## How to interpret box plot in R?

The box of a boxplot starts in the first quartile (25%) and ends in the third (75%). Hence, the box **represents the 50% of the central data, with a line inside that represents the median**. On each side of the box there is drawn a segment to the furthest data without counting **boxplot outliers**, that in case there exist, will be represented with circles.

**outlier is that observation that is very distant from the rest of the data**. A data point is said to be an outlier if it is greater than Q_3 + 1.5 \cdot IQR (right outlier), or is less than Q_1 – 1.5 \cdot IQR (left outlier), being Q_1 the first quartile, Q_3 the third quartile and IQR the interquartile range (Q_3 – Q_1) that represents the width of the box for horizontal boxplots.

## The boxplot function in R

A box and whisker plot in R base can be plotted with the `boxplot`

function. You can plot this type of graph from different inputs, like vectors or data frames, as we will review in the following subsections. In case of plotting boxplots for multiple groups in the same graph, you can also specify a formula as input. In addition, you can customize the resulting box plot with several arguments.

### Boxplot from vector

If you are wondering how to make box plot in R from vector, you just need to pass the vector to the `boxplot`

function. **By default, the boxplot will be vertical**, but you can change the orientation setting the `horizontal`

argument to `TRUE`

.

```
x <- c(8, 5, 14, -9, 19, 12, 3, 9, 7, 4,
4, 6, 8, 12, -8, 2, 0, -1, 5, 3)
```

`boxplot(x, horizontal = TRUE)`

Note that boxplots hide the underlying distribution of the data. In order to solve this issue, you can **add points to boxplot in R** with the `stripchart`

function (jittered data points will avoid to overplot the outliers) as follows:

`stripchart(x, method = "jitter", pch = 19, add = TRUE, col = "blue")`

### Box plot with confidence interval for the median

You can represent the 95% confidence intervals for the median in a R boxplot, setting the `notch`

argument to `TRUE`

.

`boxplot(x, notch = TRUE)`

Note that if the notches of two or more boxplots don’t overlap means there is strong evidence that the medians differ.

### Boxplot by group in R

If your dataset has a categorical variable containing groups, you can create a boxplot from formula. In this example, we are going to use the `chickwts`

dataset of R base.

`head(chickwts)`

```
weight feed
1 179 horsebean
2 160 horsebean
3 136 horsebean
4 227 horsebean
5 217 horsebean
6 168 horsebean
```

Now, you can create a boxplot of the weight against the type of feed. Notice that when working with datasets you can call the variable names if you specify the dataframe name in the `data`

argument.

```
boxplot(chickwts$weight ~ chickwts$feed)
boxplot(weight ~ feed, data = chickwts) # Equivalent
```

In addition, in this example you could add points to each boxplot typing:

```
stripchart(chickwts$weight ~ chickwts$feed, vertical = TRUE, method = "jitter",
pch = 19, add = TRUE, col = 1:length(levels(chickwts$feed)))
```

### Multiple boxplots

In case all variables of your dataset are numeric variables, you can directly create a boxplot from a dataframe. For illustration purposes we are going to use the `trees`

dataset.

`head(trees)`

```
Girth Height Volume
1 8.3 70 10.3
2 8.6 65 10.3
3 8.8 63 10.2
4 10.5 72 16.4
5 10.7 81 18.8
6 10.8 83 19.7
```

Note the difference respect to the `chickwts`

dataset. Nevertheless, you can convert this dataset as one of the same format as the `chickwts`

dataset with the `stack`

function.

```
stacked_df <- stack(trees)
head(stacked_df)
```

```
values ind
1 8.3 Girth
2 8.6 Girth
3 8.8 Girth
4 10.5 Girth
5 10.7 Girth
6 10.8 Girth
```

Now, you can plot the boxplot with the original or the stacked dataframe as we did in the previous section. Note that you can change the boxplot color by group with a vector of colors as parameters of the `col`

argument. Thus, each boxplot will have a different color.

```
# Boxplot from the R trees dataset
boxplot(trees, col = rainbow(ncol(trees)))
# Equivalent to:
boxplot(stacked_df$values ~ stacked_df$ind,
col = rainbow(ncol(trees)))
```

`stack`

function.
In case you need to plot a different boxplot for each column of your R dataframe you can use the `lapply`

function and iterate over each column. In this case, we will divide the graphics `par`

in one row and as many columns as the dataset has, but you could plot individual graphs. Note that the `invisible`

function avoids displaying the output text of the `lapply`

function.

```
par(mfrow = c(1, ncol(trees)))
invisible(lapply(1:ncol(trees), function(i) boxplot(trees[, i])))
```

### Reorder boxplot in R

By default, **boxplots will be plotted with the order of the factors in the data**. However, you can reorder or sort a boxplot in R reordering the data by any metric, like the median or the mean, with the `reorder`

function.

```
par(mfrow = c(1, 2))
# Lower to higher
medians <- reorder(chickwts$feed, chickwts$weight, median)
# medians <- with(chickwts, reorder(feed, weight, median)) # Equivalent
boxplot(chickwts$weight ~ medians, las = 2, xlab = "", ylab = "")
# Higher to lower
medians <- reorder(chickwts$feed, -chickwts$weight, median)
# medians <- with(chickwts, reorder(feed, -weight, median)) # Equivalent
boxplot(chickwts$weight ~ medians, las = 2, xlab = "", ylab = "")
par(mfrow = c(1, 1))
```

If you want to order the boxplot with other metric, just change `median`

for the one you prefer.

