Differences

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--- c:ps1:2025:t-test_note:output01 [2025/12/02 23:26] – created hkimscil
+++ c:ps1:2025:t-test_note:output01 [2025/12/02 23:51] (current) – hkimscil
@@ Line 47: / Line 47: @@
 > t.cal
 [1] -3
+</code>
+<code>
+> #############
+> ss <- function(x) {
++   sum((x-mean(x))^2)
++ }
+> n.a <- n.b <- 40
+> df.b <- n.b - 1
+> df.a <- n.a - 1
+> naver <- rnorm2(n.a, 7.2, 1)
+> mylab <- rnorm2(n.b, 7.9, 1)
+> ss(naver)
+[1] 39
+> pv <- (ss(naver)+ss(mylab))/(df.a + df.b)
+> pv
+[1] 1
+> se <- sqrt(pv/n.a + pv/n.b)
+> se
+[1] 0.2236068
+> t.cal <- (mean(naver)-mean(mylab))/se
+> t.cal
+[1] -3.130495
+> pt(t.cal, df.a+df.b)*2
+[1] 0.002455973
+> t.test(naver, mylab)
+	Welch Two Sample t-test
+data:  naver and mylab
+t = -3.1305, df = 78, p-value = 0.002456
+alternative hypothesis: true difference in means is not equal to 0
+percent confidence interval:
+ -1.1451669 -0.2548331
+sample estimates:
+mean of x mean of y
+.2       7.9
+</code>
+<code>
+>
+> #
+> s.n <- 100
+> s.hi <- 5200
+> s.lo <- 4980
+> s.sd <- 500
+>
+> set.seed(101)
+> s.hi <- round(rnorm(s.n, s.hi, s.sd))
+> s.lo <- round(rnorm(s.n, s.lo, s.sd))
+>
+> s.hi
+  [1] 5037 5476 4863 5307 5355 5787 5509 5144 5659 5088 5463 4803
+ [13] 5914 4467 5082 5103 4775 5229 4791 4175 5118 5554 5066 4468
+ [25] 5572 4495 5434 5140 5434 5449 5647 5340 5704 4163 5795 4838
+ [37] 5284 5660 4364 5424 5441 5579 4040 4970 4647 5401 5484 4847
+ [49] 5055 4458 4625 5063 5489 4502 5575 4674 5283 5765 5787 4986
+ [61] 5070 4494 4879 5256 5411 5393 4856 5274 5171 5163 5955 6010
+ [73] 5777 5161 4291 4681 5351 4561 5269 5175 6126 5756 4944 4928
+ [85] 4336 5435 5203 5874 5562 5976 5863 5183 5019 4840 5341 4805
+ [97] 4978 5882 5449 4793
+> s.lo
+  [1] 5114 4684 6047 5566 5353 4865 5024 3888 4747 5823 4696 4957
+ [13] 4902 5781 5364 4594 4665 4565 4684 5471 4649 4594 3971 4713
+ [25] 5197 4594 4603 4830 5812 4358 4588 5102 4908 4176 5456 4070
+ [37] 5872 5924 5725 4790 4525 4811 4274 5089 5315 4836 5215 4745
+ [49] 4860 4756 4671 5106 4603 5346 4779 3568 5211 6046 4845 5104
+ [61] 4999 5177 4228 4187 4516 5368 4590 4341 4979 4055 5206 4764
+ [73] 5337 5460 5171 5589 4971 4961 5602 4502 5438 4510 5036 5257
+ [85] 5246 4543 4887 4873 4878 5840 5081 5236 5706 5162 4542 4973
+ [97] 4618 5965 4712 4967
+>
+> df.a <- s.n - 1
+> df.b <- s.n - 1
+>
+> m.a <- mean(s.hi)
+> m.b <- mean(s.lo)
+> diff <- m.a - m.b
+> pv <- (ss(s.hi)+ss(s.lo))/(df.a + df.b)
+> pv
+[1] 235102.1
+> se <- sqrt(pv/s.n + pv/s.n)
+> se
+[1] 68.57143
+> diff
+[1] 222.38
+> t.cal <- diff / se
+> t.cal
+[1] 3.243042
+> pt(t.cal, df.a+df.b, lower.tail = F)*2
+[1] 0.001387925
+>
+> t.test(s.hi, s.lo, var.equal=T)
+	Two Sample t-test
+data:  s.hi and s.lo
+t = 3.243, df = 198, p-value = 0.001388
+alternative hypothesis: true difference in means is not equal to 0
+percent confidence interval:
+.15594 357.60406
+sample estimates:
+mean of x mean of y
+.38   4959.00
 </code>