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Quick R for Statistics

3 假設檢定

以R語言讀入資料並做假設檢定，包含常態檢定、獨立與相依t檢定。

3.1 讀入檔案

以xlsx套件的read.xlsx()函數或readxl套件的read_xlsx()函數來讀入上個單元中所存出的gData1.xlsx檔。

library(readxl)
gData1 <- read_xlsx("gData1.xlsx")
head(gData1)
## # A tibble: 6 × 8
##   學號      性別   組別  出席  影片 期中考 期末考 總成績
##   <chr>     <chr> <dbl> <dbl> <dbl>  <dbl>  <dbl>  <dbl>
## 1 102368014 M         9   8.5  82.6     32   28     56.0
## 2 102368018 M        10   9.5  82.9     66   59     78.8
## 3 102368024 F         9   8    82.6     69   68     81.2
## 4 102368027 F         9   8    82.6     68   83.5   86.0
## 5 102368030 F        11   0    66.5     39   30     45.2
## 6 100368033 M         4  12    73.3     58   79     82.1

3.2 常態檢定

以qqnorm()和qqline()來看常態Q-Q圖。

qqnorm(gData1$總成績)
qqline(gData1$總成績)

以shapiro.test()做常態檢定。

shapiro.test(gData1$總成績)
## 
##  Shapiro-Wilk normality test
## 
## data:  gData1$總成績
## W = 0.98346, p-value = 0.6243

3.3 獨立樣本t檢定

先將性別轉為factor。

gData1$性別 <- factor(gData1$性別)

以leveneTest()做變異數同質性檢定。

library(car)
leveneTest(gData1$總成績 ~ gData1$性別, center="mean")
## Levene's Test for Homogeneity of Variance (center = "mean")
##       Df F value Pr(>F)
## group  1  0.2112 0.6476
##       55

以獨立樣本t檢定比較男女在總成績上是否有差異。

t.test(gData1$總成績 ~ gData1$性別, var.equal=TRUE)
## 
##  Two Sample t-test
## 
## data:  gData1$總成績 by gData1$性別
## t = -0.62999, df = 55, p-value = 0.5313
## alternative hypothesis: true difference in means between group F and group M is not equal to 0
## 95 percent confidence interval:
##  -7.892010  4.116907
## sample estimates:
## mean in group F mean in group M 
##        73.43611        75.32366

3.4 相依樣本t檢定

以t.test()做相依樣本t檢定，比較期中考和期末考是否有差異。

t.test(gData1$期中考, gData1$期末考, pair=TRUE)
## 
##  Paired t-test
## 
## data:  gData1$期中考 and gData1$期末考
## t = -2.3616, df = 56, p-value = 0.0217
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
##  -8.3334024 -0.6841415
## sample estimates:
## mean difference 
##       -4.508772

t.test()預設為雙尾檢定，若要做單尾檢定，可加入alternative的參數，可設定為”greater” 或 “less”。

t.test(gData1$期中考, gData1$期末考, alternative='less',  pair=TRUE)
## 
##  Paired t-test
## 
## data:  gData1$期中考 and gData1$期末考
## t = -2.3616, df = 56, p-value = 0.01085
## alternative hypothesis: true mean difference is less than 0
## 95 percent confidence interval:
##       -Inf -1.315556
## sample estimates:
## mean difference 
##       -4.508772