level

confidence level of the interval.

Value

• A list with class '"icclist"' containing the following components:
• $subjects
  the number of subjects examined.
• $raters
  the number of raters.
• $model
  a character string describing the selected model for the analysis.
• $type
  a character string describing the selected type of interrater reliability.
• $unit
  a character string describing the unit of analysis.
• $icc.name
  a character string specifying the name of ICC according to McGraw & Wong (1996).
• $value
  the intraclass correlation coefficient.
• $r0
  the specified null hypothesis.
• $Fvalue
  the value of the F-statistic.
• $df1
  the numerator degrees of freedom.
• $df2
  the denominator degrees of freedom.
• $p.value
  the p-value for a two-sided test.
• $conf.level
  the confidence level for the interval.
• $lbound
  the lower bound of the confidence interval.
• $ubound
  the upper bound of the confidence interval.

Details

Missing data are omitted in a listwise way. \crWhenconsidering which form of ICC is appropriate for an actual set of data, one has take several decisions (Shrout & Fleiss, 1979): \cr1. Should only the subjects be considered as random effects ('"oneway"' model) or are subjects and raters randomly chosen from a bigger pool of persons ('"twoway"' model). \cr2. If differences in judges' mean ratings are of interest, interrater '"agreement"' instead of '"consistency"' should be computed. \cr3. If the unit of analysis is a mean of several ratings, unit should be changed to '"average"'. In most cases, however, single values (unit='"single"') are regarded.

References

Bartko, J.J. (1966). The intraclass correlation coefficient as a measure of reliability. Psychological Reports, 19, 3-11. \crMcGraw, K.O., & Wong, S.P. (1996), Forming inferences about some intraclass correlation coefficients. Psychological Methods, 1, 30-46. \crShrout, P.E., & Fleiss, J.L. (1979), Intraclass correlation: uses in assessing rater reliability. Psychological Bulletin, 86, 420-428.

See Also

finn, meancor, robinson

Examples

data(anxiety)
icc(anxiety, model="twoway", type="agreement")

r1 <- round(rnorm(20, 10, 4))
r2 <- round(r1 + 10 + rnorm(20, 0, 2))
r3 <- round(r1 + 20 + rnorm(20, 0, 2))
icc(cbind(r1, r2, r3), "twoway")              # High consistency
icc(cbind(r1, r2, r3), "twoway", "agreement") # Low agreement