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--- r:general_statistics [2017/11/05 23:25] – [e.g.,] hkimscil
+++ r:general_statistics [2019/10/10 22:56] (current) – [Forming a Confidence Interval for a Mean] hkimscil
@@ Line 497: / Line 497: @@
 ====== Forming a Confidence Interval for a Mean ======
-<code>> s <- sd(x)
+<code>
+> set.seed(1024)
+> x <- rnorm(50, mean=100, sd=15)
+> s <- sd(x)
 > m <- mean(x)
 > n <- length(x)
@@ Line 509: / Line 512: @@
 > SE
 [1] 2.458358
-> E <- qt(.975, df=n-1)*SE
+## qt fun: qt(prob, df) zscore 2점에 해당하는 점수는?
+> qtv <- qt(.975, df=n-1)
+> qtv
+[1]
+## qtv는 2에 해당하는 95퍼센트 CL
+## 이 때의 CI는
+> E <- qtv*SE
 > E
 [1] 4.940254
@@ Line 517: / Line 526: @@
 </code>
-<code>> t.test(x)
+<code>
+> t.test(x, mu=98)
 	One Sample t-test
 data:  x
-t = 39.052, df = 49, p-value < 2.2e-16
+t = 0.37089, df = 49, p-value = 0.7123
-alternative hypothesis: true mean is not equal to 0
+alternative hypothesis: true mean is not equal to 98
 percent confidence interval:
-.0636 100.9441
+.32303 103.34143
 sample estimates:
 mean of x
-.00386
+.83223
+> t.test(x, mu=100)
+	One Sample t-test
+data:  x
+t = -0.52043, df = 49, p-value = 0.6051
+alternative hypothesis: true mean is not equal to 100
+percent confidence interval:
+.32303 103.34143
+sample estimates:
+mean of x
+.83223
+> t.test(x, mu=95)
+	One Sample t-test
+data:  x
+t = 1.7079, df = 49, p-value = 0.09399
+alternative hypothesis: true mean is not equal to 95
+percent confidence interval:
+.32303 103.34143
+sample estimates:
+mean of x
+.83223
+>
 </code>
@@ Line 707: / Line 745: @@
 > 20   3.4     2 10
 </code>
-<code>sleep_wide <- data.frame(
+<code>> sleep_wide <- data.frame(
     ID=1:10,
     group1=sleep$extra[1:10],
@@ Line 728: / Line 766: @@
 <code>
- Welch t-test
+# Welch t-test
 t.test(extra ~ group, sleep)
 >
 > 	Welch Two Sample t-test
@@ Line 743: / Line 780: @@
 >            0.75            2.33
- Same for wide data (two separate vectors)
+# Same for wide data (two separate vectors)
- t.test(sleep_wide$group1, sleep_wide$group2)
+> t.test(sleep_wide$group1, sleep_wide$group2)
 </code>
@@ Line 750: / Line 787: @@
 <code>
- Student t-test
+# Student t-test
-t.test(extra ~ group, sleep, var.equal=TRUE)
+> t.test(extra ~ group, sleep, var.equal=TRUE)
+>
- 	Two Sample t-test
+> 	Two Sample t-test
+>
- data:  extra by group
+> data:  extra by group
- t = -1.8608, df = 18, p-value = 0.07919
+> t = -1.8608, df = 18, p-value = 0.07919
- alternative hypothesis: true difference in means is not equal to 0
+> alternative hypothesis: true difference in means is not equal to 0
-percent confidence interval:
+> 95 percent confidence interval:
-  -3.363874  0.203874
+>  -3.363874  0.203874
- sample estimates:
+> sample estimates:
- mean in group 1 mean in group 2
+> mean in group 1 mean in group 2
-.75            2.33
+>             0.75            2.33
 </code>
-<code> Same for wide data (two separate vectors)
+<code>#  Same for wide data (two separate vectors)
- t.test(sleep_wide$group1, sleep_wide$group2, var.equal=TRUE)
+> t.test(sleep_wide$group1, sleep_wide$group2, var.equal=TRUE)
 </code>
@@ Line 774: / Line 811: @@
 <code>
- Sort by group then ID
+# Sort by group then ID
-sleep <- sleep[order(sleep$group, sleep$ID), ]
+> sleep <- sleep[order(sleep$group, sleep$ID), ]
- Paired t-test
+# Paired t-test
-t.test(extra ~ group, sleep, paired=TRUE)
+> t.test(extra ~ group, sleep, paired=TRUE)
  	Paired t-test
@@ Line 792: / Line 829: @@
 </code>
-<code> Same for wide data (two separate vectors)
+<code># Same for wide data (two separate vectors)
- t.test(sleep.wide$group1, sleep.wide$group2, paired=TRUE)
+> t.test(sleep.wide$group1, sleep.wide$group2, paired=TRUE)
+	Paired t-test
+data:  sleep_wide$group1 and sleep_wide$group2
+t = -4.0621, df = 9, p-value = 0.002833
+alternative hypothesis: true difference in means is not equal to 0
+percent confidence interval:
+ -2.4598858 -0.7001142
+sample estimates:
+mean of the differences
+                  -1.58
 </code>
 The paired t-test is equivalent to testing whether difference between each pair of observations has a population mean of 0. (See below for comparing a single group to a population mean.)
-<code>t.test(sleep.wide$group1 - sleep.wide$group2, mu=0, var.equal=TRUE)
+<code>> t.test(sleep_wide$group1 - sleep_wide$group2, mu=0, var.equal=TRUE)
-> Error in t.test(sleep.wide$group1 - sleep.wide$group2, mu = 0, var.equal = TRUE): object 'sleep.wide' not found
+	One Sample t-test
+data:  sleep_wide$group1 - sleep_wide$group2
+t = -4.0621, df = 9, p-value = 0.002833
+alternative hypothesis: true mean is not equal to 0
+percent confidence interval:
+ -2.4598858 -0.7001142
+sample estimates:
+mean of x
+    -1.58
 </code>