标记字母法原理：

先将各处理平均数由大到小自上而下排列 ，然后在最大平均数后标记字母， 并 将该平均数与以下各平均数依次相比，凡差异不显著标记同一字母 ，直到某一个与其差异显著的平均数标记字母b ；

再以标有字母b的平均数为标准 ，与上方比它大的各个平均数比较，凡差异不显著一律再加标b ，直至显著为止；

再以标记有字母 b的最大平均数为标准，与下面各未标记字母的平均数相比，凡差异不显著，继续标记字母b，直至某一个与其差异显著的平均数标记c；

如此重复下去，直至最小一个平均数被标记、比较完毕为止。这样，各平均数间凡有一个相同字母的即为差异不显著，凡无相同字母的即为差异显著。

用小写拉丁字母表示显著水平 α=0.05 ，用大写拉丁字母表示显著水平α=0.01。

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R语言ggplot2优雅的创建字母显著性标记图

加载R包

library(tidyverse)
library(multcompView)
library(ggsci)

加载数据集

df <- ToothGrowth %>% as_tibble() %>% mutate(dose=as.factor(dose))

方差分析

anova <- aov(len~dose,data=df)
summary(anova)
> summary(anova)
            Df Sum Sq Mean Sq F value   Pr(>F)    
dose         2   2426    1213   67.42 9.53e-16 ***
Residuals   57   1026      18                     
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Tukey多重配对比较

tukey <- TukeyHSD(anova)
  Tukey multiple comparisons of means
    95% family-wise confidence level

Fit: aov(formula = len ~ dose, data = df)

$dose
        diff       lwr       upr    p adj
1-0.5  9.130  5.901805 12.358195 0.00e+00
2-0.5 15.495 12.266805 18.723195 0.00e+00
2-1    6.365  3.136805  9.593195 4.25e-05

创建字母

cld <- multcompLetters4(anova,tukey)

整合数据

dt <- df %>% group_by(dose) %>%
  summarise(w=mean(len), sd = sd(len)) %>%
  arrange(desc(w)) %>%
  ungroup() %>% 
  left_join(.,as.data.frame.list(cld$dose) %>% select(1) %>% 
              rownames_to_column("dose"))
  dose      w    sd Letters
  <chr> <dbl> <dbl> <chr>  
1 2      26.1  3.77 a      
2 1      19.7  4.42 b      
3 0.5    10.6  4.50 c      

绘制条形图

ggplot(dt, aes(dose, w)) + 
  geom_bar(stat = "identity",aes(fill=dose),show.legend = FALSE,width=0.5) +
  geom_errorbar(aes(ymin = w-sd, ymax=w+sd), width = 0.1) +
  geom_text(aes(label = Letters, y = w + sd), vjust = -0.5)+
  scale_fill_jco()+
  scale_y_continuous(expand = expansion(0),
                     limits = c(0,35),
                     breaks = seq(0,35,5))+
  labs(x=NULL,y=NULL)+
  theme(
    plot.margin = unit(c(0.2,0.2,0.2,0.2), "cm"),
    panel.background = element_blank(),
    axis.line = element_line(color = "black"),
    axis.title = element_text(size = 10, color = "black",
                              face = "bold"),
    axis.text = element_text(size = 10,color = "black"),
    axis.text.x = element_text(margin=margin(t =3)),
    axis.text.y = element_text(size = 10),
    axis.title.y = element_text(margin = margin(r = 10)),
    axis.ticks.x = element_blank())

双因素方差分析

anova <- aov(len~dose*supp,data=df)
summary(anova)
dt <- df %>% group_by(dose,supp) %>%
  summarise(w=mean(len), sd = sd(len)) %>%
  arrange(desc(w)) %>%
  ungroup()

cld <- TukeyHSD(anova) %>% multcompLetters4(anova,.)
le <- as.data.frame.list(cld$`dose:supp`)
dt$Tukey <- le$Letters

dt

ggplot(dt, aes(dose, w)) + 
  geom_bar(stat = "identity",aes(fill=dose),show.legend = FALSE,width=0.5) +
  geom_errorbar(aes(ymin = w-sd, ymax=w+sd), width = 0.1) +
  geom_text(aes(label = Tukey, y = w + sd), vjust = -0.5)+
  facet_wrap(~supp)+
  scale_fill_jco()+
  scale_y_continuous(expand = expansion(0),
                     limits = c(0,35),
                     breaks = seq(0,35,5))+
  labs(x=NULL,y=NULL)+
  theme_test()+
  theme(panel.background = element_blank(),
    axis.line = element_line(color = "black"),
    axis.text = element_text(size = 10,color = "black"),
    axis.text.x = element_text(margin=margin(t =3)),
    axis.text.y = element_text(size = 10),
    axis.title.y = element_text(margin = margin(r = 10)),
    axis.ticks.x = element_blank())