rm(list = ls())
cnt=c(6,16,2,4,2,4,6,6)
a=c(1,1,1,1,2,2,2,2)
A=3-2*a
b=c(1,1,2,2,1,1,2,2)
B=3-2*b
c=c(1,2,1,2,1,2,1,2)
AB=A*B
C=3-2*c
y=log(cnt)


ts <- lm(y ~ A+B+AB+C,weights = cnt)
tsp=summary(ts)
tsp
anova(ts)

# new standard errors
coef(tsp)[,2]/tsp$sigma
# new z scores
coef(tsp)[,3]*tsp$sigma