### Boxplot customization

A boxplot can be fully customized for a nice result. In the following block of code we show a wide example of how to customize an R box plot and how to add a grid. Note that there are even more arguments than the ones in the following example to customize the boxplot, like `boxlty`

, `boxlwd`

, `medlty`

or `staplelwd`

. Review the full list of graphical boxplot parameters in the `pars`

argument of `help(bxp)`

or `?bxp`

.

```
plot.new()
set.seed(1)
# Light gray background
rect(par("usr")[1], par("usr")[3], par("usr")[2], par("usr")[4],
col = "#ebebeb")
# Add white grid
grid(nx = NULL, ny = NULL, col = "white", lty = 1,
lwd = par("lwd"), equilogs = TRUE)
# Boxplot
par(new = TRUE)
boxplot(rnorm(500), # Data
horizontal = FALSE, # Horizontal or vertical plot
lwd = 2, # Lines width
col = rgb(1, 0, 0, alpha = 0.4), # Color
xlab = "X label", # X-axis label
ylab = "Y label", # Y-axis label
main = "Customized boxplot in R base", # Title
notch = TRUE, # Add notch if TRUE
border = "black", # Boxplot border color
outpch = 25, # Outliers symbol
outbg = "green", # Outliers color
whiskcol = "blue", # Whisker color
whisklty = 2, # Whisker line type
lty = 1) # Line type (box and median)
# Add a legend
legend("topright", legend = "Boxplot", # Position and title
fill = rgb(1, 0, 0, alpha = 0.4), # Color
inset = c(0.03, 0.05), # Modify margins
bg = "white") # Legend background color
```

## Add mean point to boxplot in R

By default, when you create a boxplot the median is displayed. Nevertheless, **you may also like to display the mean or other characteristic of the data**. For that purpose, you can use the `segments`

function if you want to display a line as the median, or the `points`

function to just add points. Note that **the code is slightly different if you create a vertical boxplot or a horizontal boxplot**.

In the following code block we show you how to **add mean points** and segments to both type of boxplots when working with a **single boxplot**.

```
par(mfrow = c(1, 2))
#-----------------
# Vertical boxplot
#-----------------
boxplot(x)
# Add mean line
segments(x0 = 0.8, y0 = mean(x),
x1 = 1.2, y1 = mean(x),
col = "red", lwd = 2)
# abline(h = mean(x), col = 2, lwd = 2) # Entire line
# Add mean point
points(mean(x), col = 3, pch = 19)
#-------------------
# Horizontal boxplot
#-------------------
boxplot(x, horizontal = TRUE)
# Add mean line
segments(x0 = mean(x), y0 = 0.8,
x1 = mean(x), y1 = 1.2,
col = "red", lwd = 2)
# abline(v = mean(x), col = 2, lwd = 2) # Entire line
# Add mean point
points(mean(x), 1, col = 3, pch = 19)
par(mfrow = c(1, 1))
```

Note that, in this case, the mean and the median are almost equal, as the distribution is symmetric.

`mean`

function of the previous code for other function to display other measures.
You can also **add the mean point to boxplot by group**. In this case, you can make use of the `lapply`

function to avoid `for`

loops. In order to calculate the `mean`

for each group you can use the `apply`

function by columns or the `colMeans`

function. You can follow the code block to add the lines and points for horizontal and vertical box and whiskers diagrams.

```
par(mfrow = c(1, 2))
my_df <- trees
#--------------------------
# Vertical boxplot by group
#--------------------------
boxplot(my_df, col = rgb(0, 1, 1, alpha = 0.25))
# Add mean lines
invisible(lapply(1:ncol(my_df),
function(i) segments(x0 = i - 0.4,
y0 = mean(my_df[, i]),
x1 = i + 0.4,
y1 = mean(my_df[, i]),
col = "red", lwd = 2)))
# Add mean points
means <- apply(my_df, 2, mean)
means <- colMeans(my_df) # Equivalent (more efficient)
points(means, col = "red", pch = 19)
#----------------------------
# Horizontal boxplot by group
#----------------------------
boxplot(my_df, col = rgb(0, 1, 1, alpha = 0.25),
horizontal = TRUE)
# Add mean lines
invisible(lapply(1:ncol(my_df),
function(i) segments(x0 = mean(my_df[, i]),
y0 = i - 0.4,
x1 = mean(my_df[, i]),
y1 = i + 0.4,
col = "red", lwd = 2)))
# Add mean points
means <- apply(my_df, 2, mean)
means <- colMeans(my_df) # Equivalent (more efficient)
points(means, 1:ncol(my_df), col = "red", pch = 19)
par(mfrow = c(1, 1))
```

