Those of us working in industry with Excel are familiar with scatter plots, line graphs, bar charts, pie charts and maybe a couple of other graph types. Some of us have occasionally used the Analysis Pack to create histograms that don’t update when our data changes (though there is a way to make dynamic histograms in Excel; perhaps I’ll cover this in another blog post).

One of the most important steps in data analysis is to just look at the data. What does the data look like? When we have time-dependent data, we can lay it out as a time-series or, better still, as a control chart (a.k.a. “natural process behavior chart”). Sometimes we just want to see how the data looks as a group. Maybe we want to look at the product weight or the cycle time across production shifts.

Unless you have Minitab, R or another good data analysis tool at your disposal, you have probably never used—maybe never heard of—boxplots. That’s unfortunate, because boxplots should be one of the “go-to” tools in your data analysis tool belt. It’s a real oversight that Excel doesn’t provide a good way to create them.

For the purpose of demonstration, let’s start with creating some randomly generated data:

head(df)

## variable value
## 1 group1 -1.5609
## 2 group1 -0.3708
## 3 group1 1.4242
## 4 group1 1.3375
## 5 group1 0.3007
## 6 group1 1.9717

tail(df)

## variable value
## 395 group1 1.4591
## 396 group1 -1.5895
## 397 group1 -0.4692
## 398 group1 0.1450
## 399 group1 -0.3332
## 400 group1 -2.3644

If we don’t have much data, we can just plot the points:

library(ggplot2)
ggplot(data = df[1:10,]) +
geom_point(aes(x = variable, y = value)) +
coord_flip() +
theme_bw()

But if we have lots of data, it becomes hard to see the distribution due to *overplotting*:

ggplot(data = df) +
geom_point(aes(x = variable, y = value)) +
coord_flip() +
theme_bw()

We can try to fix this by changing some parameters, like adding semi-transparency (alpha blending) and using an open plot symbol, but for the most part this just makes the data points harder to see; the distribution is largely lost:

ggplot(data = df) +
geom_point(aes(x = variable, y = value), alpha = 0.3, shape = 1) +
coord_flip() +
theme_bw()

The natural solution is to use histograms, another “go-to” data analysis tool that Excel doesn’t provide in a convenient way:

ggplot(data = df) +
geom_histogram(aes(x = value), binwidth = 1) +
theme_bw()

But histograms don’t scale well when you want to compare multiple groups; the histograms get too short (or too narrow) to really provide useful information. Here I’ve broken the data into eight groups:

head(df)

## variable value
## 1 group1 -1.5609
## 2 group1 -0.3708
## 3 group1 1.4242
## 4 group1 1.3375
## 5 group1 0.3007
## 6 group1 1.9717

tail(df)

## variable value
## 395 group8 -0.6384
## 396 group8 -3.0245
## 397 group8 1.5866
## 398 group8 1.9747
## 399 group8 0.2377
## 400 group8 -0.3468

ggplot(data = df) +
geom_histogram(aes(x = value), binwidth = 1) +
facet_grid(variable ~ .) +
theme_bw()

Either the histograms need to be taller, making the stack too tall to fit on a page, or we need a better solution.

The solution is the box plot:

ggplot() +
geom_boxplot(data = df, aes(y = value, x = variable)) +
coord_flip() +
theme_bw()

The boxplot provides a nice, compact representation of the distribution of a set of data, and makes it easy to compare across a large number of groups.

There’s a lot of information packed into that graph, so let’s unpack it:

Median
A measure of the central tendency of the data that is a little more robust than the mean (or arithmetic average). Half (50%) of the data falls below this mark. The other half falls above it.
First quartile (25th percentile) hinge
Twenty-five percent (25%) of the data falls below this mark.
Third quartile (75th percentile) hinge
Seventy-five percent (75%) of the data falls below this mark.
Inter-Quartile Range (IQR)
The middle half (50%) of the data falls within this band, drawn between the 25th percentile and 75th percentile hinges.
Lower whisker
The lower whisker connects the first quartile hinge to the lowest data point within 1.5 * IQR of the hinge.
Upper whisker
The upper whisker connects the third quartile hinge to the highest data point within 1.5 * IQR of the hinge.
Outliers
Any data points below 1.5 * IQR of the first quartile hinge, or above 1.5 * IQR of the third quartile hinge, are marked individually as outliers.
We can add additional values to these plots. For instance, it’s sometimes useful to add the mean (average) when the distributions are heavily skewed:

ggplot(data = df, aes(y = value, x = variable)) +
geom_boxplot() +
stat_summary(fun.y = mean, geom="point", shape = 10, size = 3, colour = "blue") +
coord_flip() +
theme_bw()

Graphs created in the R programming language using the ggplot2 and gridExtra packages.

### References

- R Core Team (2014). R: A language and environment for statistical computing. R Foundation for Statistical

Computing, Vienna, Austria. URL http://www.R-project.org/.
- H. Wickham. ggplot2: elegant graphics for data analysis. Springer New York, 2009.
- Baptiste Auguie (2012). gridExtra: functions in Grid graphics. R package version 0.9.1.

http://CRAN.R-project.org/package=gridExtra

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