误差线(Error bars)和显著性标记

1. 简介

误差线(Error bars)是数据变异性的图形显示，用于表明被测值的误差或不确定性。它指示了被测值的准确性、或被测值和真实值的差异性。可用来表示standard deviation、standard error 或 confidence interval，由于它们的值不尽相同，所以需要在图中特别说明。

标准差(sd)是描述性统计里用来表示数据本身均值范围的，sd越小，表明数据越集中在均值附近。标准差与均数结合估计参考值范围，计算变异系数，计算标准误。标准差(sd)不牵扯均值对比推测，仅仅是描述性的。

标准误(se)表示样本平均数对总体平均数的变异程度，反映抽样误差的大小；标准误(se)用于预测样本数据准确性 ，标准误越小，样本均值和总体均值差距越小，样本数据越能代表总体数据。

2. 作图

基于ggplot2的扩展包，ggpubr
和ggsignif 可以很简便的做出相应的图，但代价是作图过程中很多内部数据变换过程被封装起来了，不利于学习。

require(tidyverse)

#以species为分组变量，求petal.wdith 的sd，se和ci

conf.interval = 0.95
data <- iris %>% 
  group_by(Species) %>% 
  summarise(mean = mean(Petal.Width, na.rm = T),
            sd = sd(Petal.Width, na.rm = T),
            N = length(Petal.Width),
            se = sd/sqrt(N),
            ciMult = qt(conf.interval/2 + 0.5, N - 1),
            ci = se * ciMult)

#不做统计变换的柱状图
col_plot <- ggplot() + 
  geom_col(data = data, aes(x = Species, 
                            y = mean, fill = Species), width = 0.5)

#误差线
p <- col_plot + geom_errorbar(data = data, aes(x = Species, 
                                        ymin = mean-se, 
                                        ymax = mean + se, 
                                        group = Species,
                                        width = 0.2), 
                       position = position_dodge(width = 0.8))

col_plot.png

例2

# 计算均值和sd
require(tidyverse)
set.seed(13)
set.seed(13)
data <- diamonds %>% 
  sample_n(1000) 

sum_data <- data %>% 
  group_by(cut) %>% 
  summarise(
    mean_price = mean(price ),
    sd_price   = sd(price )) 
# 作图
p <- ggplot(data = sum_data, aes(x = cut, y = mean_price)) +
  geom_col(aes(fill = cut), color = "black", width = 0.85) +
  geom_errorbar(aes(ymin = mean_price - sd_price,
                    ymax = mean_price + sd_price),
                color = "#22292F",
                width = .1) +
  labs(
    y = "Mean Price",
    title = "Mean price in Different cuts",
    caption = "Error bars indicate standard deviations"
  ) 

Rplot.png

方差分析

用agricolae进行多重比较。

require(agricolae)
cut.aov <- aov(price ~ cut, data =data)
LSD <- LSD.test(cut.aov, "cut", p.adj="bonferroni")$groups
cut <- rownames(LSD)
LSD <- cbind(cut, LSD)
data_c <- merge(sum_data, LSD, by = "cut")

p + geom_text(data = data_c , aes(x = cut, 
                                  y = 2*mean_price + sd_price, 
                                  label = groups), 
              position = position_dodge(0.9), 
              size = 5, fontface = "bold")+ 
  labs(
  caption = "Barchart with Significance Tests"
) 

Rplot01.png

两两比较

# 跟据最高y设定连线坐标
sign <- tibble(
  x = c("Fair", "Fair", "Very Good", "Very Good"),
  y = c(8200,8400,8400,8200))
        
p + geom_line(data =sign, 
              aes(x = x, y = y, group = 1)) +
  annotate("text", x = 2, y = 8600,  # 跟据x，y设定星号坐标
                                                      # x = 2, 来源于cut 转换为了levels
           label = "***",
           size = 8, color = "#22292F")

Rplot02.png