這篇文章第一次使用markdown格式，如果排版感覺不太舒服，還望讀者們提出。本文以Bernard Rosner的《Fundamentals of Biostatistics》的一道習(xí)題為例，整理總結(jié)了t-檢驗(yàn)和wilcoxon符號(hào)秩檢驗(yàn)的相關(guān)R代碼。如有改進(jìn)之處，歡迎交流！

高血壓——紅花油對(duì)SBD的效果評(píng)價(jià)報(bào)告

背景：
飲食中多不飽和脂肪酸對(duì)心血管病的一些危險(xiǎn)因素有有利影響，其中多不飽和脂肪酸主要是亞油酸。為了檢驗(yàn)飲食中補(bǔ)充亞油酸對(duì)血壓的影響，選17例成人連續(xù)4周每日消耗23g紅花油（亞油酸含量高）。在基線（攝入紅花油以前）及1個(gè)月后測(cè)量血壓，每次隨訪時(shí)取幾次讀數(shù)的平均值，數(shù)據(jù)見表1。

1. 要檢驗(yàn)亞油酸對(duì)血壓的影響，用什么參數(shù)檢驗(yàn)方法？
2. 用1的方法進(jìn)行檢驗(yàn)，給出p值。
3. 要檢驗(yàn)亞油酸對(duì)血壓的影響，用什么非參數(shù)方法？
4. 用3的上述方法進(jìn)行檢驗(yàn)，給出p值。
   5.比較2和4的結(jié)果，討論你認(rèn)為哪一種方法適合。

P1:

用配對(duì)雙樣本t檢驗(yàn)

P2:

• 首先使用levene test進(jìn)行方差齊性檢驗(yàn)，p=0.9587>0.05，故接受備擇假設(shè)：基線SBP和1個(gè)月后的SBP的方差沒有顯著差異；
• 然后使用Shapiro-Wilk normality test對(duì)差值進(jìn)行差值正態(tài)性檢驗(yàn)，p=0.975>0.05，說明差值數(shù)據(jù)服從正態(tài)整體分布；
• 利用配對(duì)雙樣本t檢驗(yàn)來檢驗(yàn)亞油酸對(duì)血壓的影響：p-value = 0.0009303，說明亞油酸能顯著降低SBP，雙尾檢驗(yàn)的結(jié)果為p=0.001861
• t-test代碼：

library(carData)
library(car)
library(ggpubr)
library(ggplot2)
library(magrittr)

SBP0 = c(119.67,100.00,123.56,109.89,96.22,133.33,115.78,126.39,122.78
         ,117.44,111.33,117.33,120.67,131.67,92.39,134.44,108.67
)
SBP1 = c(117.33,98.78,123.83,107.67,95.67,128.89,113.22,121.56,126.33
         ,110.39,107.00,108.44,117.00,126.89,93.06,126.67,108.67
)
#方差齊性檢驗(yàn)
y=c(SBP0,SBP1)
p=rep(1,17)
group = as.factor(c(rep(1,17),rep(2,17)))
leveneTest(y,group)
#差值正態(tài)性檢驗(yàn)
dSBP = c(2.34,1.22,-0.27,2.22,0.55,4.44,2.56,4.83,-3.55
         ,7.05,4.33,8.89,3.67,4.78,-0.67,7.77,0.00
)
shapiro.test(dSBP)
#t檢驗(yàn)
t1=t.test(SBP0, SBP1, paired=T, alternative="two.sided", cond.lvel=0.95)    #雙尾檢驗(yàn)
t2=t.test(SBP0, SBP1, paired=T, alternative="greater", cond.lvel=0.95)        #單尾檢驗(yàn)

下面繪制箱型圖，

mydata = data.frame(group = rep(c("Conrtrast", "Trial"), each = 17),
                    SBP = c(SBP0,SBP1)
)
mydata$group=as.factor(mydata$group)
my_comparisons = list(c("Conrtrast", "Trial"))
pdf(file="t.test.boxplot.pdf", width=6, height=5)
ggboxplot(mydata
          ,x="group"
          ,y = "SBP"
          ,fill = "group"
          ,palette = "npg"
          ,linetype = "solid"
          ,bxp.errorbar=T
          ,bxp.errorbar.width=0.1
          ,add = "point"
          ,short.panel.labs = FALSE
)+ 
  stat_compare_means(comparisons=my_comparisons
                     ,aes(label = ..p.format..)
                     ,method = "t.test"
                     ,paired=T
                     ,label.x = 1.5)+
  theme(
    axis.text.x   = element_text(color = 'black', size = 16, angle = 0)
    ,axis.text.y   = element_text(color = 'black', size = 16, angle = 0)
    ,axis.title.x  = element_text(color = 'black', size = 16, angle = 0)
    ,axis.title.y  = element_text(color = 'black', size = 16, angle = 90)
    ,legend.title  = element_text(color = 'black', size  = 16)
    ,legend.text   = element_text(color = 'black', size   = 16)
    ,axis.line.y = element_line(color = 'black', linetype = 'solid')
    ,axis.line.x = element_line (color = 'black',linetype = 'solid') 
    ,panel.border = element_rect(linetype = 'solid', size = 1.2,fill = NA) # 圖四周框起來
  )

