Loading Data

data("ToothGrowth")


str(ToothGrowth)

## 'data.frame':    60 obs. of  3 variables:
##  $ len : num  4.2 11.5 7.3 5.8 6.4 10 11.2 11.2 5.2 7 ...
##  $ supp: Factor w/ 2 levels "OJ","VC": 2 2 2 2 2 2 2 2 2 2 ...
##  $ dose: num  0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 ...

ToothGrowth$dose <- as.factor(ToothGrowth$dose)

Table 함수를 사용하여서 Cross -Table 확인하기

## 2개의 suppplement 별 Dosage 량 확인 
table(ToothGrowth$supp, ToothGrowth$dose)

##     
##      0.5  1  2
##   OJ  10 10 10
##   VC  10 10 10

DescribeBy 사용하여, supplement 별 Length 와 Dosage 기초 통계량 확인

# 기초 통계량 확인 describeBy 함수 사용 

describeBy(ToothGrowth[,c(1,3)], group = ToothGrowth$supp)

## 
##  Descriptive statistics by group 
## group: OJ
##       vars  n  mean   sd median trimmed  mad min  max range  skew kurtosis   se
## len      1 30 20.66 6.61   22.7   21.04 5.49 8.2 30.9  22.7 -0.52    -1.03 1.21
## dose*    2 30  2.00 0.83    2.0    2.00 1.48 1.0  3.0   2.0  0.00    -1.60 0.15
## ------------------------------------------------------------ 
## group: VC
##       vars  n  mean   sd median trimmed  mad min  max range skew kurtosis   se
## len      1 30 16.96 8.27   16.5   16.57 9.27 4.2 33.9  29.7 0.28    -0.93 1.51
## dose*    2 30  2.00 0.83    2.0    2.00 1.48 1.0  3.0   2.0 0.00    -1.60 0.15

정규성 확인하기 - qqplot 사용하기

ggqqplot(ToothGrowth$len)

• Histogram

ggplot(ToothGrowth, aes(len))+
  geom_histogram(aes(y=..density..), color ="indianred2", fill="white")+
  stat_function(fun=dnorm, 
                args= list(mean =mean(ToothGrowth$len, na.rm = TRUE),
                     sd = sd(ToothGrowth$len, na.rm =TRUE)))

hchart(ToothGrowth$len, name = "Length")

• Shaipro_Wilk 정규성 검사

shapiro.test(ToothGrowth$len)

## 
##  Shapiro-Wilk normality test
## 
## data:  ToothGrowth$len
## W = 0.96743, p-value = 0.1091

Length VS Supplement

• H0 : Supplement (2 종류)에 따라 치아 Length 길이의 차이가 있다.

• H1 : Supplement (2 종류)에 따라 치아 Length 길이의 차이가 없다.

t.test(len ~ supp, paired= FALSE,
       data=subset(ToothGrowth, ToothGrowth$supp !="Shoe"))

## 
##  Welch Two Sample t-test
## 
## data:  len by supp
## t = 1.9153, df = 55.309, p-value = 0.06063
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.1710156  7.5710156
## sample estimates:
## mean in group OJ mean in group VC 
##         20.66333         16.96333

Length VS Suuplement - 0.5 vs 1.0

t.test(len ~ dose, paired= FALSE,
       data= subset(ToothGrowth, ToothGrowth$dose %in% c(0.5,1)))

## 
##  Welch Two Sample t-test
## 
## data:  len by dose
## t = -6.4766, df = 37.986, p-value = 1.268e-07
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -11.983781  -6.276219
## sample estimates:
## mean in group 0.5   mean in group 1 
##            10.605            19.735

Length vs Dosage - 1.0 vs 2.0

t.test(len ~ dose, paired = FALSE, 
       data= subset(ToothGrowth, ToothGrowth$dose %in% c(1,2)))

## 
##  Welch Two Sample t-test
## 
## data:  len by dose
## t = -4.9005, df = 37.101, p-value = 1.906e-05
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -8.996481 -3.733519
## sample estimates:
## mean in group 1 mean in group 2 
##          19.735          26.100

# Dosage factor, Supplement Factor 두 개 범주형 자료 

ggplot(ToothGrowth, aes(dose, len))+
  geom_boxplot(aes(fill = supp))+
  theme_grey()

두 집단의 평균 차이

Test 1 : Dosage 량이 0.5 이면서, Supplement 가 OJ, VC 인 두 그룹간의 평균 Length의 차이

ToothGrowth %>% 
  rename(Length = len,
         Supplement = supp,
         Dosage = dose) -> df1



subset(df1, df1$Supplement== "OJ" & df1$Dosage=="0.5") -> Group_A
subset(df1, df1$Supplement== "VC" & df1$Dosage=="0.5") -> Group_B 


t.test(Group_A$Length, Group_B$Length, alternative = "two.sided", paired = FALSE)

## 
##  Welch Two Sample t-test
## 
## data:  Group_A$Length and Group_B$Length
## t = 3.1697, df = 14.969, p-value = 0.006359
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  1.719057 8.780943
## sample estimates:
## mean of x mean of y 
##     13.23      7.98

Test 2 : Dosage “1.0”

subset(df1, df1$Supplement== "OJ" & df1$Dosage=="1") -> Group_A
subset(df1, df1$Supplement== "VC" & df1$Dosage=="1") -> Group_B 



t.test(Group_A$Length, Group_B$Length, alternative = "two.sided", paired = FALSE)

## 
##  Welch Two Sample t-test
## 
## data:  Group_A$Length and Group_B$Length
## t = 4.0328, df = 15.358, p-value = 0.001038
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  2.802148 9.057852
## sample estimates:
## mean of x mean of y 
##     22.70     16.77

subset(df1, df1$Supplement== "OJ" & df1$Dosage=="2") -> Group_A
subset(df1, df1$Supplement== "VC" & df1$Dosage=="2") -> Group_B 

t.test(Group_A$Length, Group_B$Length, alternative = "two.sided", paired = FALSE)

## 
##  Welch Two Sample t-test
## 
## data:  Group_A$Length and Group_B$Length
## t = -0.046136, df = 14.04, p-value = 0.9639
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -3.79807  3.63807
## sample estimates:
## mean of x mean of y 
##     26.06     26.14

Test Dosage t p-value confidence interval (95%) Comment

A |0.5 (mg) |3.1697 |0.0063 |1.7191 to 8.7809 |Average tooth length is significantly different| B |1.0 (mg) |4.0328 |0.0010 |2.8021 to 9.0579 |Average tooth length is significantly different| C |2.0 (mg) |-0.046 |0.9639 |-3.798 to 3.6381 |At 2mg there is not a significant difference in avg. length|