effect of measurement error.R

n=10000
beta=.4
#no effect

p=c()
for(i in 1:n){
s=rnorm(30,0,1)
sm=s+rnorm(30,0,1) #with measurement error
x=rnorm(30,0,1)
p=c(p,summary(lm(sm~x))$coefficients[2,4])
}
r1=length(c(p[p<.025],p[p>.975])) 

n=10000
beta=.4
#no effect

p=c()
for(i in 1:n){
s=rnorm(30,0,1)
sm=s+rnorm(30,0,1) #with measurement error
x=rnorm(30,0,1)
p=c(p,summary(lm(sm~x))$coefficients[2,4])
}
r1=length(c(p[p<.05])) 


p=c()
for(i in 1:n){
  s=rnorm(30,0,1)
  sm=s #+rnorm(30,0,1) #without measurement error
  x=rnorm(30,0,1)
  p=c(p,summary(lm(sm~x))$coefficients[2,4])
}
r2=length(c(p[p<.05]))


#some effect

p=c()
for(i in 1:n){
  s=rnorm(30,0,1)
  x=rnorm(30,0,1)
  sm=s+beta*x+rnorm(30,0,1) #with measurement error
  p=c(p,summary(lm(sm~x))$coefficients[2,4])
}
r3=length(c(p[p<.05]))


p=c()
for(i in 1:n){
  s=rnorm(30,0,1)
  x=rnorm(30,0,1)
  sm=s+beta*x #+rnorm(30,0,1) #without measurement error
  p=c(p,summary(lm(sm~x))$coefficients[2,4])
}
r4=length(c(p[p<.05]))

#proportion of sig results that are true when no measurement error:
r4/(r2+r4)

#proportion of sig results that are true when measurement error:
r3/(r1+r3)


p=c()
for(i in 1:n){
  s=rnorm(30,0,1)
  sm=s #+rnorm(30,0,1) #without measurement error
  x=rnorm(30,0,1)
  p=c(p,summary(lm(sm~x))$coefficients[2,4])
}
r2=length(c(p[p<.025],p[p>.975]))


#some effect

p=c()
for(i in 1:n){
  s=rnorm(30,0,1)
  x=rnorm(30,0,1)
  sm=s+beta*x+rnorm(30,0,1) #with measurement error
  p=c(p,summary(lm(sm~x))$coefficients[2,4])
}
r3=length(c(p[p<.025],p[p>.975]))


p=c()
for(i in 1:n){
  s=rnorm(30,0,1)
  x=rnorm(30,0,1)
  sm=s+beta*x #+rnorm(30,0,1) #without measurement error
  p=c(p,summary(lm(sm~x))$coefficients[2,4])
}
r4=length(c(p[p<.025],p[p>.975]))

#proportion of sig results that are true when no measurement error:
r4/(r2+r4)

#proportion of sig results that are true when measurement error:
r3/(r1+r3)