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### Highlights from Intraclass Correlation Coefficient (ICC)

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# Intraclass Correlation Coefficient (ICC)

### Arash Salarian (view profile)

14 Nov 2008 (Updated )

Calculate any of 6 different ICCs with confidence intervals

File Information
Description

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. This function calls anova_rm (provided inside the zip file).

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 maded 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.

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

Acknowledgements

Repeated Measures Anova inspired this file.

This file inspired Ipn Tools For Test Retest Reliability Analysis.

Required Products Statistics and Machine Learning Toolbox
MATLAB release MATLAB 7.2 (R2006a)
03 Jun 2015 Jeffrey Girard

### Jeffrey Girard (view profile)

@Matthieu, The two-way random effects model and two-way mixed effects model are equivalent in their calculation and only differ in their interpretation. As such, this script provides a calculation of both.

19 Feb 2015 Matthieu

### Matthieu (view profile)

I was wondering if there was a way to pick 2-way mixed or random model in this function?

Comment only
27 Sep 2011 Philip West

### Philip West (view profile)

I used 'nanmean' and 'nanstd' instead of mean_nan and std_nan and it worked fine

Comment only
25 May 2011 ted p teng

### ted p teng (view profile)

Great function, easy to use, and it also outputs the confidence interval and a reference for it! Excellent work!!

11 Feb 2011 Andrew

### Andrew (view profile)

A phenomenal function for ICC--quick, painless, and complete. The only minor inconvenience is the fact that there are several functions that must be put into the code, but that is a small price to pay.