Intraclass and interclass correlation coefficient

Interclass correlation, or Pearson correlation,¹ is a correlation in the ordinary sense.² It is used to estimate the correlation between two different variables, or between two groups.¹

The intraclass correlation is not the correlation between a predictor variable and the dependent variable but it reflects the extent to which members of the same group or class tend to act alike.³ It is the proportion of the total variability in the measured factor that is due to the variability between individuals.⁴  

Intraclass correlation can be used in the following way. First a normative grand average waveform for typically developing children in a given age band is computed.⁵ The grand average is the average of sample⁶ or subgroup averages.⁷ The next step is to compute the intraclass correlation coefficient (ICC) between that grand average and an individual child’s waveform in the same region.⁵

In Bishop’s study, the ICC was computed between datapoints between two waveforms: a normative waveform, which was the grand average for the control group, and a comparison waveform, which is the waveform of an individual child. To ensure total independence of normative and comparison waveforms, the comparison waveform was never included in the average used for the normative waveform: i.e. when computing the ICC for a typically developing child, the normative grand average was based on all the other control children. However, normative waveforms formed by dropping one subject from a sample of 47 were virtually identical.
A low ICC means that the individual child differs from the group; whereas average or high ICC means that the individual child shows the same pattern as the rest of the group.⁸  

The ICC is similar to the more familiar Pearson correlation coefficient, except that it is sensitive to absolute size of the values in two arrays. Thus whereas the Pearson correlation coefficient would be unchanged by adding a constant to all the values in one of two correlated arrays, the ICC would decrease as the mean of the two arrays became more discrepant. The ICC thus gives a global index of similarity between two waveforms; a low ICC can arise if there are either amplitude or latency differences in peaks and troughs. The ICC agrees well with ratings of waveform similarity made by untrained observers on the basis of visual inspection.⁵

References:
1. http://www.listserv.uga.edu/cgi-bin/wa?A2=ind9602&L=spssx-l&P=4445
2. W. Paul Vogt: Dictionary of Statistics & Methodology: A Nontechnical Guide for the Social Sciences, 2005
3. Scott E. Maxwell & Harold D. Delaney: Designing Experiments and Analyzing Data: A Model Comparison Perspective, 2003
4. Moyses Szklo and F. Javier Nieto: Epidemiology: Beyond the Basics, 2004
5. D.V.M. Bishop et al: Maturation of the long-latency auditory ERP: step function changes at start and end of adolescence, 2007
6. http://www.toolingu.com/definition-900210-5357-grand-average.html
7. http://www.qualitydigest.com/apr/spctool.html
8. D.V.M. Bishop et al: Atypical long-latency auditory event-related potentials in a subset of children with specific language impairment, 2007