title: ggplot2 stat_summary mean_sdl not the same as mean +/- sd
body: <p>I am unsure as to why the error bars generated by the mean_sdl function (from Hmisc) in ggplot2 are significantly broader than the error bars generated manually and plotting mean + sd and mean - sd. My code:</p>
  
  <pre><code>library(drc)
  library(tidyverse)
  
  test_dataset &lt;- 
    structure(
      list(
        X = c(1e-10, 1e-08, 3e-08, 1e-07, 3e-07, 1e-06, 3e-06, 1e-05, 3e-05, 1e-04, 3e-04),
        AY1 = c(0, 11, 125, 190, 258, 322, 354, 348, NA, 412, NA),
        AY2 = c(3, 33, 141, 218, 289, 353, 359, 298, NA, 378, NA),
        AY3 = c(2, 25, 160, 196, 345, 328, 369, 372, NA, 399, NA),
        BY1 = c(3, NA, 11, 52, 80, 171, 289, 272, 359, 352, 389),
        BY2 = c(5, NA, 25, 55, 77, 195, 230, 333, 306, 320, 338),
        BY3 = c(4, NA, 28, 61, 44, 246, 243, 310, 297, 365, NA)
      ),
      class = c("tbl_df", "tbl", "data.frame"),
      row.names = c(NA,-11L),
      .Names = c("X", "AY1", "AY2", "AY3", "BY1", "BY2", "BY3")
    )
  
  test_dataset2 &lt;- test_dataset %&gt;% 
    rename(conc = X) %&gt;% 
    gather(-conc, key = "measurement", value = "signal") %&gt;% 
    separate(col = measurement, into = c("mAb", "rep"), sep = "Y")
  
  plot_with_mean_sdl &lt;- ggplot(test_dataset2, aes(x = conc, y = signal, col = mAb)) + 
    scale_x_log10() +
    stat_summary(fun.data = mean_se, 
                 geom = "point",
                 size = 2
                 ) +
    # geom_errorbar(data = (test_dataset2 %&gt;% group_by(mAb, conc) %&gt;% 
    # summarise(AVG = mean(signal), SD = sd(signal)) %&gt;% 
    # dplyr::filter(AVG != "NA") %&gt;% 
    # mutate(top = AVG + SD, bottom = AVG - SD)), aes(x = conc, y = AVG, ymin = bottom, ymax = top)) + 
    stat_summary(fun.data = mean_sdl, geom = "errorbar") +
    stat_smooth(method = "drm",
                method.args=list(fct = L.4()),
                se = F,
                n = 300
                )
  
  plot_with_manual_errorbars &lt;- ggplot(test_dataset2, aes(x = conc, y = signal, col = mAb)) + 
    scale_x_log10() +
    stat_summary(fun.data = mean_se, 
                 geom = "point",
                 size = 2
                 ) +
    geom_errorbar(data = (test_dataset2 %&gt;% group_by(mAb, conc) %&gt;%
    summarise(AVG = mean(signal), SD = sd(signal)) %&gt;%
    dplyr::filter(AVG != "NA") %&gt;%
    mutate(top = AVG + SD, bottom = AVG - SD)), aes(x = conc, y = AVG, ymin = bottom, ymax = top)) +
    # stat_summary(fun.data = mean_sdl, geom = "errorbar") +
    stat_smooth(method = "drm",
                method.args=list(fct = L.4()),
                se = F,
                n = 300
                )
  </code></pre>
  
  <p>I thought the smean_sdl function from the Hmisc package was supposed to plot the mean +/- a constant number of standard deviations from the mean. What am I not getting right?</p>
  
  <p>Thanks.</p>