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Graham Wright
Graham Wright
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I'm not sure who said "ICC is the correlation between observations within the same group" but to me that is not a very helpful way of thinking about it.

The ICC is the proportion of total variance in the dependent variable that is "at the group level" or "due to differences between (as opposed to within) groups." It is calculated by dividing the group-level variance by the sum of group and individual level variances. So it can range from 0 to 1. An ICC of 10% means that 10% of the variance in the dependent variable is due to between-group differences, and the remaining 90% is due to within-group differences.

That being said, the statement you cite is still broadly accurate because, as the ICC increases, the correlation between observations in the same group will tend to go up. At the limit case, an ICC of 1 means that 100% of the variance in the DV is due to between group differences and 0% is due to within-group differences. That in turn implies that all observations that share a group will all have exactly the same value for the DV. Thus the correlation between observations within a given group is perfect. At the other end, an ICC of zero means that 0% of the variance is due to between group differences, which in turn implies that the average value of the DV for observations within a particular group is identical, no matter what group you choose. So the ICC does have implications for within- and between-group correlations

But fundamentally, the ICC tells you about the proportion of variance at different analytic levels. In my view, any definition that doesn't emphasize that risks confusing people.

I'm not sure who said "ICC is the correlation between observations within the same group" but to me that is not a very helpful way of thinking about it.

The ICC is the proportion of total variance in the dependent variable that is "at the group level" or "due to differences between (as opposed to within) groups. It is calculated by dividing the group-level variance by the sum of group and individual level variances. So it can range from 0 to 1. An ICC of 10% means that 10% of the variance in the dependent variable is due to between-group differences, and the remaining 90% is due to within-group differences.

That being said, the statement you cite is still broadly accurate because, as the ICC increases, the correlation between observations in the same group will tend to go up. At the limit case, an ICC of 1 means that 100% of the variance in the DV is due to between group differences and 0% is due to within-group differences. That in turn implies that all observations that share a group will all have exactly the same value for the DV. Thus the correlation between observations within a given group is perfect. At the other end, an ICC of zero means that 0% of the variance is due to between group differences, which in turn implies that the average value of the DV for observations within a particular group is identical, no matter what group you choose. So the ICC does have implications for within- and between-group correlations

But fundamentally, the ICC tells you about the proportion of variance at different analytic levels. In my view, any definition that doesn't emphasize that risks confusing people.

I'm not sure who said "ICC is the correlation between observations within the same group" but to me that is not a very helpful way of thinking about it.

The ICC is the proportion of total variance in the dependent variable that is "at the group level" or "due to differences between (as opposed to within) groups." It is calculated by dividing the group-level variance by the sum of group and individual level variances. So it can range from 0 to 1. An ICC of 10% means that 10% of the variance in the dependent variable is due to between-group differences, and the remaining 90% is due to within-group differences.

That being said, the statement you cite is still broadly accurate because, as the ICC increases, the correlation between observations in the same group will tend to go up. At the limit case, an ICC of 1 means that 100% of the variance in the DV is due to between group differences and 0% is due to within-group differences. That in turn implies that all observations that share a group will all have exactly the same value for the DV. Thus the correlation between observations within a given group is perfect. At the other end, an ICC of zero means that 0% of the variance is due to between group differences, which in turn implies that the average value of the DV for observations within a particular group is identical, no matter what group you choose. So the ICC does have implications for within- and between-group correlations

But fundamentally, the ICC tells you about the proportion of variance at different analytic levels. In my view, any definition that doesn't emphasize that risks confusing people.

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Graham Wright
Graham Wright
  • 7.4k
  • 12
  • 33

I'm not sure who said "ICC is the correlation between observations within the same group" but to me that is not a very helpful way of thinking about it.

The ICC is the proportion of total variance in the dependent variable that is "at the group level" or "due to differences between (as opposed to within) groups. It is calculated by dividing the group-level variance by the sum of group and individual level variances. So it can range from 0 to 1. An ICC of 10% means that 10% of the variance in the dependent variable is due to between-group differences, and the remaining 90% is due to within-group differences.

That being said, the statement you cite is still broadly accurate because, as the ICC increases, the correlation between observations in the same group will tend to go up. At the limit case, an ICC of 1 means that 100% of the variance in the DV is due to between group differences and 0% is due to within-group differences. That in turn implies that all observations that share a group will all have exactly the same value for the DV. Thus the correlation between observations within a given group is perfect. At the other end, an ICC of zero means that 0% of the variance is due to between group differences, which in turn implies that the average value of the DV for observations within a particular group is identical, no matter what group you choose. So the ICC does have implications for within- and between-group correlations

But fundamentally, the ICC tells you about the proportion of variance at different analytic levels. In my view, any definition that doesn't emphasize that risks confusing people.