Differences

This shows you the differences between two versions of the page.

--- t-test_summary [2026/04/12 23:19] – [ro.hypothesis.testing] hkimscil
+++ t-test_summary [2026/04/16 01:27] (current) – hkimscil
@@ Line 120: / Line 120: @@
 # 새로운 UI로 게임을 하도록 한 후
-# UI점수를 10명에게 구했다고 가정하고
+# UI점수를 sz 명에게 구했다고 가정하고
 # 새로운 UI점수가 기존의 p1 paramter와
 # 다른지 테스트 해보라
@@ Line 443: / Line 443: @@
 >
 </code>
-{{pasted:20260412-231954.png}}
+{{pasted:20260412-232126.png}}
 <code>
@@ Line 517: / Line 517: @@
 > # 하면 샘플의 평균과 p1의 평균은 다르다고 판단될 것이다.
 > # 아래는 그럼에도 불구하고 실패하는 경우이다.
-> set.seed(111)
+> set.seed(110)
 > smp <- sample(p2, sz, replace=T)
 > m.smp <- mean(smp)
 > m.smp
-[1] 104.4742
+[1] 104.5958
 > diff <- m.smp - mean(p1)
 > se.z <- sqrt(var(p1)/sz)
@@ Line 527: / Line 527: @@
 > prob1 <- pnorm(abs(z.cal1), lower.tail = F)*2
 > print(c(z.cal1, sz, prob1))
-[1]  1.4148817 10.0000000  0.1571032
+[1]  2.906626913 40.000000000  0.003653487
 > z.test(smp, mean(p1), sd(p1))
- z value: 1.41488
+ z value: 2.90663
- p value: 0.1571032
+ p value: 0.00365349
- diff:    104.4742 - 100 = 4.474249
+ diff:    104.5958 - 100 = 4.595781
- se:      3.162278
+ se:      1.581139
-% CI:  93.80205 106.198>
+% CI:  96.90102 103.099>
 > curve(dnorm(x), from = -4, to = z.p2+4,
-+       main = "normalized distribution of sample means \n testing with a sample from p2 (failed)",
++       main = "normalized distribution of sample means
++       testing with a sample from p2 (failed)",
 +       ylab = "Density", xlab = "z-value", col = "black", lwd = 2)
 > abline(v=0, col="black", lwd=2)
@@ Line 545: / Line 546: @@
 +                    "\n", "pnorm(-z.cal1)*2 =", round(prob1,4)),
 +      pos=4, col='red')
+>
 >
 </code>
-{{pasted:20260412-063636.png}}
+{{pasted:20260412-233253.png}}
 <code>
 > # 같은 방법으로 했는데 성공한 경우
 > set.seed(211)
@@ Line 555: / Line 557: @@
 > m.smp <- mean(smp)
 > m.smp
-[1] 110.1154
+[1] 107.6795
 > diff <- m.smp - mean(p1)
 > se.z <- sqrt(var(p1)/sz)
@@ Line 561: / Line 563: @@
 > prob2 <- pnorm(abs(z.cal2), lower.tail = F)*2
 > print(c(z.cal2, sz, prob2))
-[1]  3.198763975 10.000000000  0.001380181
+[1] 4.856940e+00 4.000000e+01 1.192138e-06
 > z.test(smp, mean(p1), sd(p1))
- z value: 3.19876
+ z value: 4.85694
- p value: 0.00138018
+ p value: 1.19e-06
- diff:    110.1154 - 100 = 10.11538
+ diff:    107.6795 - 100 = 7.679496
- se:      3.162278
+ se:      1.581139
-% CI:  93.80205 106.198>
+% CI:  96.90102 103.099>
-> z.p2 <- (mean(p2)-mean(p1))/se2
+> z.p2 <- (mean(p2)-mean(p1))/se.z
 > z.p2
-[1] 1.897367
+         [,1]
+[1,] 3.794733
 > curve(dnorm(x), from = -5, to = z.p2+5,
