r:general_statistics
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r:general_statistics [2017/11/06 07:48] – [Testing Categorical Variables for Independence] 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 685: | Line 723: | ||
===== e.g., ===== | ===== e.g., ===== | ||
< | < | ||
- | #> extra group ID | + | > extra group ID |
- | #> 1 0.7 | + | > 1 0.7 |
- | #> 2 | + | > 2 |
- | #> 3 | + | > 3 |
- | #> 4 | + | > 4 |
- | #> 5 | + | > 5 |
- | #> 6 3.4 | + | > 6 3.4 |
- | #> 7 3.7 | + | > 7 3.7 |
- | #> 8 0.8 | + | > 8 0.8 |
- | #> 9 0.0 | + | > 9 0.0 |
- | #> 10 | + | > 10 |
- | #> 11 | + | > 11 |
- | #> 12 | + | > 12 |
- | #> 13 | + | > 13 |
- | #> 14 | + | > 14 |
- | #> 15 -0.1 | + | > 15 -0.1 |
- | #> 16 | + | > 16 |
- | #> 17 | + | > 17 |
- | #> 18 | + | > 18 |
- | #> 19 | + | > 19 |
- | #> 20 | + | > 20 |
</ | </ | ||
- | < | + | <code>> sleep_wide <- data.frame( |
ID=1:10, | ID=1:10, | ||
group1=sleep$extra[1: | group1=sleep$extra[1: | ||
Line 713: | Line 751: | ||
) | ) | ||
sleep_wide | sleep_wide | ||
- | #> ID group1 group2 | + | > ID group1 group2 |
- | #> 1 | + | > 1 |
- | #> 2 | + | > 2 |
- | #> 3 | + | > 3 |
- | #> 4 | + | > 4 |
- | #> 5 | + | > 5 |
- | #> 6 | + | > 6 |
- | #> 7 | + | > 7 |
- | #> 8 | + | > 8 |
- | #> 9 | + | > 9 |
- | #> 10 10 2.0 3.4 | + | > 10 10 2.0 3.4 |
</ | </ | ||
Ignore the ID variable for a convenience. | Ignore the ID variable for a convenience. | ||
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# 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 | + | > |
- | #> | + | > data: extra by group |
- | #> data: extra by group | + | > t = -1.8608, df = 17.776, p-value = 0.07939 |
- | #> t = -1.8608, df = 17.776, p-value = 0.07939 | + | > alternative hypothesis: true difference in means is not equal to 0 |
- | #> alternative hypothesis: true difference in means is not equal to 0 | + | > 95 percent confidence interval: |
- | #> 95 percent confidence interval: | + | > -3.3654832 |
- | #> -3.3654832 | + | > sample estimates: |
- | #> 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 | + | |
# Same for wide data (two separate vectors) | # Same for wide data (two separate vectors) | ||
- | # t.test(sleep_wide$group1, | + | > t.test(sleep_wide$group1, |
</ | </ | ||
Line 751: | Line 788: | ||
< | < | ||
# 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$group1, | + | > t.test(sleep_wide$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 793: | Line 830: | ||
< | < | ||
- | # t.test(sleep.wide$group1, | + | > t.test(sleep.wide$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 | ||
</ | </ | ||
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< | < | ||
t.test(sleep$extra, | t.test(sleep$extra, | ||
- | #> | + | > |
- | #> One Sample t-test | + | > One Sample t-test |
- | #> | + | > |
- | #> data: sleep$extra | + | > data: sleep$extra |
- | #> t = 3.413, df = 19, p-value = 0.002918 | + | > t = 3.413, df = 19, p-value = 0.002918 |
- | #> alternative hypothesis: true mean is not equal to 0 | + | > alternative hypothesis: true mean is not equal to 0 |
- | #> 95 percent confidence interval: | + | > 95 percent confidence interval: |
- | #> 0.5955845 2.4844155 | + | > 0.5955845 2.4844155 |
- | #> sample estimates: | + | > sample estimates: |
- | #> mean of x | + | > mean of x |
- | #> 1.54 | + | > 1.54 |
</ | </ | ||
r/general_statistics.txt · Last modified: 2019/10/11 07:56 by hkimscil