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--- summary_of_hypothesis_testing:code01 [2025/11/30 15:29] – created hkimscil
+++ summary_of_hypothesis_testing:code01 [2025/11/30 22:51] (current) – hkimscil
@@ Line 17: / Line 17: @@
 sd.p2 <- sd(p2)
-n.s <- 36
+n.s <- 25
 se.z1 <- c(sqrt(var(p1)/n.s))
 se.z2 <- c(sqrt(var(p2)/n.s))
@@ Line 38: / Line 38: @@
 plot(x.p1, y.p1, type = "l",
      lwd=3,
-     main = "Sample means from p1 and p2 (imaginary)",
+     main = paste0("sample (n = ",n.s, ") means from p1 and p2 (unknown)"),
      xlab = "Value", ylab = "Density")
 lines(x.p2, y.p2, lty=2, lwd=3)
@@ Line 59: / Line 59: @@
 diff <- m.treated.s-mean(p1)
 diff/se.z1
-zscore <- diff/se.z1
+zscore <- abs(diff/se.z1)
 pnorm(zscore, lower.tail = F)*2
 tscore <- zscore
-pt(tscore, df=length(treated.s)-1, lower.tail = F)*2
+pt(tscore, df=n.s-1, lower.tail = F)*2
 # usual way - using sample's variance
@@ Line 111: / Line 111: @@
 m.p2
+x.p.est <- seq(m.treated.s-5*se.s,
+               m.treated.s+5*se.z1,
+               length.out = 500)
+y.p.est <- dnorm(x.p.est, m.treated.s, se.s)
+plot(x.p.est, y.p.est, type = "l",
+     lwd=3,
+     main = paste0("mu (", m.p2, ") estimation \n", "from a sample ", "mean=", round(m.treated.s,2)),
+     xlab = paste0("Value"), ylab = "Density")
+se1 <- c(m.treated.s-se.s, m.treated.s+se.s)
+se2 <- c(m.treated.s-2*se.s, m.treated.s+2*se.s)
+se3 <- c(m.treated.s-3*se.s, m.treated.s+3*se.s)
+abline(v=c(m.treated.s,se1,se2,se3),
+       col=c('black', 'darkorange', 'darkorange',
+             'darkgreen', 'darkgreen',
+             'darkblue', 'darkblue'),
+       lwd=2)
-pt(diff/se.s, df=n.s-1, lower.tail = F) * 2
+tscore <- abs(diff/se.s)
+pt(tscore, df=n.s-1, lower.tail = F) * 2
 t.test(treated.s, mu=m.p1, var.equal = T)
 </code>