 +       main = "normalized distribution of sample means \n testing with a sample from p2 (succeeded)",
@@ Line 577: / Line 580: @@
 > z.cal1
          [,1]
-[1,] 1.414882
+[1,] 2.906627
 > z.cal2
-         [,1]
+        [,1]
-[1,] 3.198764
+[1,] 4.85694
 > two <- qnorm(.05/2)
 > two
@@ Line 593: / Line 596: @@
 +      label=paste(round(-z.cal2,4)),
 +      col="darkgreen", cex=1, pos=2)
+>
 >
 </code>
-{{pasted:20260412-063652.png}}
+{{pasted:20260412-233208.png}}
 <code>
 > # type i and type ii error
-> z.p2 <- (mean(p2)-mean(p1))/se2
+> two <- qnorm(.05/2)
-> z.p2
+> two
-[1] 1.897367
+[1] -1.959964
+>
 > curve(dnorm(x), from = -4.7, to = z.p2+4,
 +       main = "Distribution Curve",
 +       ylab = "Density", xlab = "z-value", col = "black", lwd = 2)
-> curve(dnorm(x-(z.p2)), from = z.p2-3, to = z.p2+3, add = T,
+> curve(dnorm(x-c(z.p2)), from = z.p2-3, to = z.p2+3, add = T,
 +       main = "Distribution Curve",
 +       ylab = "Density", xlab = "z-value", col = "blue", lwd = 2, lty=2)
 > abline(v=0, col='black', lwd=2)
-> z.cal1
-         [,1]
-[1,] 1.414882
-> z.cal2
-         [,1]
-[1,] 3.198764
-> two <- qnorm(.05/2)
-> two
-[1] -1.959964
 > abline(v=c(two, -two), col='black', lwd=2)
 > abline(v=c(-z.cal1, z.cal1), col='red', lwd=2)
@@ Line 636: / Line 632: @@
 +      label=paste(round(-z.cal2,4)),
 +      col="darkgreen", cex=1, pos=2)
+>
 >
 </code>
-{{pasted:20260412-063709.png}}
+{{pasted:20260412-233411.png}}
 <code>
->
 > ############################
 > # one sample t-test
@@ Line 686: / Line 682: @@
 > print(c(m.smp+lo2*se.z, m.smp+hi2*se.z))
 [1] 102.5239 110.0970
-> cat("t =", t.cal, ", df =", round(df.smp,0), ", p-value =", prob,
+> cat(" t =", t.cal, ", df =", round(df.smp,0), ", p-value =", prob,
 + "\n", "95% confidence interval =", m.smp+lo2*se.z, m.smp+hi2*se.z)
-t = 3.488087 , df = 19 , p-value = 0.002460977
+ t = 3.488087 , df = 19 , p-value = 0.002460977
 % confidence interval = 102.5239 110.097> t.test(smp, mu=mean(p1))
@@ Line 701: / Line 697: @@
 mean of x
 .3104
 >
 > #################################
@@ Line 779: / Line 774: @@
 +      pos=4, col='red')
 >
 </code>
 {{pasted:20260412-063739.png}}
@@ Line 800: / Line 796: @@
 > t.cal
 [1] -3.070212
-> # t.cal=diff/se
-> t.cal * se.s
-[1] -8.871414
-> diff
-[1] -8.871414
-> diff+lo2*se.s
-[1] -14.68117
-> diff+hi2*se.s
-[1] -3.061661
-> (t.cal+lo2)*se.s
-[1] -14.68117
-> (t.cal+hi2)*se.s
-[1] -3.061661
 >
 > ######################
@@ Line 880: / Line 863: @@
 +      col="red", pos=4)
 > text(x=t.cal, y=.2, label=c(round(t.cal,3)), col="red", pos=2)
+>
+> cat(t.cal, sz-1, prob)
+-3.88213 39 0.0003888961
+>
 </code>
 {{pasted:20260412-063758.png}}