## CI to percentage change in ICC

I'm running fixed effects models to estimate changes in intra class correlations.

I first run an unconditional model and then a second model including only level-2 factors. I'm interested in the reduction of the icc when adding only level-2 factors.

I'm interested in expressing the decrease in the intra class correlation as percentage. However, I don't know how to obtain confidence intervals when doing this.

For example, icc in the unconditional model is 0.3 (95% CI 0.29-0.31). icc in the second model with only one level-2 factor added is 0.25 (95% CI 0.24-0.26). The reduction in icc expect in percentage would be 16%. However, I don't know how I should calculate confidence intervals for this percentage.

I'm doing a longitudinal study and wants to be able to show if any change in the percentage over time is statistically significantly or just fluctuation.

To clarify. Let say I'm studying students grades and the students are nested in classes. I also have information on each class teachers number of years working as a teacher. I have information on grades for 4 birth cohorts (1980-1984).

The icc for the first birth cohort is 0.25 (CI 0.24-0.26) meaning that 25% of the variation in grades can be explained by the class the student belongs to.

The icc in grades for the four cohorts:
1980 0.25 (CI 0.24-0.26)
1981 0.26 (CI 0.25-0.27)
1982 0.29 (CI 0.28-0.31)
1983 0.29 (CI 0.28-0.31)

Adding information on each class teachers teacher experience gives the following ICC:
1980 0.20 (CI 0.19-0.21)
1981 0.20 (CI 0.19-0.21)
1982 0.20 (CI 0.19-0.21)
1983 0.16 (CI 0.15-0.17)

Thus, the reduction in icc after adding one level-2 factor is then
1980 20%
1981 23%
1982 31%
1983 45%

I express this as "for the 1980 cohort 20% of the classmates similarly in grades can be explained by their teacher teaching experience.

Does anyone know how I could obtain confidence intervals to these percentages?

Thankful for all input.