Data Management
- R-base에서 제공하고 있는 sleep data 는 long form data frame 으로 주어져 있음.
sleep
## extra group ID
## 1 0.7 1 1
## 2 -1.6 1 2
## 3 -0.2 1 3
## 4 -1.2 1 4
## 5 -0.1 1 5
## 6 3.4 1 6
## 7 3.7 1 7
## 8 0.8 1 8
## 9 0.0 1 9
## 10 2.0 1 10
## 11 1.9 2 1
## 12 0.8 2 2
## 13 1.1 2 3
## 14 0.1 2 4
## 15 -0.1 2 5
## 16 4.4 2 6
## 17 5.5 2 7
## 18 1.6 2 8
## 19 4.6 2 9
## 20 3.4 2 10
str(sleep)
## 'data.frame': 20 obs. of 3 variables:
## $ extra: num 0.7 -1.6 -0.2 -1.2 -0.1 3.4 3.7 0.8 0 2 ...
## $ group: Factor w/ 2 levels "1","2": 1 1 1 1 1 1 1 1 1 1 ...
## $ ID : Factor w/ 10 levels "1","2","3","4",..: 1 2 3 4 5 6 7 8 9 10 ...
- long form을 wide form으로 변환하고, 각각의 경우에 적절한 t-test를 시도해 볼 것임. 먼저 wide form 으로 변환하는 작업은 결국 data frame을 새로 구성하는 것일 뿐이므로 다음으로 완료됨.
sleep.wide<-data.frame(A=sleep[sleep$group==1,1], B=sleep[sleep$group==2,1])
sleep.wide
## A B
## 1 0.7 1.9
## 2 -1.6 0.8
## 3 -0.2 1.1
## 4 -1.2 0.1
## 5 -0.1 -0.1
## 6 3.4 4.4
## 7 3.7 5.5
## 8 0.8 1.6
## 9 0.0 4.6
## 10 2.0 3.4
One Sample T test
- long form 에서 각 수면제의 효과가 없다는 가설을 t-test 하려면
t.test(sleep$extra[sleep$group==1], alternative="greater")
##
## One Sample t-test
##
## data: sleep$extra[sleep$group == 1]
## t = 1.3257, df = 9, p-value = 0.1088
## alternative hypothesis: true mean is greater than 0
## 95 percent confidence interval:
## -0.2870553 Inf
## sample estimates:
## mean of x
## 0.75
t.test(sleep$extra[sleep$group==2], alternative="greater")
##
## One Sample t-test
##
## data: sleep$extra[sleep$group == 2]
## t = 3.6799, df = 9, p-value = 0.002538
## alternative hypothesis: true mean is greater than 0
## 95 percent confidence interval:
## 1.169334 Inf
## sample estimates:
## mean of x
## 2.33
- 둘을 단번에 수행하려면 tapply()를 이용하여
tapply(sleep$extra, sleep$group, t.test, alternative="greater")
## $`1`
##
## One Sample t-test
##
## data: X[[1L]]
## t = 1.3257, df = 9, p-value = 0.1088
## alternative hypothesis: true mean is greater than 0
## 95 percent confidence interval:
## -0.2870553 Inf
## sample estimates:
## mean of x
## 0.75
##
##
## $`2`
##
## One Sample t-test
##
## data: X[[2L]]
## t = 3.6799, df = 9, p-value = 0.002538
## alternative hypothesis: true mean is greater than 0
## 95 percent confidence interval:
## 1.169334 Inf
## sample estimates:
## mean of x
## 2.33
- 두 수면제 간의 효과에 차이가 없다는 가설을 검증하려면, paired 임을 유념하여야 함.
t.test(sleep$extra[sleep$group==1], sleep$extra[sleep$group==2], paired=T)
##
## Paired t-test
##
## data: sleep$extra[sleep$group == 1] and sleep$extra[sleep$group == 2]
## t = -4.0621, df = 9, p-value = 0.002833
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -2.4598858 -0.7001142
## sample estimates:
## mean of the differences
## -1.58
- formula 형식을 빌리면 다음과 같이 비교적 간결하게 기술할 수 있음.
t.test(extra~group, data=sleep, paired=T)
##
## Paired t-test
##
## data: extra by group
## t = -4.0621, df = 9, p-value = 0.002833
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -2.4598858 -0.7001142
## sample estimates:
## mean of the differences
## -1.58
- 두 수면제의 효과를 boxplot을 그려 비교하면(산점도를 그려 비교하려면 어떻게?)
plot(extra~group, data=sleep, main="Using Long Form")
attach(sleep.wide)
t.test(A, alternative="greater")
##
## One Sample t-test
##
## data: A
## t = 1.3257, df = 9, p-value = 0.1088
## alternative hypothesis: true mean is greater than 0
## 95 percent confidence interval:
## -0.2870553 Inf
## sample estimates:
## mean of x
## 0.75
t.test(B, alternative="greater")
##
## One Sample t-test
##
## data: B
## t = 3.6799, df = 9, p-value = 0.002538
## alternative hypothesis: true mean is greater than 0
## 95 percent confidence interval:
## 1.169334 Inf
## sample estimates:
## mean of x
## 2.33
apply(sleep.wide, 2, t.test, alternative="greater")
## $A
##
## One Sample t-test
##
## data: newX[, i]
## t = 1.3257, df = 9, p-value = 0.1088
## alternative hypothesis: true mean is greater than 0
## 95 percent confidence interval:
## -0.2870553 Inf
## sample estimates:
## mean of x
## 0.75
##
##
## $B
##
## One Sample t-test
##
## data: newX[, i]
## t = 3.6799, df = 9, p-value = 0.002538
## alternative hypothesis: true mean is greater than 0
## 95 percent confidence interval:
## 1.169334 Inf
## sample estimates:
## mean of x
## 2.33
t.test(A, B, paired=T)
##
## Paired t-test
##
## data: A and B
## t = -4.0621, df = 9, p-value = 0.002833
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -2.4598858 -0.7001142
## sample estimates:
## mean of the differences
## -1.58
plot(A, B, main="Using Wide Form", xlim=c(-2,6), ylim=c(-2,6))
abline(a=0, b=1, col="red")
text(x=4, y=3, labels="y=x")
library(nortest)
apply(sleep.wide, 2, ad.test)
## $A
##
## Anderson-Darling normality test
##
## data: newX[, i]
## A = 0.3469, p-value = 0.4019
##
##
## $B
##
## Anderson-Darling normality test
##
## data: newX[, i]
## A = 0.3572, p-value = 0.3785
save(file="sleep.rda", "sleep.wide")
detach()