配對(duì)樣本t檢驗(yàn)結(jié)果

P3:

用Wilcoxon signed-rank檢驗(yàn)。

P4:

• 單尾檢驗(yàn)的p-value=0.002053
• 雙尾檢驗(yàn)的p-value= 0.004107
  代碼跟t-test類似，因?yàn)槭欠菂?shù)檢驗(yàn)，所以少了對(duì)方差的檢驗(yàn)：

library(ggpubr)
library(ggplot2)
library(magrittr)

SBP0 = c(119.67,100.00,123.56,109.89,96.22,133.33,115.78,126.39,122.78
         ,117.44,111.33,117.33,120.67,131.67,92.39,134.44,108.67
)
SBP1 = c(117.33,98.78,123.83,107.67,95.67,128.89,113.22,121.56,126.33
         ,110.39,107.00,108.44,117.00,126.89,93.06,126.67,108.67
)
#Wilcoxon符號(hào)秩檢驗(yàn)
wiltest1=wilcox.test(SBP0, SBP1, paired=T, alternative="two.sided", cond.lvel=0.95)
wiltest2=wilcox.test(SBP0, SBP1, paired=T, alternative="greater", cond.lvel=0.95)

下面繪制箱型圖：

mydata = data.frame(group = rep(c("Conrtrast", "Trial"), each = 17),
                    SBP = c(SBP0,SBP1)
)
mydata$group=as.factor(mydata$group)
my_comparisons = list(c("Conrtrast", "Trial"))
pdf(file="wilcox.test.boxplot.pdf", width=6, height=5)
ggboxplot(mydata
          ,x="group"
          ,y = "SBP"
          ,fill = "group"
          ,palette = "npg"
          ,linetype = "solid"
          ,bxp.errorbar=T
          ,bxp.errorbar.width=0.1
          ,add = "point"
          ,short.panel.labs = FALSE
)+ 
  stat_compare_means(comparisons=my_comparisons         #設(shè)置比較組
                     ,aes(label = ..p.format..)
                     ,method = "wilcox.test"         #默認(rèn)方法
                     ,paired=T
                     ,label.x = 1.5)+
  theme(
    axis.text.x   = element_text(color = 'black', size = 16, angle = 0)
    ,axis.text.y   = element_text(color = 'black', size = 16, angle = 0)
    ,axis.title.x  = element_text(color = 'black', size = 16, angle = 0)
    ,axis.title.y  = element_text(color = 'black', size = 16, angle = 90)
    ,legend.title  = element_text(color = 'black', size  = 16)
    ,legend.text   = element_text(color = 'black', size   = 16)
    ,axis.line.y = element_line(color = 'black', linetype = 'solid')
    ,axis.line.x = element_line (color = 'black',linetype = 'solid') 
    ,panel.border = element_rect(linetype = 'solid', size = 1.2,fill = NA) # 圖四周框起來
  )

如下圖所示：

Wilcoxon signed-rank檢驗(yàn)結(jié)果

P5:

t檢驗(yàn)的p值更小，所以t檢驗(yàn)更好。(這個(gè)回答可能有誤，還望指正。)

在醫(yī)學(xué)寫作中，Wilcoxon檢驗(yàn)相對(duì)t檢驗(yàn)使用得更多，因?yàn)閿?shù)據(jù)的可能不能通過方差齊性檢驗(yàn)，尤其是對(duì)照實(shí)驗(yàn)，也就是配對(duì)t檢驗(yàn)；但一旦能夠滿足t檢驗(yàn)的條件，參數(shù)檢驗(yàn)將會(huì)被我們優(yōu)先考慮使用，繪制箱型圖時(shí)使用了ggpubr這個(gè)包，相對(duì)只用ggplot2來繪制方便了許多，并且能夠通過參數(shù)設(shè)定不同期刊的繪圖風(fēng)格，另外這次在寫代碼時(shí)有意識(shí)地將逗號(hào)寫在前面，養(yǎng)成良好的編寫習(xí)慣，方便后期修改，之后會(huì)整理總結(jié)利用循環(huán)對(duì)features進(jìn)行分組wilcoxon符號(hào)秩檢驗(yàn)。