[R] intra-class correlation? coherence among multiple ordinal responses

William Revelle lists at revelle.net
Sat Aug 22 17:22:36 CEST 2009

At 6:15 PM -0400 8/21/09, Daniel Malter wrote:
>I have a quick statistical question and hoped somebody has a tip for me
>without me having to go to the local statistician on Monday.
>I assess 4 statements from 90 subjects. Each of the 4 statements receives
>one of three responses (say -1, 0, or 1). I can use Cramer's V or Spearman
>correlations to assess the correlation between each pair of statements, but
>I am looking for a measure of coherence across/among all 4 statements. To
>me, this seems to be intraclass correlation. So I was wondering whether I
>can apply it here (specifically, ICC(2,1) or ICC(3,1)) or whether I should
>use an alternative procedure given that my responses are ordinal.


The intraclass correlation is used if raters are all of the same 
``class".  That is, there is no logical way of distinguishing them. 
Examples include correlations between  pairs of twins, correlations 
between raters.  If the variables are logically distinguishable 
(e.g., different items on a test), then the more typical coefficient 
is based upon the inter-class correlation (e.g., a Pearson r) and a 
statistic such as alpha or omega might be used.

The differences between the 3 types of ICCs are the type of 
generalization you want to make.

Note that ICC3n is the same as coefficient alpha.

ICC, alpha, and omega are all part of the psych package.


William Revelle		http://personality-project.org/revelle.html
Professor			http://personality-project.org/personality.html
Department of Psychology             http://www.wcas.northwestern.edu/psych/
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