gistfile1.txt

# effect on total variance
library(dplyr)

N=10000
prob <-  .25

e_var = 1
u_var = .25*e_var  # see http://www.wolframalpha.com/input/?i=.1%3Db%2F%28a%2Bb%29
icc = u_var/(u_var+e_var)
icc

e_sd = sqrt(e_var)
u_sd = sqrt(u_var)

df <- data.frame(
  e = rnorm(N, sd=e_sd),
  u = rnorm(N, sd=u_sd)
)

dat <- df %>% mutate(
  ue= e + u,
  itt = u>qnorm(prob, sd=sd(.$u)),
  uerct = ifelse(itt, ue, NA)
)

var(dat$uerct, na.rm=T)/var(dat$ue)






# And the effect on tx estimate of underestimating true variance in 
# one cell

library(reshape2)

rct <- data.frame(
  a=rnorm(200000, mean=0, sd=1),
  b=rnorm(200000, mean=.5, sd=1)
) %>% melt() 

# t value halves when sd(b) is set to 2
summary(lm(value~factor(variable), data=rct))

rct <- data.frame(
  a=rnorm(200000, mean=0, sd=1),
  b=rnorm(200000, mean=.5, sd=2)
) %>% melt() 

# F value halves when sd(b) is set to 2
summary(lm(value~factor(variable), data=rct))