这篇文章第一次使用markdown格式，如果排版感觉不太舒服，还望读者们提出。本文以Bernard Rosner的《Fundamentals of Biostatistics》的一道习题为例，整理总结了t-检验和wilcoxon符号秩检验的相关R代码。如有改进之处，欢迎交流！
高血压——红花油对SBD的效果评价报告
背景：
饮食中多不饱和脂肪酸对心血管病的一些危险因素有有利影响，其中多不饱和脂肪酸主要是亚油酸。为了检验饮食中补充亚油酸对血压的影响，选17例成人连续4周每日消耗23g红花油（亚油酸含量高）。在基线（摄入红花油以前）及1个月后测量血压，每次随访时取几次读数的平均值，数据见表1。
- 要检验亚油酸对血压的影响，用什么参数检验方法？
- 用1的方法进行检验，给出p值。
- 要检验亚油酸对血压的影响，用什么非参数方法？
- 用3的上述方法进行检验，给出p值。
5.比较2和4的结果，讨论你认为哪一种方法适合。
P1:
用配对双样本t检验
P2:
- 首先使用levene test进行方差齐性检验，p=0.9587>0.05，故接受备择假设：基线SBP和1个月后的SBP的方差没有显著差异；
- 然后使用Shapiro-Wilk normality test对差值进行差值正态性检验，p=0.975>0.05，说明差值数据服从正态整体分布；
- 利用配对双样本t检验来检验亚油酸对血压的影响：p-value = 0.0009303，说明亚油酸能显著降低SBP，双尾检验的结果为p=0.001861
- t-test代码：
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
)
#方差齐性检验
y=c(SBP0,SBP1)
p=rep(1,17)
group = as.factor(c(rep(1,17),rep(2,17)))
leveneTest(y,group)
#差值正态性检验
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检验
t1=t.test(SBP0, SBP1, paired=T, alternative="two.sided", cond.lvel=0.95) #双尾检验
t2=t.test(SBP0, SBP1, paired=T, alternative="greater", cond.lvel=0.95) #单尾检验
下面绘制箱型图，
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) # 图四周框起来
)
配对样本t检验结果
P3:
用Wilcoxon signed-rank检验。
P4:
- 单尾检验的p-value=0.002053
- 双尾检验的p-value= 0.004107
代码跟t-test类似，因为是非参数检验，所以少了对方差的检验：
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符号秩检验
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)
下面绘制箱型图：
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 #设置比较组
,aes(label = ..p.format..)
,method = "wilcox.test" #默认方法
,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) # 图四周框起来
)
如下图所示：
Wilcoxon signed-rank检验结果
P5:
t检验的p值更小，所以t检验更好。(这个回答可能有误，还望指正。)
