ci.icc: Confidence interval for an intraclass reliablity coefficient

In statpsych: Statistical Methods for Psychologists

Confidence interval for an intraclass reliablity coefficient

Description

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

\insertRef

McGraw1996statpsych

\insertRef

Bonett2021statpsych

Examples

ci.icc(.05, 48.2, 11.3, 5, 30)

# 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
 

statpsych documentation built on Jan. 13, 2026, 1:07 a.m.