summary_of_hypothesis_testing:output01
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> rm(list=ls())
>
> rnorm2 <- function(n,mean,sd){
+ mean+sd*scale(rnorm(n))
+ }
>
> n.p <- 100000
> m.p <- 100
> sd.p <- 10
> p1 <- rnorm2(n.p, m.p, sd.p)
> m.p1 <- mean(p1)
> sd.p1 <- sd(p1)
>
> p2 <- rnorm2(n.p, m.p+4, sd.p)
> m.p2 <- mean(p2)
> sd.p2 <- sd(p2)
>
> n.s <- 36
> se.z1 <- c(sqrt(var(p1)/n.s))
> se.z2 <- c(sqrt(var(p2)/n.s))
> se.z1
[1] 1.666667
> se.z2
[1] 1.666667
>
> x.p1 <- seq(mean(p1)-5*se.z1,
+ mean(p2)+5*se.z1,
+ length.out = 500)
> x.p2 <- seq(mean(p2)-5*se.z1,
+ mean(p2)+5*se.z1,
+ length.out = 500)
>
> # Calculate the probability
> # density for a normal distribution
> y.p1 <- dnorm(x.p1, mean(p1), se.z1)
> y.p2 <- dnorm(x.p2, mean(p2), se.z2)
>
> # Plot the theoretical PDF
> plot(x.p1, y.p1, type = "l",
+ lwd=3,
+ main = "Sample means from p1 and p2 (imaginary)",
+ xlab = "Value", ylab = "Density")
> lines(x.p2, y.p2, lty=2, lwd=3)
>
>
> m.p1 <- mean(p1)
> se1 <- c(m.p1-se.z1, m.p1+se.z1)
> se2 <- c(m.p1-2*se.z1, m.p1+2*se.z1)
> se3 <- c(m.p1-3*se.z1, m.p1+3*se.z1)
> abline(v=c(m.p1,se1,se2,se3),
+ col=c('black', 'orange', 'orange',
+ 'green', 'green',
+ 'blue', 'blue'),
+ lwd=1)
>
> treated.s <- sample(p2, n.s)
> m.treated.s <- mean(treated.s)
> abline(v=m.treated.s, col='red', lwd=2)
>
> diff <- m.treated.s-mean(p1)
> diff/se.z1
[1] 1.451929
> zscore <- diff/se.z1
> pnorm(zscore, lower.tail = F)*2
[1] 0.1465213
> tscore <- zscore
> pt(tscore, df=length(treated.s)-1, lower.tail = F)*2
[1] 0.1554272
>
> # usual way - using sample's variance
> # instead of p1's variance to get
> # standard error value
> se.s <- sqrt(var(treated.s)/n.s)
> se.s
[1] 1.549221
> tscore <- diff/se.s
> tscore
[1] 1.562
>
>
> se1 <- c(m.p1-se.s, m.p1+se.s)
> se2 <- c(m.p1-2*se.s, m.p1+2*se.s)
> se3 <- c(m.p1-3*se.s, m.p1+3*se.s)
> abline(v=c(se1,se2,se3),
+ col=c('darkorange', 'darkorange',
+ 'darkgreen', 'darkgreen',
+ 'darkblue', 'darkblue'),
+ lwd=2)
>
>
>
>
> plot(x.p1, y.p1, type = "l",
+ lwd=3,
+ main = "Sample means from p1 and p2 (imaginary)",
+ xlab = "Value", ylab = "Density")
> lines(x.p2, y.p2, lty=2, lwd=3)
>
>
> m.p1 <- mean(p1)
> se1 <- c(m.p1-se.s, m.p1+se.s)
> se2 <- c(m.p1-2*se.s, m.p1+2*se.s)
> se3 <- c(m.p1-3*se.s, m.p1+3*se.s)
> abline(v=c(m.p1,se1,se2,se3),
+ col=c('black', 'darkorange', 'darkorange',
+ 'darkgreen', 'darkgreen',
+ 'darkblue', 'darkblue'),
+ lwd=2)
> abline(v=m.treated.s, col='red', lwd=3)
> se.s
[1] 1.549221
> se.z1
[1] 1.666667
>
> c(m.treated.s-2*se.s, m.treated.s+2*se.s)
[1] 99.32144 105.51832
> c <- qt(0.975, n.s-1)
> c
[1] 2.030108
> c(m.treated.s-c*se.s, m.treated.s+c*se.s)
[1] 99.2748 105.5650
> m.p2
[1] 104
>
>
> pt(diff/se.s, df=n.s-1, lower.tail = F) * 2
[1] 0.1272858
> t.test(treated.s, mu=m.p1, var.equal = T)
One Sample t-test
data: treated.s
t = 1.562, df = 35, p-value = 0.1273
alternative hypothesis: true mean is not equal to 100
95 percent confidence interval:
99.2748 105.5650
sample estimates:
mean of x
102.4199
>
summary_of_hypothesis_testing/output01.1764516700.txt.gz · Last modified: by hkimscil