# Compute sample size for an intra-class correlation (ICC)

#### twentyseven

##### New Member
We want to compare three different methods to measure blood haemoglobin levels. So, as we are speaking about continous variables, we thought that intra-class correlation coefficient would be an addequate option.

In order to calculate the sample size that we will need, we discovered a Stata module called sampicc (https://ideas.repec.org/c/boc/bocode/s456978.html).

So we used it to calculate the sample size for an expected ICC of 0.6 and allowing for a variability among 0.45 and 0.75 (width: 0.15). We applied the sintaxis and we got the following result:

Code:
. sampicc 0.6 3, width(0.15) ci

****************************************************************
Sample Size for the Width of a Confidence Interval for ICC
****************************************************************

Given:
Expected Value (P1):  0.60
Number of Replicates:    3
CI level:   95%
Specified Width:  0.15

****************************************************************

Esimtated sample size is:  177

****************************************************************
But we wanted to give it a try to a higher ICC, and we ran the sintax again:

Code:
. sampicc 0.8 3, width(0.15) ci

****************************************************************
Sample Size for the Width of a Confidence Interval for ICC
****************************************************************

Given:
Expected Value (P1):  0.80
Number of Replicates:    3
CI level:   95%
Specified Width:  0.15

****************************************************************

Esimtated sample size is:   63

****************************************************************
Surprisingly, the sample size needed to reach a higher agreement is smaller.

Does anyone know why we are getting this result? If we specify higher ICCs, we get smaller sample sizes.

#### spunky

##### Can't make spagetti
We want to compare three different methods to measure blood haemoglobin levels. So, as we are speaking about continous variables, we thought that intra-class correlation coefficient would be an addequate option.

In order to calculate the sample size that we will need, we discovered a Stata module called sampicc (https://ideas.repec.org/c/boc/bocode/s456978.html).

So we used it to calculate the sample size for an expected ICC of 0.6 and allowing for a variability among 0.45 and 0.75 (width: 0.15). We applied the sintaxis and we got the following result:

Code:
. sampicc 0.6 3, width(0.15) ci

****************************************************************
Sample Size for the Width of a Confidence Interval for ICC
****************************************************************

Given:
Expected Value (P1):  0.60
Number of Replicates:    3
CI level:   95%
Specified Width:  0.15

****************************************************************

Esimtated sample size is:  177

****************************************************************
But we wanted to give it a try to a higher ICC, and we ran the sintax again:

Code:
. sampicc 0.8 3, width(0.15) ci

****************************************************************
Sample Size for the Width of a Confidence Interval for ICC
****************************************************************

Given:
Expected Value (P1):  0.80
Number of Replicates:    3
CI level:   95%
Specified Width:  0.15

****************************************************************

Esimtated sample size is:   63

****************************************************************
Surprisingly, the sample size needed to reach a higher agreement is smaller.

Does anyone know why we are getting this result? If we specify higher ICCs, we get smaller sample sizes.