Don't trust boxplot
TOC
- write a function for generating data
- use melt for rearranging data
- create a base plot
- add a boxplot to the base plot
- add a jiiter plot to the base plot
- create a figure for explaining the box plot (the fun part of this post)
- create another dataset
- add boxplot + jiiter plot
- what's happening?
#+++++++°+++++++++°+++++++++°+++++++++°+++++++++°+++++++++°+++++++++°+++++++++°
# loading required libraries for this notebook
#+++++++°+++++++++°+++++++++°+++++++++°+++++++++°+++++++++°+++++++++°+++++++++°
#loading libraries
library(ggplot2)
library(gridExtra)
library(data.table)
library(RColorBrewer)
library(ggpubr)
library(rstatix, warn.conflicts = FALSE)
library(ggrepel)
library(ggpubr)
library(patchwork)
#+++++++°+++++++++°+++++++++°+++++++++°+++++++++°+++++++++°+++++++++°+++++++++°
# creating a function for generating a dataset
#+++++++°+++++++++°+++++++++°+++++++++°+++++++++°+++++++++°+++++++++°+++++++++°
# function for generating data with custom number of rows, means and sds
simpleDataset <- function(number_of_rows,means,sds)
{
l <- length(means)
res <- lapply(seq(1:l),function(x)
eval(
parse(
text=paste("rnorm(",number_of_rows,",",means[x],",",sds[x],")",sep=""))
)
)
dat <- data.frame((sapply(res,c)))
id <- rownames(dat)
dat <- cbind(id=id,dat)
dt <- data.table(dat)
return(dt)
}
dat1 <- simpleDataset(number_of_rows=100,
means=runif(10,100,150),
sds=runif(10,10,40))
outliers <- simpleDataset(number_of_rows=5,
means=runif(10,60,80),
sds=runif(10,10,10))
dato <-rbind(dat1,outliers)
dt.melt <- melt(dat1, id.vars="id")
colnames(dt.melt) <- c("id","category","var1")
dt.melt$ncat <- as.numeric(dt.melt$category)
#+++++++°+++++++++°+++++++++°+++++++++°+++++++++°+++++++++°+++++++++°+++++++++°
# Jiitter plots + boxplot + brackets
#+++++++°+++++++++°+++++++++°+++++++++°+++++++++°+++++++++°+++++++++°+++++++++°
#setting up dimensions
options(repr.plot.width=8.9, repr.plot.height=8.9,units="cm")
#adding jiitter plot
p <- ggplot(dt.melt,aes(x=factor(ncat),y=var1)) +
geom_jitter(position = position_jitter(0.15),alpha=0.5,size = 3) +
geom_boxplot(alpha = 0,lwd=0.2) + theme_minimal(base_size =24)
p +theme_light(base_size=24)
So for now everything on track. We created a dataset using a custom function. 10 variables with 100 points each and them we plot them using scatter plots. Before plotting a few more data we need to answer the question How are boxplot constructed? (warning: shameless self-promotion ahead) First of all you can check on my book/ebook https://amzn.com/B08W8W5WSF Now it starts the fun part we will recreate a plot on the anatomy of a boxplot (see here) using ggplot.
#
y <- c(60,63,105,155,rnorm(100,80,25))
box <- ggplot() +
theme_void() +
geom_boxplot(aes(x=0,y=y),width=1,notch = FALSE,lwd=2) +
theme(legend.position = "none") +
lims(x=c(-2,2))
#how can we get out data? using the function ggplot_build()
#need to change it to a data.frame and rename cols
box_data <- (ggplot_build(box)$data)[[1]]
box_data
bdata <- data.frame(t(box_data[c(1,2,3,4,5,14)]))
colnames(bdata) <- c("y")
#we need to transpose the data and convert them to a data frame
#now we extract the ourliers
outl <- data.frame(box_data$outliers)
colnames(outl) <- c("outl")
#now that I got the data I plot everything with labels
p2 <- box + geom_text (data=bdata,aes(
x=1.5,
y=y,
label = c("min (no outliers)","Lower Q","Median","Upper Q","max","outliers")),size=8) +
geom_segment(data=bdata, aes(x = 0.8, y = y, xend = 0.6, yend =y),lwd=1)
#since we have created the dataset WITH outliers we include labels also for them
#if your dataset has no outliers you need to commet this part out
p2 + geom_text_repel(data=outl,aes(x=0.1, y=outl,label=format(round(outl, 2), nsmall = 2)),size=6)
notes on the code: we create our variable y with rnorm and we add a few outliers by hand then we create the boxplot
with an empty theme using theme_void(). The funny part start when we ask ggplot to show how the plot was built with the
ggplot_build. We then need to rotate (t) the selected columns c(1,2,3,4,5,14) ,convert the results into a data.frame,
rename the columns (colnames) and then use them (our y) to add labvels to our plot using geom_text
