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--- summary_of_hypothesis_testing [2025/11/30 15:44] – [output] hkimscil
+++ summary_of_hypothesis_testing [2025/11/30 23:00] (current) – hkimscil
@@ Line 1: / Line 1: @@
 ====== Hypothesis testing ======
 see also [[:types of error]]
 ====== Basic ======
 see first [[:sampling distribution and z-test]]
-====== Hypothesis testing, exp ======
+====== Hypothesis testing, 가설검증에 실패한 경우 (n=25) ======
-...
+샘플은 p2에서 (mu.p2 = 104) probability sampling을 한 샘플. 그러나, 샘플의 평균이 101.05가 나와서 가설 검증에 실패. 이런 경우가 type 2 error를 범한 경우. 효과가 4만큼 나타나는 모집단에서 샘플이 나왔음에도 불구하고 평균이 100인 집단의 샘플로 추정되어 영가설을 부정하지 못하고, 연구가설을 채택하지 못함.
 <tabbed>
   * :summary of hypothesis testing:code01
@@ Line 11: / Line 12: @@
 </tabbed>
+====== Hypothesis testing, 가설검증에 성공한 경우 (n=25) ======
-====== se value and sample size ======
+<tabbed>
+  * :summary of hypothesis testing:code03
-<code>
+  * *:summary of hypothesis testing:output03
-n.ajstu <- 100000
+</tabbed>
-mean.ajstu <- 100
-sd.ajstu <- 10
-set.seed(1024)
-ajstu <- rnorm2(n.ajstu, mean=mean.ajstu, sd=sd.ajstu)
-mean(ajstu)
-sd(ajstu)
-var(ajstu)
-iter <- 10000 # # of sampling
-n.4 <- 4
-means4 <- rep (NA, iter)
-for(i in 1:iter){
-  means4[i] = mean(sample(ajstu, n.4))
-}
-n.25 <- 25
-means25 <- rep (NA, iter)
-for(i in 1:iter){
-  means25[i] = mean(sample(ajstu, n.25))
-}
-n.100 <- 100
-means100 <- rep (NA, iter)
-for(i in 1:iter){
-  means100[i] = mean(sample(ajstu, n.100))
-}
-n.400 <- 400
-means400 <- rep (NA, iter)
-for(i in 1:iter){
-  means400[i] = mean(sample(ajstu, n.400))
-}
-n.900 <- 900
-means900 <- rep (NA, iter)
-for(i in 1:iter){
-  means900[i] = mean(sample(ajstu, n.900))
-}
-n.1600 <- 1600
-means1600 <- rep (NA, iter)
-for(i in 1:iter){
-  means1600[i] = mean(sample(ajstu, n.1600))
-}
-n.2500 <- 2500
-means2500 <- rep (NA, iter)
-for(i in 1:iter){
-  means2500[i] = mean(sample(ajstu, n.2500))
-}
-h4 <- hist(means4)
-h25 <- hist(means25)
-h100 <- hist(means100)
-h400 <- hist(means400)
-h900 <- hist(means900)
-h1600 <- hist(means1600)
-h2500 <- hist(means2500)
-plot(h4, ylim=c(0,3000), col="red")
-plot(h25, add = T, col="blue")
-plot(h100, add = T, col="green")
-plot(h400, add = T, col="grey")
-plot(h900, add = T, col="yellow")
-m4 <- mean(means4)
-m25 <- mean(means25)
-m100 <- mean(means100)
-m400 <- mean(means400)
-m900 <- mean(means900)
-m1600 <- mean(means1600)
-m2500 <- mean(means2500)
-s4 <- sd(means4)
-s25 <- sd(means25)
-s100 <- sd(means100)
-s400 <- sd(means400)
-s900 <- sd(means900)
-s1600 <- sd(means1600)
-s2500 <- sd(means2500)
-sss <- c(4,25,100,400,900,1600,2500) # sss sample sizes
-means <- c(m4, m25, m100, m400, m900, m1600, m2500)
-sds <- c(s4, s25, s100, s400, s900, s1600, s2500)
-temp <- data.frame(sss,
-                   means,
-                   sds)
-temp
-ses <- rep (NA, length(sss)) # std error memory
-for(i in 1:length(sss)){
-  ses[i] = sqrt(var(ajstu)/sss[i])  # std errors by theorem
-}
-data.frame(ses)
-se.1 <- ses
-se.2 <- 2 * ses
-lower.s2 <- mean(ajstu)-se.2
-upper.s2 <- mean(ajstu)+se.2
-data.frame(cbind(sss, ses, lower.s2, upper.s2))
-# 12/2 lecture
-# note that we draw the statistical calculation
-# by "diff/se" = "diff/random_error"
-n <- 80
-mean.sample <- 103
-sample <- rnorm2(n, mean.sample, sd.ajstu)
-mean(sample)
-sd(sample)
-diff <- mean.sample - mean.ajstu # this is actual difference
-se <- sd.ajstu / sqrt(n) # this is random error
-t.cal <- diff/se
-t.cal
-qnorm(0.025, lower.tail = F)
-qnorm(0.01/2, lower.tail = F)
-qt(0.05/2, n-1, lower.tail=F)
-t.test(sample, mu=mean.ajstu)
-# or we obtain the exact p value
-p.value <- pt(t.cal, n-1, lower.tail = F)
-p.value*2
+====== se value and sample size ======
+<tabbed>
+  * :summary of hypothesis testing:code2
+  * *:summary of hypothesis testing:output2
+</tabbed>
-</code>