Intraclass Correlation Coefficient (ICC)

Calculate any of 6 different ICCs with confidence intervals

This function can calculate any of the 6 different ICCs defined by McGraw as well as their confidence intervals. In addition a hypothesis test is performed with the null hypothesis that ICC = r0.
Syntax:
[r, LB, UB, F, df1, df2, p] = ICC(M, type, alpha, r0)
M is matrix of observations. Each row is an object of measurement and each column is a judge or measurement.
'type' is a string that can be one of the six possible codes for the desired type of ICC:
'1-1': The degree of absolute agreement among measurements made on randomly seleted objects. It estimates the correlation of any two measurements.
'1-k': The degree of absolute agreement of measurements that are averages of k independent measurements on randomly selected objects.
'C-1': case 2: The degree of consistency among measurements. Also known as norm-referenced reliability and as Winer's adjustment for anchor points. case 3: The degree of consistency among measurements maded under the fixed levels of the column factor. This ICC estimates the corrlation of any two measurements, but when interaction is present, it underestimates reliability.
'C-k': case 2: The degree of consistency for measurements that are averages of k independent measurements on randomly selected onbjectgs. Known as Cronbach's alpha in psychometrics. case 3: The degree of consistency for averages of k independent measures made under the fixed levels of column factor.
'A-1': case 2: The degree of absolute agreement among measurements. Also known as criterion-referenced reliability. case 3: The absolute agreement of measurements made under the fixed levels of the column factor.
'A-k': case 2: The degree of absolute agreement for measurements that are averages of k independent measurements on randomly selected objects. case 3: he degree of absolute agreement for measurements that are based on k independent measurements made under the fixed levels of the column factor.

ICC is the estimated intraclass correlation. LB and UB are upper and lower bounds of the ICC with alpha level of significance.

In addition to estimation of ICC, a hypothesis test is performed with the null hypothesis that ICC = r0. The F value, degrees of freedom and the corresponding p-value of the this test are reported.

(The code names for ICC classes correspond to the Table 7 in the reference).

Reference: McGraw, K. O., Wong, S. P., "Forming Inferences About Some Intraclass Correlation Coefficients", Psychological Methods, Vol. 1, No. 1, pp. 30-46, 1996