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Confidence interval for an intraclass reliablity coefficient

Source: R/statpsych2.R
ci.icc.Rd

Computes a confidence interval for a population intraclass reliability coefficient using mean squared estimates from a two-way ANOVA. This function will compute point and interval estimates of the ICC(C, 1) and ICC(C, r) reliability coefficients where ICC(C, 1) is the reliability of a single measurements (e.g., a single rater or a single form of a test) and ICC(C, r) is the reliability of a sum or average of r measurements. ICC(C, r) is the same as Cronbach's reliability coefficient. The ci.cronbach function uses a point estimate of Cronbach's reliability as input. The confidence intervals used in this function assume parallel measurements which implies a compound symmetric covariance matrix of the r measurements.

Usage

ci.icc(alpha, MSr, MSe, r, n)

Arguments

alpha

alpha level for 1-alpha confidence

MSr

mean square for rows

MSe

error mean square

r

number of measurements (items, raters, forms)

n

sample size

Value

Returns a 2-row matrix. The first row results are for ICC(C, 1) and the second row results are for ICC(C, r). The columns are:

  • Estimate - estimated reliability

  • SE - standard error

  • LL - lower limit of the confidence interval

  • UL - upper limit of the confidence interval

References

McGraw KO, Wong SP (1996). “Forming inferences about some intraclass correlation coefficients.” Psychological Methods, 1(1), 30–46. doi:10.1037/1082-989X.1.1.30 .

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.icc(.05, 48.2, 11.3, 5, 30)
#>           Estimate      SE     LL     UL
#> ICC(C, 1)   0.3951 0.09166 0.2311 0.5853
#> ICC(C, r)   0.7656 0.07005 0.6005 0.8759

# Should return:
#           Estimate      SE     LL     UL
# ICC(C, 1)   0.3951 0.09166 0.2311 0.5853
# ICC(C, r)   0.7656 0.07005 0.6005 0.8759