6.2.4. Intraclass Correlation Coefficients
The intraclass correlation coefficient is a multivariate generalisation of the more commonly used Correlation Coefficients on paired data. It can be considered as a correlation coefficient for k categories (columns) with n cases (rows). Its most common application is, like the Kappa tests (see 6.5.10. Kappa Test for InterObserver Variation), the test of agreement between k raters on n subjects.
UNISTAT supports six categories of intraclass correlation coefficient, each representing a combination of the following properties:
Oneway / Twoway: The degree of agreement when, raters are assigned to subjects randomly / all raters rate all subjects, respectively.
Consistency / Agreement: The degree of, consistency among / absolute agreement for, subjects respectively.
Single / Average: The agreement, among subjects / for the average of n independent subjects, respectively.
The output options include the ANOVA table, six correlation coefficients, their significance tests and confidence intervals.
ANOVA: A oneway repeated measures ANOVA table is displayed.
ICC(1): Intraclass correlation coefficient for the case of oneway, single measurement.
ICC(K): Intraclass correlation coefficient for oneway, average measurement.
ICC(C,1): Intraclass correlation coefficient for twoway, consistency, single measurement.
ICC(C,N): Intraclass correlation coefficient for twoway, consistency, average measurement.
ICC(A,1): Intraclass correlation coefficient for twoway, absolute agreement, single measurement.
ICC(A,N): Intraclass correlation coefficient for twoway, absolute agreement, average measurement.
See Shrout, P. E., and Fleiss, J. L. (1979) and McGraw, K. O. & Wong, S. P. (1996) for details.
Example
The data is taken from Shrout P.E. and Fleiss J.L. (1979).
Open CORRCOEF, select Statistics 1 → Nonparametric Tests (Multisample) → Intraclass Correlation Coefficients and select Rater 1 to Rater 4 (C9 to C12) as [Variable]s to obtain the following results:
Intraclass Correlation Coefficients
Variables Selected: Rater 1, Rater 2, Rater 3, Rater 4
Number of Columns: 4
Number of Rows: 6
ANOVA
Due To 
Sum of Squares 
DoF 
Mean Square 
FStat 
Prob 
Between Raters 
97.458 
3 
32.486 
31.866 
0.1293 
Between Subjects 
56.208 
5 
11.242 
11.027 
0.2246 
Within Subjects 
112.750 
18 
6.264 
6.144 
0.3086 
Error 
15.292 
15 
1.019 


Total 
168.958 
23 
7.346 


Intraclass Correlation Coefficients

Value 
FStatistic 
d.f. Numerator 
d.f. Denominator 
ICC(1): oneway, single 
0.1657 
1.7947 
5 
18 
ICC(K): oneway, average 
0.4428 
1.7947 
5 
18 
ICC(C,1): twoway, consistency, single 
0.7148 
11.0272 
5 
15 
ICC(C,N): twoway, consistency, average 
0.9093 
11.0272 
5 
15 
ICC(A,1): twoway, agreement, single 
0.2898 
11.0272 
5 
5 
ICC(A,N): twoway, agreement, average 
0.6201 
11.0272 
5 
5 

RightTail Probability 
2Tail Probability 
Lower 95% 
Upper 95% 
ICC(1): oneway, single 
0.1648 
0.3295 
0.1329 
0.7226 
ICC(K): oneway, average 
0.1648 
0.3295 
0.8844 
0.9124 
ICC(C,1): twoway, consistency, single 
0.0001 
0.0003 
0.3425 
0.9459 
ICC(C,N): twoway, consistency, average 
0.0001 
0.0003 
0.6757 
0.9859 
ICC(A,1): twoway, agreement, single 
0.0099 
0.0198 
0.0188 
0.7611 
ICC(A,N): twoway, agreement, average 
0.0099 
0.0198 
0.0711 
0.9272 