So the bound of the box refers to upper and lower quartile. The lower quartile splits off the lowest 25% of the data (also called 25% percentile) while the third quartile splits off the highest 25% of data from the lowest 75% (75% percentile). But what is a quartile? when a set of n measurements of the variable x has been arranged in order of magnitude the pth percentile is the value of x greater than p of the measurements. The 25th and 75th percentile are called the lower and upper quartiles and the 50th percentile is the median of the dataset. the IQR interquartile range (IQR) for a set of measurement is the difference between the upper and lower quartile
Another representation of boxplot can also include notch. the default is not to visualuize them but just adding notch=true to the previous plot we will do the trick
boxnotch <- ggplot() +
theme_void() +
geom_boxplot(aes(x=0,y=y),width=1,notch = TRUE,lwd=2) +
theme(legend.position = "none") +
lims(x=c(-2,4))
notchdata <- data.frame(t(box_data[c(7,8)]))
colnames(notchdata) <- c("y_notch")
#we need to transpose the data and convert them to a data frame
#now that I got the data I plot everything with labels
p3 <- boxnotch + geom_segment(data=notchdata, aes(x = 0.8,
y = mean(y_notch),
xend = 0.6, yend = y_notch
),lwd=1)
p4 <- p3 + annotate(geom="text", x=2.5, y= mean(notchdata$y_notch),
label="notch (95% confidence\ninterval of median)",size=10)
p4
so having a look at the the page we can see that
the following case can happen. we will load the dataset from the datasauRus package
options(repr.plot.width=8.9, repr.plot.height=8.9,units="cm")
library(datasauRus)
summary(box_plots)
p1 <-ggplot(stack(box_plots), aes(x = ind, y = values)) +
geom_jitter(alpha=0.05) +
theme_void()
p2 <- ggplot(stack(box_plots), aes(x = ind, y = values))+
geom_boxplot(lwd=1) +
theme_void()
p1+p2
options(repr.plot.width=12, repr.plot.height=12)
pnotch <- ggplot(stack(box_plots), aes(x = ind, y = values)) +
geom_boxplot(notch=TRUE,lwd=1) + ggtitle("(notch=TRUE)") +
theme_void()
pjitter <-ggplot(stack(box_plots), aes(x = ind, y = values)) +
geom_jitter(alpha=0.05) + ggtitle("geom_jitter") +
theme_void()
pviolin <- ggplot(stack(box_plots), aes(x = ind, y = values)) +
geom_violin(lwd=1) + ggtitle("geom_violin") +
theme_void()
pnotch + pjitter + pviolin
Other packages
- beeswarm plot ggbeeswarm [https://github.com/eclarke/ggbeeswarm] (and here the things start getting artistic too!) (note: not all representation for this dataset work due to the number of points)
library(ggbeeswarm)
p_qrandom0 <- ggplot(stack(box_plots), aes(x = ind, y = values)) +
geom_quasirandom(alpha=0.05) + ggtitle("quasi_random") +
theme_void(base_size=20)
#p_qrandom0
p_qrandom1 <- ggplot(stack(box_plots), aes(x = ind, y = values)) +
geom_quasirandom(alpha=0.05,method = "tukey") + ggtitle("Tukey") +
theme_void(base_size=20)
#p_qrandom1
p_qrandom2 <- ggplot(stack(box_plots), aes(x = ind, y = values)) +
geom_quasirandom(alpha=0.05,method = "tukeyDense") + ggtitle("Tukey + density") +
theme_void(base_size=20)
#p_qrandom2
p_qrandom3 <- ggplot(stack(box_plots), aes(x = ind, y = values)) +
geom_quasirandom(alpha=0.05,method = "tukeyDense") + ggtitle("Banded frowns") +
theme_void(base_size=20)
#p_qrandom3
p_qrandom4 <- ggplot(stack(box_plots), aes(x = ind, y = values)) +
geom_quasirandom(alpha=0.05,method = "frowney") + ggtitle("Banded smiles") +
theme_void(base_size=20)
#p_qrandom4
#too many points
#p_beeswarm <- ggplot(stack(box_plots), aes(x = ind, y = values)) +
#geom_beeswarm(alpha=0.05) + ggtitle("beeswarm") +
#theme_void()
p_qrandom0 + p_qrandom1+p_qrandom2
you can halso mix plot a useful package for that is gghalves that you can find here
library(gghalves)
point_half <- ggplot(stack(box_plots), aes(x = ind, y = values)) +
geom_half_point(alpha=0.05) +theme_void(base_size=20)
violin_half <- ggplot(stack(box_plots), aes(x = ind, y = values)) +
geom_half_violin() +theme_void(base_size=20)
point_half + violin_half
finally a very useful package, also my favorite one for EDA ggstatplotthat you can find here that calculate also a lot of useful stats and combine different kind of plot in one plot
library(ggstatsplot)
stackbox <- stack(box_plots)
pstack <- ggbetweenstats(
data = stackbox,
x = ind,
y = values,
)
pstack + theme(text = element_text(size = 22),
plot.subtitle = element_text(size = 20),
legend.title = element_text(size = 22),
legend.text = element_text(size = 22))
