Could we compute the sample size required to find significant an ICC of at least r=0.5 for example?
in order to determine the sample size for reliability studies (to which the icc fits for) one needs consider previously the class of the icc (ie, if icc relates to 1way ANOVA or 2way ANOVA).
Walter, Eliasziw and Donner find a solution for study-designs ICC(1,1)-related
http://onlinelibrary.wiley.com/doi/10.1002/(SICI)1097-0258(19980115)17:1%3C101::AID-SIM727%3E3.0.CO;2-E/pdf
The optimal sample size for ICC(2,1)-related studies has been addressed in:
Doros and Lew (2010). Design Based on Intra-Class Correlation Coefficients. American Journal of Biostatistics 1 (1): 1-8, 2010.
icc is a measure of "agreement" that is used to test the convergence or homogeneity of responses within groups. It should not get confused with the canonical Pearson's correlation coefficient,which is an inter-class coefficient. Pearson's correlation coefficient measures the "association" between variables when their objects are distinguishable.
Association in statistical sense, is something different from agreement; the former subsumes a linear relationship between the coupled outcomes of the variables (as effect of their covariation). Agreement means that a score in one variable is reproducible by the score of the other variable. Interestingly, we can represent this epistemologic difference in geometrical terms, so that association would measure the angle between two vectors whilst agreement would relate to the modulus, ie the distance, between two vectors.
Once you have your sample size calculated without the ICC, you can use the equation n'=n(1+ρ(m-1)) to find your adjusted sample size. Here: n' is your adjusted sample size, ρ is your ICC, m is the number of people/animals sampled per cluster. Does that help? Forgive me if I misunderstood the question.
EDIT: I see I misunderstood the question. ;)
Hi,
I do not think that handling an ICC correlation coefficient makes problems since no matter within which class a correlation coefficient is calculated it should follow a given sample distribution as first stated By Sir R.Fisher: Fisher, R.A. (1915). "Frequency distribution of the values of the correlation coefficient in samples of an indefinitely large population". Biometrika (Biometrika Trust) 10 (4): 507–521.
So i think you can compute your power calcolation using standard packages in SAS I use this for a correlation coeff of 0.5 vs a null Hyp r=0 two tails and 80% power...
proc power;
onecorr dist=fisherz
corr = 0.5
nullcorr = 0
sides = 2
ntotal = .
power = .80;
run;
cheers
Thank you Cristian! I miss to say that I want to know how many replicates I need when having a fixed number of patients?
in order to determine the sample size for reliability studies (to which the icc fits for) one needs consider previously the class of the icc (ie, if icc relates to 1way ANOVA or 2way ANOVA).
Walter, Eliasziw and Donner find a solution for study-designs ICC(1,1)-related
http://onlinelibrary.wiley.com/doi/10.1002/(SICI)1097-0258(19980115)17:1%3C101::AID-SIM727%3E3.0.CO;2-E/pdf
The optimal sample size for ICC(2,1)-related studies has been addressed in:
Doros and Lew (2010). Design Based on Intra-Class Correlation Coefficients. American Journal of Biostatistics 1 (1): 1-8, 2010.
icc is a measure of "agreement" that is used to test the convergence or homogeneity of responses within groups. It should not get confused with the canonical Pearson's correlation coefficient,which is an inter-class coefficient. Pearson's correlation coefficient measures the "association" between variables when their objects are distinguishable.
Association in statistical sense, is something different from agreement; the former subsumes a linear relationship between the coupled outcomes of the variables (as effect of their covariation). Agreement means that a score in one variable is reproducible by the score of the other variable. Interestingly, we can represent this epistemologic difference in geometrical terms, so that association would measure the angle between two vectors whilst agreement would relate to the modulus, ie the distance, between two vectors.
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