Interpreting boxplots

In a boxplot:

• The thick line across the middle of the box is the median or midpoint of the data

• The height of the box indicates the interquartile range (IQR). This means the box contains 50% of the datapoints. A wider IQR indicates greater variation (spread) in a dataset.

• The meaning of the “whiskers” (the lines above the top, and below the bottom of the box) varies a little bit depending on the software you use — but they always show the range/spread of the data. The default in ggplot() are whiskers with lengths covering data points no more, or less than 1.5 times the IQR.

• Any data point outside the range of the whiskers is described as an ‘outlying point’ or ‘outlier’. Each outlier is plotted individually as a dot.

Columns vs variables

The word variable gets used in at least 4 different ways in quantitative research, and this confuses a lot of people.

We can’t avoid all ambiguity because these different usages are common in the field, but it helps to know about them in advance. The main usages are:

• variables in a theoretical model. That is, things or constructs we think exist, and which cause other things to happen. An example might be “empathy”, or “working memory”. These are psychological constructs which many theories include, and those theories say these constructs play a causal role in how we behave or perform on certain tasks.

• variables in a study design. An example here might an experimental group allocation, or an attribute of participants like their age or gender.

• variables in a dataset. Sometimes people want to refer to a column of numbers in a dataset (e.g. a spreadsheet), where the column has a name, and use the term variable again. This usage overlaps with the previous two, but it doesn’t have to. For example, we might have a column of numbers recording the date and time participants’ completed an empathy questionnaire. Analysed a certain way these timestamps might tell us something useful, but the column of timestamps isn’t a variable in our theoretical model, and they might not be used as a variable in our experiment.

[ Finally, we have ]

• variables in R and computer programs: This type of variable is a general purpose container which can store anything. Variables in R can contain columns of numbers, but they can also contain whole datasets, or graphs, or the results of statistical tests. A variable in R often isn’t the same thing as an experimental variable or a column in a dataset.

In this short course use variable to mean either an experimental/theoretical variable or an R container.

When we mean a column of data in a dataset we will use the word column instead.

Types of variable

OK so let’s focus for a minute on variables in a study design.

There are a few main types of these variable to consider. You might be familiar with some of these terms already:

• categorical or nominal variables (sometimes also called factors): e.g. gender, education status

• binary variables (a special category that is either TRUE or FALSE): e.g. smoker/non-smoker

• ordinal variables (categorical responses where the order is important): e.g. a 1-7 response on a Likert-style question

• interval or continuous variables: e.g. weight in kg, time in milliseconds

• count variables (a frequency, measured in whole numbers): e.g. the number of social contacts per week

• text variables: e.g. free text responses to open-ended questionnaire items

Types of column

OK, so those are the types of variable.

We can also think about the types of column that our dataset stores.

Datasets have multiple columns, each with a unique name.

In R, every column has a data type. These data types are normally determined by the type of variable. But there is some overlap, and different data types could be used to store the same variable.

We sometimes need to convert between data types.

There are four data types you need to know about in R: factors, text, numeric and logical columns.

• Factors, which are used for categorical data (and sometimes ordinal data too)
• Text, also called character or string data.
• Numeric columns can called be either integer or double. Double is computer speak for ‘double-precision number’, which just means decimals and really big numbers are allowed
• Logical, which can be used to store values that can only be either True or False.

The important thing to know is that— although different types of variable are usually stored in different types of column in R— this isn’t always the case.

Sometimes data can be stored as the wrong type—e.g. categorical data could end up stored as numeric data — and in these cases we need to convert from one format to another.

You can see which data type is used to store a variable when using the glimpse() command introduced in Session 1 (see here).

iris %>% glimpse()

Rows: 150
Columns: 5
$ Sepal.Length <dbl> 5.1, 4.9, 4.7, 4.6, 5.0, 5.4, 4.6, 5.0, 4.4, 4.9, 5.4, 4.8, 4.8, 4.3, 5.8, 5.7, …
$ Sepal.Width  <dbl> 3.5, 3.0, 3.2, 3.1, 3.6, 3.9, 3.4, 3.4, 2.9, 3.1, 3.7, 3.4, 3.0, 3.0, 4.0, 4.4, …
$ Petal.Length <dbl> 1.4, 1.4, 1.3, 1.5, 1.4, 1.7, 1.4, 1.5, 1.4, 1.5, 1.5, 1.6, 1.4, 1.1, 1.2, 1.5, …
$ Petal.Width  <dbl> 0.2, 0.2, 0.2, 0.2, 0.2, 0.4, 0.3, 0.2, 0.2, 0.1, 0.2, 0.2, 0.1, 0.1, 0.2, 0.4, …
$ Species      <fct> setosa, setosa, setosa, setosa, setosa, setosa, setosa, setosa, setosa, setosa, …

In the output you can see the variable names listed on the left, followed by text in angle brackets, e.g.: <dbl> which is the abbreviated name of data type.

In this built-in dataset, most of the data is numeric (dbl), but the Species variable is categorical, and stored as a factor (fct).

It’s possible to convert columns from one type to another, to suit our needs. We’ll see more of this later.

