r:general_statistics
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r:general_statistics [2017/11/06 07:55] – [e.g.,] hkimscil | r:general_statistics [2019/10/11 07:56] (current) – [Forming a Confidence Interval for a Mean] hkimscil | ||
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====== Forming a Confidence Interval for a Mean ====== | ====== Forming a Confidence Interval for a Mean ====== | ||
- | < | + | < |
+ | > set.seed(1024) | ||
+ | > x <- rnorm(50, mean=100, sd=15) | ||
+ | > s <- sd(x) | ||
> m <- mean(x) | > m <- mean(x) | ||
> n <- length(x) | > n <- length(x) | ||
Line 509: | Line 512: | ||
> SE | > SE | ||
[1] 2.458358 | [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 | > E | ||
[1] 4.940254 | [1] 4.940254 | ||
Line 517: | Line 526: | ||
</ | </ | ||
- | < | + | < |
+ | > t.test(x, mu=98) | ||
One Sample t-test | One Sample t-test | ||
data: x | data: x | ||
- | t = 39.052, df = 49, p-value | + | t = 0.37089, df = 49, p-value |
- | alternative hypothesis: true mean is not equal to 0 | + | alternative hypothesis: true mean is not equal to 98 |
95 percent confidence interval: | 95 percent confidence interval: | ||
- | | + | |
sample estimates: | sample estimates: | ||
mean of x | mean of x | ||
- | 96.00386 | + | 98.83223 |
+ | |||
+ | > 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 | ||
+ | 95 percent confidence interval: | ||
+ | 94.32303 103.34143 | ||
+ | sample estimates: | ||
+ | mean of x | ||
+ | | ||
+ | |||
+ | > 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 | ||
+ | 95 percent confidence interval: | ||
+ | 94.32303 103.34143 | ||
+ | sample estimates: | ||
+ | mean of x | ||
+ | | ||
+ | |||
+ | > | ||
</ | </ | ||
Line 707: | Line 745: | ||
> 20 | > 20 | ||
</ | </ | ||
- | < | + | <code>> sleep_wide <- data.frame( |
ID=1:10, | ID=1:10, | ||
group1=sleep$extra[1: | group1=sleep$extra[1: | ||
Line 728: | Line 766: | ||
< | < | ||
- | Welch t-test | + | # Welch t-test |
t.test(extra ~ group, sleep) | t.test(extra ~ group, sleep) | ||
- | |||
> | > | ||
> Welch Two Sample t-test | > Welch Two Sample t-test | ||
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> 0.75 2.33 | > 0.75 2.33 | ||
- | Same for wide data (two separate vectors) | + | # Same for wide data (two separate vectors) |
- | | + | > t.test(sleep_wide$group1, |
</ | </ | ||
Line 750: | Line 787: | ||
< | < | ||
- | Student t-test | + | # Student t-test |
- | t.test(extra ~ group, sleep, var.equal=TRUE) | + | > t.test(extra ~ group, sleep, var.equal=TRUE) |
- | + | > | |
- | Two Sample t-test | + | > Two Sample t-test |
- | + | > | |
- | | + | > data: extra by group |
- | t = -1.8608, df = 18, p-value = 0.07919 | + | > t = -1.8608, df = 18, p-value = 0.07919 |
- | | + | > alternative hypothesis: true difference in means is not equal to 0 |
- | 95 percent confidence interval: | + | > 95 percent confidence interval: |
- | -3.363874 | + | > |
- | | + | > sample estimates: |
- | mean in group 1 mean in group 2 | + | > mean in group 1 mean in group 2 |
- | 0.75 2.33 | + | > 0.75 2.33 |
</ | </ | ||
- | < | + | < |
- | | + | > t.test(sleep_wide$group1, |
</ | </ | ||
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< | < | ||
- | Sort by group then ID | + | # Sort by group then ID |
- | sleep <- sleep[order(sleep$group, | + | > sleep <- sleep[order(sleep$group, |
- | Paired t-test | + | # Paired t-test |
- | t.test(extra ~ group, sleep, paired=TRUE) | + | > t.test(extra ~ group, sleep, paired=TRUE) |
| | ||
Line 792: | Line 829: | ||
</ | </ | ||
- | < | + | < |
- | | + | > t.test(sleep.wide$group1, |
+ | |||
+ | Paired t-test | ||
+ | |||
+ | data: sleep_wide$group1 and sleep_wide$group2 | ||
+ | t = -4.0621, df = 9, p-value = 0.002833 | ||
+ | alternative hypothesis: true difference in means is not equal to 0 | ||
+ | 95 percent confidence interval: | ||
+ | | ||
+ | sample estimates: | ||
+ | mean of the differences | ||
+ | -1.58 | ||
</ | </ | ||
The paired t-test is equivalent to testing whether difference between each pair of observations has a population mean of 0. (See below for comparing a single group to a population mean.) | The paired t-test is equivalent to testing whether difference between each pair of observations has a population mean of 0. (See below for comparing a single group to a population mean.) | ||
- | < | + | <code>> t.test(sleep_wide$group1 - sleep_wide$group2, mu=0, var.equal=TRUE) |
- | > Error in t.test(sleep.wide$group1 - sleep.wide$group2, | + | |
+ | One Sample | ||
+ | |||
+ | data: sleep_wide$group1 - sleep_wide$group2 | ||
+ | t = -4.0621, df = 9, p-value = 0.002833 | ||
+ | alternative hypothesis: true mean is not equal to 0 | ||
+ | 95 percent confidence interval: | ||
+ | -2.4598858 -0.7001142 | ||
+ | sample estimates: | ||
+ | mean of x | ||
+ | -1.58 | ||
</ | </ | ||
r/general_statistics.txt · Last modified: 2019/10/11 07:56 by hkimscil