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fig04.Rmd
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fig04.Rmd
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---
title: 'A guide to robust statistical methods in neuroscience: Figure 4'
author: "Rand R. Wilcox & Guillaume A. Rousselet"
date: "`r Sys.Date()`"
output:
pdf_document:
fig_caption: no
number_sections: no
toc: yes
toc_depth: 2
---
Illustrate normal and contaminated normal populations, and sampling distributions for n=30 using three measures of central tendency: mean, 20% trimmed mean and median.
# Dependencies
```{r}
library(ggplot2)
library(cowplot)
library(tidyr)
library(tibble)
source("./code/Rallfun-v40.txt")
source("./code/theme_gar.txt")
source("./code/xtrafun.R")
```
# Panel A ---------------------------------
## generate data
```{r}
x <- seq(-3.5,3.5,.01)
y1 <- dnorm(x)
y2 <- dnorm(x,0,10)
mixed <- .9 * y1 + .1 * y2
standard <- y1
```
## create data frame
```{r}
df <- tibble(x,standard,mixed)
df <- tidyr::gather(df,Distribution,y,standard:mixed)
df$Distribution <- as.factor(df$Distribution)
df$Distribution <- keeporder(df$Distribution)
```
## make figure
```{r}
panelA <- ggplot(df, aes(x,y, group=Distribution)) + theme_gar +
geom_line(aes(linetype=Distribution, colour=Distribution), linewidth=0.75) +
scale_linetype_manual(values=c("solid","dashed")) +
scale_color_manual(values=c('black','black')) +
scale_x_continuous(breaks=seq(-3,3,1)) +
theme(axis.title.x = element_blank(),
axis.text = element_text(size = 16),
legend.key.width = unit(2,"cm"),
legend.position = c(0.175, 0.75),
axis.title.y = element_text(size = 18),
panel.grid.minor = element_blank(),
panel.grid.major.y = element_blank(),
axis.text.y = element_blank(),
axis.ticks.y = element_blank()) +
ylab("Density")
panelA
```
# Panel B - samples from normal distribution -------------
## generate data
```{r}
set.seed(45)
n <- 100000 # number of samples / experiments
v1 <- vector(mode = "numeric", length = n)
v2 <- vector(mode = "numeric", length = n)
v3 <- vector(mode = "numeric", length = n)
for(i in 1:n){
x <- rnorm(30) # samples from normal population
v1[i] <- mean(x)
v2[i] <- tmean(x)
v3[i] <- median(x)
}
```
## make data frame
```{r}
df <- tibble('Mean'=v1, 'Trimmed Mean'=v2, 'Median'=v3)
df <- tidyr::gather(df, Estimator, Value, c(1:3))
df$Estimator <- as.factor(df$Estimator)
df$Estimator <- keeporder(df$Estimator)
```
## make figure -- boxplot version
```{r}
panelB <- ggplot(df, aes(Estimator, Value)) + theme_gar +
geom_boxplot(outlier.colour = "grey70", outlier.shape = 16,
outlier.size = 3, outlier.alpha = .5, size = 0.75) +
scale_y_continuous(breaks=seq(-1,1,0.5), limits = c(-1,1)) +
theme(axis.title.x = element_blank(),
axis.title.y = element_text(size = 18),
axis.text = element_text(size = 16))
panelB
```
## make figure -- kernel density version
```{r, warning=FALSE}
panelB <- ggplot(df, aes(x = Value, colour = Estimator)) + theme_gar +
stat_density(geom="line", position="identity",
linewidth=0.75, trim=TRUE) +
scale_colour_manual(values = c("#56B4E9", "#D55E00", "black")) + #009E73
scale_x_continuous(breaks=seq(-4,4,1), limits = c(-3,3)) +
theme(axis.title = element_text(size = 18),
axis.text = element_text(size = 16),
panel.grid.minor = element_blank(),
panel.grid.major.y = element_blank(),
axis.text.y = element_blank(),
axis.ticks.y = element_blank(),
legend.position = c(.2, .7)) +
# plot.title = element_text(vjust = -7, hjust = 0.025),
# plot.margin = unit(c(5.5, 5.5, 5.5, 5.5), "pt")
xlab("Sample estimates (n=30)") +
ylab("Density")
# annotate("text", x=-2.2, y=2.2, label="Normal population", size=8)
panelB
```
# Panel C - samples from contaminated normal distribution
## generate data
```{r}
set.seed(45)
n <- 100000 # number of samples / experiments
v1 <- vector(mode = "numeric", length = n)
v2 <- vector(mode = "numeric", length = n)
v3 <- vector(mode = "numeric", length = n)
for(i in 1:n){
x <- cnorm(30) # samples from mixed population
v1[i] <- mean(x)
v2[i] <- tmean(x)
v3[i] <- median(x)
}
```
## make data frame
```{r}
df <- tibble('Mean'=v1, 'Trimmed Mean'=v2, 'Median'=v3)
df <- tidyr::gather(df, Estimator, Value, c(1:3))
df$Estimator <- as.factor(df$Estimator)
df$Estimator <- keeporder(df$Estimator)
```
## make figure -- boxplot version
```{r}
panelC <- ggplot(df, aes(Estimator, Value)) + theme_gar +
geom_boxplot(outlier.colour = "grey70", outlier.shape = 16,
outlier.size = 3, outlier.alpha = .5, size = 0.75) +
scale_y_continuous(breaks=seq(-4,4,1), limits = c(-4,4)) +
theme(axis.title.x = element_blank(),
axis.title.y = element_text(size = 18),
axis.text = element_text(size = 16))
panelC
```
## make figure -- kernel density version
```{r, warning=FALSE}
panelC <- ggplot(df, aes(x = Value, colour = Estimator)) + theme_gar +
stat_density(geom="line", position="identity",
linewidth=0.75, trim=TRUE, show.legend = FALSE) +
scale_colour_manual(values = c("#56B4E9", "#D55E00", "black")) + #009E73
scale_x_continuous(breaks=seq(-4,4,1)) +
coord_cartesian(xlim = c(-3.5,3.5)) +
theme(axis.title = element_text(size = 18),
axis.text = element_text(size = 16),
panel.grid.minor = element_blank(),
panel.grid.major.y = element_blank(),
axis.text.y = element_blank(),
axis.ticks.y = element_blank()) +
xlab("Sample estimates (n=30)") +
ylab("Density")
# annotate("text", x=-2.4, y=2.2, label="Mixed population", size=8)
panelC
```
# combine panels into one figure
```{r, eval=FALSE}
cowplot::plot_grid(panelA, panelB, panelC,
labels=c("A", "B", "C"),
ncol = 1,
nrow = 3,
rel_heights = c(1, 1, 1),
label_size = 20,
hjust = -0.5,
scale=.95,
align = "v")
# save figure
ggsave(filename='./figures/figure4.pdf',width=7,height=9)
```