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--- standard_deviation [2025/03/24 07:57] – hkimscil
+++ standard_deviation [2025/03/24 08:10] (current) – hkimscil
@@ Line 27: / Line 27: @@
 <code>
-> # qnorm((1-0.68)/2)
+> one.sd <- .68
-> qnorm((0.16)
+> two.sd <- .95
+> thr.sd <- .99
+> 1-one.sd
+[1] 0.32
+> (1-one.sd)/2
+[1] 0.16
+> qnorm(0.16)
 [1] -0.9944579
-> # qnorm((1-0.68)/2+0.68)
+> qnorm(1-0.16)
-> qnorm(0.84)
 [1] 0.9944579
 >
->
+> 1-two.sd
+[1] 0.05
+> (1-two.sd)/2
+[1] 0.025
+> qnorm(0.025)
+[1] -1.959964
 > qnorm(0.975)
 [1] 1.959964
-> qnorm(0.025)
-[1] -1.959964
 >
-> 0.01/2
+> 1-thr.sd
+[1] 0.01
+> (1-thr.sd)/2
 [1] 0.005
 > qnorm(0.005)
@@ Line 49: / Line 59: @@
 </code>
 위의 값은 정확은 하지만 개념적으로 표준편차의 특징을 이해하는데 방해가 되는 면이 있다. 따라서 표준편차 1, 2, 3 만큼은 각각 68, 95, 99%로 기억해두는 것이 편리하다.
-<code>
-> # .95 부분을 찾기 위해서는
-> # qnorm을 사용해 본다
-> # qnorm(percent, mean=0, sd=1)
-> perc68h <- .68 + (.32*.5)
-> perc68l <- .32*.5
-> perc68h
-[1] 0.84
-> perc68l
-[1] 0.16
->
-> ahi1 <- qnorm(perc68h, mean=0, sd=1)
-> alo1 <- qnorm(perc68l)
-> ahi1
-[1] 0.9944579
-> alo1
-[1] -0.9944579
-> pnorm(ahi1)-pnorm(alo1)
-[1] 0.68
->
-> ahi2 <- qnorm(.975)
-> alo2 <- qnorm(.025)
->
-> ahi2
-[1] 1.959964
-> alo2
-[1] -1.959964
-> pnorm(ahi2)-pnorm(alo2)
-[1] 0.95
->
-> (1-1/200)
-[1] 0.995
-> ahi3 <- qnorm(.995)
-> alo3 <- qnorm(.005)
-> pnorm(ahi3)-pnorm(alo3)
-[1] 0.99
->
-</code>