CW4

##先檢視資料

structure(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

summary(sleep)

##      extra        group        ID   
##  Min.   :-1.600   1:10   1      :2  
##  1st Qu.:-0.025   2:10   2      :2  
##  Median : 0.950          3      :2  
##  Mean   : 1.540          4      :2  
##  3rd Qu.: 3.400          5      :2  
##  Max.   : 5.500          6      :2  
##                          (Other):8

densityplot( ~ extra, groups = group, data = sleep,auto.key = TRUE,lty = c(1, 2), plot.points = T, type = "g", xlab = "numeric increase in hours of sleep", main = "numeric increase in hours of sleep for 2 type of drugs ")

##由上圖可以看出，就整體分布而言，在”numeric increase in hours of sleep”的結果中，增長0以上的部分GROUP2大於GROUP1，所以GROUP2的效果maybe較好

qq(group ~ extra, data = sleep,type = c("p", "g"),pch = ".",cex = 5 ,aspect = 1)

##從上圖可以看出，GROUP2在”numeric increase in hours of sleep”的結果高於GROUP1

##接著做t-Test

t.test(extra ~ group, data = sleep)

## 
##  Welch Two Sample t-test
## 
## data:  extra by group
## t = -1.8608, df = 17.776, p-value = 0.07939
## alternative hypothesis: true difference in means between group 1 and group 2 is not equal to 0
## 95 percent confidence interval:
##  -3.3654832  0.2054832
## sample estimates:
## mean in group 1 mean in group 2 
##            0.75            2.33

##從t-Test的結果看到

##在虛無假設為兩組沒有差異之下，P值>0.05，故無法拒絕虛無假設，因此兩組沒有顯著差異

##95 percent confidence interval包含0，表示兩組的差異未達顯著水準

##t = -1.8608 的絕對值<2，表示兩組的差異未達顯著水準