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 Inter-Observer 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:
One-way / Two-way: 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 one-way repeated measures ANOVA table is displayed.
ICC(1): Intraclass correlation coefficient for the case of one-way, single measurement.
ICC(K): Intraclass correlation coefficient for one-way, average measurement.
ICC(C,1): Intraclass correlation coefficient for two-way, consistency, single measurement.
ICC(C,N): Intraclass correlation coefficient for two-way, consistency, average measurement.
ICC(A,1): Intraclass correlation coefficient for two-way, absolute agreement, single measurement.
ICC(A,N): Intraclass correlation coefficient for two-way, 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 |
F-Stat |
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 |
F-Statistic |
d.f. Numerator |
d.f. Denominator |
|
ICC(1): one-way, single |
0.1657 |
1.7947 |
5 |
18 |
|
ICC(K): one-way, average |
0.4428 |
1.7947 |
5 |
18 |
|
ICC(C,1): two-way, consistency, single |
0.7148 |
11.0272 |
5 |
15 |
|
ICC(C,N): two-way, consistency, average |
0.9093 |
11.0272 |
5 |
15 |
|
ICC(A,1): two-way, agreement, single |
0.2898 |
11.0272 |
5 |
5 |
|
ICC(A,N): two-way, agreement, average |
0.6201 |
11.0272 |
5 |
5 |
|
|
Right-Tail Probability |
2-Tail Probability |
Lower 95% |
Upper 95% |
|
ICC(1): one-way, single |
0.1648 |
0.3295 |
-0.1329 |
0.7226 |
|
ICC(K): one-way, average |
0.1648 |
0.3295 |
-0.8844 |
0.9124 |
|
ICC(C,1): two-way, consistency, single |
0.0001 |
0.0003 |
0.3425 |
0.9459 |
|
ICC(C,N): two-way, consistency, average |
0.0001 |
0.0003 |
0.6757 |
0.9859 |
|
ICC(A,1): two-way, agreement, single |
0.0099 |
0.0198 |
0.0188 |
0.7611 |
|
ICC(A,N): two-way, agreement, average |
0.0099 |
0.0198 |
0.0711 |
0.9272 |