Column types determine the scales on graphs

If we look at the fuel data (from psydata) we can see that most of the columns are stored as numeric data (dbl):

fuel %>% glimpse()

Rows: 32
Columns: 7
$ mpg         <dbl> 21.0, 21.0, 22.8, 21.4, 18.7, 18.1, 14.3, 24.4, 22.8, 19.2, 17.8, 16.4, 17.3, 15.…
$ cyl         <dbl> 6, 6, 4, 6, 8, 6, 8, 4, 4, 6, 6, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 8, 8, 8, 8, 4, 4, …
$ engine_size <dbl> 2620, 2620, 1770, 4230, 5900, 3690, 5900, 2400, 2310, 2750, 2750, 4520, 4520, 452…
$ power       <dbl> 110, 110, 93, 110, 175, 105, 245, 62, 95, 123, 123, 180, 180, 180, 205, 215, 230,…
$ weight      <dbl> 1188, 1304, 1052, 1458, 1560, 1569, 1619, 1447, 1429, 1560, 1560, 1846, 1692, 171…
$ gear        <dbl> 4, 4, 4, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 4, 4, 4, 3, 3, 3, 3, 3, 4, 5, …
$ automatic   <lgl> TRUE, TRUE, TRUE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, …

This is fine if we want to make a scatter plot.

In the example below we have ‘miles per gallon’ vs the weight of cars in the fuel dataset (in psydata):

fuel %>%
  ggplot(aes(weight, mpg)) +
    geom_point()       

In this example of a scatterplot both the x and y axes are continuous. That is, we expect them to be real numbers, and they are stored as numeric columns.

However, if we want to make a boxplot of the mpg column using cyl (number of cylinders) as the x axis then we have a problem:

fuel %>%
  ggplot(aes(cyl, mpg)) +
  geom_boxplot()

Warning: Continuous x aesthetic
ℹ did you forget `aes(group = ...)`?

The warning message says Continuous x aesthetic -- did you forget aes(group=...)?. This is a clue as to what has gone wrong.

We might have expected to see;

• miles per gallon on the \(y\) axis
• three separate boxes, one each for 4, 6 and 8 cylinders

It didn’t work as expected though.

R spots that cyl is stored as numeric data, and because it doesn’t know better it creates a _continuous scale) on the \(x\) axis.

Only one box is drawn at the midpoint of all the values of cyl; because cyl ranges from 4 to 6 the box appears at 6.

Although R often has good defaults, it isn’t smart — if it doesn’t behave as we expect we need to be more specific.

Here we want to use cyl as a categorical variable, so we need to give R precise instructions. We should convert cyl to a factor explictly. Then our plot will work properly.

We can use the command factor(cyl) to tell R that the \(x\)-axis is a factor:

fuel %>%
  ggplot(aes(factor(cyl), mpg)) +
  geom_boxplot()

This gives us the boxplot we were expecting.

The only change was to replace cyl with factor(cyl). This tells R to convert the variable cyl to a factor, and ggplot() can then set the scale of the x-axis correctly.

Using filter() and summarise()

One option would be to filter our data first and then summarise each subset in turn:

funimagery %>%
  filter(intervention=="MI") %>%
  summarise(mean(weight_lost_end_trt))

This output shows us the mean for the MI group. We then have to repeat that code for the FIT group:

funimagery %>%
  filter(intervention=="FIT") %>%
  summarise(mean(weight_lost_end_trt))

This is a bit repetitive, and would worse if there were lots of categories. Imagine doing something similar for each continent in the development data, for example.

Using group_by()

Instead of using filter(), we can use group_by() to split our dataset into multiple groups, summarising each one separately:

funimagery %>%
  group_by(intervention) %>%
  summarise(mean(weight_lost_end_trt))

Using group_by() before summarise() splits up the data, in thise case depending on which intervention the participant received.

The summarise() function calculates the mean for each group separately.

The result is a new data.frame with two columns: The name of the intervention, and the average weight lost. We could save this in a new variable for use later, if we liked:

average_weight_losses <- funimagery %>%
                          group_by(intervention) %>%
                          summarise(mean(weight_lost_end_trt))

You can see the new variable in the Environment, so it’s stored for later.

Nested groups

Sometimes we might want to group by more than one variable at once.

Imagine we wanted to see if men and women responded differently to the two treatments?

With group_by() this is really easy: just add the name of another column to group on (gender), separated with a comma:

funimagery %>%
  group_by(gender, intervention) %>%
  summarise(mean(weight_lost_end_trt))

It looks like women lost a bit more weight on average

but both men and women lost more weight after FIT relative to MI.

Multiple statistics

With summarise() we can calculate multiple statistics at once for each of the groups:

funimagery %>%
  group_by(intervention) %>%
  summarise(mean(weight_lost_end_trt), sd(weight_lost_end_trt))

Here, we’ve calculated both the mean and standard deviation for each intervention.

Give your new variables a name

R gives the new columns a name based on the function we use to summarise() them.

For example, if we use mean() on the weight_lost_end_trt variable then the new column is called mean(weight_lost_end_trt).

Unfortunately, these new variable names contain parentheses and (sometimes) spaces which makes them harder to work with. It’s much better to give the new column a specific name like this:

funimagery %>%
  group_by(intervention) %>%
  summarise(mean_weight_lost_end_trt = mean(weight_lost_end_trt), sd_weight_lost_end_trt = sd(weight_lost_end_trt))

Remember, the column names you use shouldn’t include spaces or other ‘special’ characters.