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### HW4 Q10
### Random intercepts model: sigma_b^2 = 7 (subject effect), sigma^2 = 34 (error).
### ICC = sigma_b^2 / (sigma_b^2 + sigma^2) = proportion of total variance between subjects.
### ! Rscript "/mnt/c/Users/kirch/OneDrive/Documents/dev/ut-11-hdi/docs/part2/hw4_q10.R"
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sigma2.b = 7
sigma2   = 34
total    = sigma2.b + sigma2
icc      = sigma2.b / total
cat("total variance sigma_b^2 + sigma^2 :", total, "\n")
cat("ICC = 7 / 41                       :", icc, "\n")
cat("within-subject share, for contrast :", sigma2 / total, "\n")
cat("ANSWER (2 dp)                      :", round(icc, 2), "\n")