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Quantify a single distribution

Guillaume A. Rousselet 2020-07-10

library(cowplot)
library(ggplot2)

Given a sufficiently large sample size, a single distribution can be quantified in more details, by including confidence intervals of the quantiles. The figure below illustrates such detailed representation using event-related potential onsets from 120 participants (Bieniek et al., 2016). In that case, the earliest latencies are particularly interesting, so it is useful to quantify the first deciles in addition to the median.

#> --------------------------------------
#> Inference on the deciles of ERP onsets
#> --------------------------------------
#> load data:
load("./data/onsets.RData") # onsets

#> -----------------------------------
#> Panel A: scatterplot + deciles
#> -----------------------------------

df <- mkt1(onsets) # make data frame

#> scatterplot
p <- plot_scat2(df,
  xlabel = "",
  ylabel = "ERP onsets in ms",
  alpha = 1,
  shape = 21,
  colour = "grey10",
  fill = "grey90",
  size = 3) + 
  theme(axis.text.y = element_blank(),
        axis.title.y = element_blank(),
        axis.ticks.y = element_blank())
 
#> add vertical lines marking the deciles
p <- plot_hd_bars(p, 
                  q_seq = seq(.1,.9,.1),
                  col = "black",
                  q_size = 0.5,
                  md_size = 1.5,
                  alpha = 1) 

#> flip axes
#> one ERP onsets at 284 ms is masked
p <- p + coord_flip(ylim = c(50,200)) 
# p

#> ---------------------------------------
#> Panel B: deciles + confidence intervals
#> ---------------------------------------

#> compute deciles + confidence intervals
set.seed(7)
out <- quantiles_pbci(onsets,q=seq(1,9)/10,nboot=2000,alpha=0.05)

#> decile plot
decile_plot <- plot_hd_ci(data=out,plotzero=TRUE,label.x="ERP onsets in ms",
                           hjust=-.05,vjust=.5,size_text=5,
                           colour_q = "grey10",fill_q = "grey90",
                           colour_line = "grey10", linetype_line = 1, size_line = 1) +
                scale_y_continuous(limits=c(50, 140),breaks=seq(50,140,10))
# decile_plot

#> combine scatterplots + decile plot
cowplot::plot_grid(p, decile_plot,
                             labels=c("A", "B"),
                             ncol = 1,
                             nrow = 2,
                             rel_heights = c(1, 1.5),
                             label_size = 20,
                             hjust = -0.5,
                             scale=.95,
                             align = "v")

(A) The scatterplot illustrates the distribution of event-related potential (ERP) onsets in ms. Points were scattered along the y-axis to avoid overlap. Vertical lines indicate the deciles, with the median shown with a thicker line. One outlier (> 200 ms) is not shown.

(B) Deciles and their 95% percentile bootstrap confidence intervals. The vertical black line marks the median.

We can also answer useful questions, such as the proportion of onsets less than 100 ms, which is 0.61.

References

Bieniek, M.M., Bennett, P.J., Sekuler, A.B. & Rousselet, G.A. (2016) A robust and representative lower bound on object processing speed in humans. The European journal of neuroscience, 44, 1804-1814. [article] [reproducibility package]

Rousselet, G.A., Pernet, C.R. & Wilcox, R.R. (2017) Beyond differences in means: robust graphical methods to compare two groups in neuroscience. The European journal of neuroscience, 46, 1738-1748. [article] [preprint] [reproducibility package]