自动STAT_SUMMARY统计与手动标准误差之间的差异

我使用{ggplot2}绘制分组变量的平均值和可信区间，并注意到如果我手工计算或使用stat_summary()计算可信区间，我得到的结果略有不同.

有人知道是什么导致了这种差异吗？

下面是可复制的代码(注意-变量y故意倾斜以模拟我的实际数据集，但想知道这是否是导致问题的原因).

# Generate data
# Number of observations per group
n_per_group <- 50

# Generate left-skewed data
group1 <- rgamma(n_per_group, shape = 2, scale = 1)
group2 <- rgamma(n_per_group, shape = 3, scale = 1.5)
group3 <- rgamma(n_per_group, shape = 4, scale = 2)

# Combine data into a single data frame
df <- data.frame(
  y = rep(c("Group 1", "Group 2", "Group 3"), each = n_per_group),
  x = c(group1, group2, group3)
)

# Using stat_summary()
df %>%
  ggplot(., aes(x = x, y = y, group = y)) +
  stat_summary(fun = "mean", geom = "point") +
  stat_summary(fun.data = "mean_se", 
               geom = "errorbar", 
               width = 0.1) +
  scale_x_continuous(breaks = seq(1, 10, by = 0.5))

# By hand
df %>%
  group_by(y) %>%
  summarise(mean = mean(x, na.rm = T), 
            std.dev = sd(x, na.rm = T), 
            n = n(),
            se = std.dev / sqrt(n)) %>%
  
  ggplot(., aes(y = y)) + 
  geom_errorbar(aes(xmin = mean - 1.96*se, 
                    xmax = mean + 1.96*se), 
                width = 0.1) + 
  geom_point(aes(x = mean)) +
  scale_x_continuous(breaks = seq(1, 10, by = 0.5))