## Return values from boxplot

If you assign the boxplot to a variable, you can return a list with different components. Create a boxplot with the `trees`

dataset and store it in a variable:

```
res <- boxplot(trees)
res
```

```
$`stats`
[, 1] [, 2] [, 3]
[1, ] 8.30 63 10.2
[2, ] 11.05 72 19.4
[3, ] 12.90 76 24.2
[4, ] 15.25 80 37.3
[5, ] 20.60 87 58.3
$n
[1] 31 31 31
$conf
[, 1] [, 2] [, 3]
[1, ] 11.70814 73.72979 19.1204
[2, ] 14.09186 78.27021 29.2796
$out
[1] 77
$group
[1] 3
$names
[1] "Girth" "Height" "Volume"
```

The output will contain six elements described below:

**stats**: each column represents the lower whisker, the first quartile, the median, the third quartile and the upper whisker of each group.**n**: number of observations of each group.**conf**: each column represents the lower and upper extremes of the confidence interval of the median.**out**: total number of outliers.**group**: total number of groups.**names**: names of each group.

It is worth to mention that you can create a boxplot from the variable you have just created (`res`

) with the `bxp`

function.

`bxp(res)`

## Boxplot and histogram

One limitation of box plots is that there are **not designed to detect multimodality**. For that reason, it is also recommended plotting a boxplot combined with a histogram or a density line.

```
par(mfrow = c(1, 1))
# Multimodal data
n <- 20000
ii <- rbinom(n, 1, 0.5)
dat <- rnorm(n, mean = 110, sd = 11) * ii +
rnorm(n, mean = 70, sd = 5) * (1 - ii)
# Histogram
hist(dat, probability = TRUE, ylab = "", col = "grey",
axes = FALSE, main = "")
# Axis
axis(1)
# Density
lines(density(dat), col = "red", lwd = 2)
# Add boxplot
par(new = TRUE)
boxplot(dat, horizontal = TRUE, axes = FALSE,
lwd = 2, col = rgb(0, 1, 1, alpha = 0.15))
```

**boxplot can’t detect multimodality**in the data.

As an alternative to this problem you can use violin plots or beanplots.

## Boxplot in R ggplot2

The boxplots we created in the previous sections can also be plotted with `ggplot2`

library.

### Boxplot in ggplot2 from vector

The input of the `ggplot`

library has to be a data frame, so you will need convert the vector to `data.frame`

class. Then, you can use the `geom_boxplot`

function to create and customize the box and the `stat_boxplot`

function to add the error bars.

```
# install.packages("ggplot2")
library(ggplot2)
# Transform our 'x' vector
x <- data.frame(x)
# Boxplot with vector
ggplot(data = x, aes(x = "", y = x)) +
stat_boxplot(geom = "errorbar", # Error bars
width = 0.2) +
geom_boxplot(fill = "#4271AE", # Box color
outlier.colour = "red", # Outliers color
alpha = 0.9) + # Box color transparency
ggtitle("Boxplot with vector") + # Plot title
xlab("") + # X-axis label
coord_flip() # Horizontal boxplot
```

### Boxplot in ggplot2 by group

If you want to create a ggplot boxplot by group, you will need to specify variables in the `aes`

argument as follows:

```
# Boxplot by group
ggplot(data = chickwts, aes(x = feed, y = weight)) +
stat_boxplot(geom = "errorbar", # Boxplot with error bars
width = 0.2) +
geom_boxplot(fill = "#4271AE", colour = "#1F3552", # Colors
alpha = 0.9, outlier.colour = "red") +
scale_y_continuous(name = "Weight") + # Continuous variable label
scale_x_discrete(name = "Feed") + # Group label
ggtitle("Boxplot by groups ggplot2") + # Plot title
theme(axis.line = element_line(colour = "black", # Theme customization
size = 0.25))
```

### Boxplot in ggplot2 from dataframe

Finally, for creating a boxplot with `ggplot2`

with a data frame like the `trees`

dataset, you will need to stack the data with the `stack`

function:

```
# Boxplot from dataframe
ggplot(data = stack(trees), aes(x = ind, y = values)) +
stat_boxplot(geom = "errorbar", # Boxplot with error bars
width = 0.2) +
geom_boxplot(fill = "#4271AE", colour = "#1F3552", # Colors
alpha = 0.9, outlier.colour = "red") +
scale_y_continuous(name = "Weight") + # Continuous variable label
scale_x_discrete(name = "Feed") + # Group label
ggtitle("Boxplot from data frame ggplot2") + # Plot title
theme(axis.line = element_line(colour = "black", # Theme customization
size = 0.25))
```