4.2 Essentials of EDA

If a good exploratory technique gives you more data, then maybe
good exploratory data analysis gives you more questions, or better questions.
More refined, more focused, and with a sharper point.

Roger Peng (2019), Simply Statistics

Having learned what exploratory data analysis (EDA) is and wants, we are curious to learn how to do an EDA. Our characterizations of EDA as a particular attitude, a process, and a mindset has emphasized that we must not expect a fixed recipe of steps, but rather a loose set of principles and practices to help us making sense of data.

The following sections illustrate some of the principles and practices of EDA that promote the ideal of transparent data analysis and reproducible research. While such practices are indispensable when working with a team of colleagues and the wider scientific community, organizing our workflow in a clear and consistent fashion is also beneficial for our own projects and one of the most important persons in our lives — our future self.

4.2.1 Setting the stage

Before embarking on any actual analysis, we pay tribute to 2 principles that appear to be so simple that their benefits are easily overlooked:

  • Principle 1: Start with a clean slate and explicitly load all data and all packages required.

Although the RStudio IDE provides options for saving your workspace and for loading data or packages by clicking buttons or checking boxes, doing so renders the process of your analysis intransparent for anyone not observing your actions. To make sure that others and yourself can repeat the same sequence of steps tomorrow or next year, it is advisable to always start with a clean slate and explicitly state which packages and which datasets are required for the current analysis (unless there are good reasons to deviate from them):27

Cleaning up

Clean your workspace and define some custom objects (like colors or functions):

An important caveat: Cleaning up your workspace by deleting everyting is helpful when you are starting a new file or project and want to ensure that your current file works in a self-contained fashion (i.e., without relying on any earlier or external results). However, deleting everything should be avoided if you are working on something that may become a component of another project or a part of someone else’s workflow. In these cases, deleting all objects is not just impolite and impertinent, but outright dangerous.

Loading packages and data

Different computers and people differ in the many different ways (e.g., by running different versions of R or using different packages). Being explicit which packages and data files are needed in a project makes it transparent which environment you are assuming for your current project. Similarly, explicitly loading all required data files (rather than using corresponding menu commands) reminds you and anyone else which files were actually used.

Load all required packages and data files (see Section B.1 of Appendix B for details):

If you are loading inputs from or saving outputs to subfolders (e.g., loading data files from data or saving images to images), using the here package (Müller, 2017) is a good idea. It provides a function here() that defaults to the root of your current file or project.

Customizations

If you require some special commands or objects throughout your project, it is good practice to explicate them in your file (e.g., by loading other files with the source function). In projects with visualizations, it is advisable to define some colors for promoting a more uniform visual appearance (or corporate identity). For instance, we can define a color seeblau and use it in subsequent visualizations:

Note: This color corresponds to the color Seeblau of the unikn package.

4.2.2 Clarity

Our second principle is just as innocuous, but becomes crucial as your analyses get longer and more complicated:

  • Principle 2: Structure and comment your analysis.

While mentioning or adhering to this principle may seem superfluous at first, you and your collaborators will benefit from transparent structure and clear comments as things get longer, messier, and tougher (e.g., when analyses involve different tests or are distributed over multiple datasets and scripts). A consistent document structure, meaningful object names, and clear comments are indispensable when sharing your data or scripts with others. Using R Markdown (see Appendix F for details) encourages and facilitates structuring a document, provided that you use some consistent way of combining text and code chunks. Good comments can structure a longer sequences of text or code into parts and briefly state the content of each part (what). More importantly, however, comments should note the goals and reasons for your decisions (i.e., explain why, rather than how you do something).

When trying to be clear, even seemingly trivial and tiny things matter. Some examples include:

  • Your text should contain clear headings, which includes using consistent levels and lengths, as well as brief paragraphs of text that motivate code chunks and summarize intermediate results and conclusions.

  • Messy code often works, but is just as annoying as bad spelling: yucAnlivewith outit, but it sure makes life a lot easier. So do yourself and others a favor by writing human-readable code (e.g., putting spaces between operators and objects, putting new steps on new lines, and indenting your code according to the structure of its syntax.28 Incidentally, one of the most powerful ways to increase the clarity of code is by using space: While adding horizontal space seperates symbols and allows structuring things into levels and columns, adding vertical space structures code/text into different steps/sentences, chunks/paragraphs, or larger functional units/sections. And whereas printed media typically need to cut and save characters, space comes for free in electronic documents — so make use of this great resource!

  • Use clear and consistent punctuation in your comments: A heading or comment that refers to subsequent lines should end with a colon (“:”), whereas a comment or conclusion that refers to something before or above itself should end with a period (“.”).

Yes, all this sounds terribly pedantic and nitpicky, but trust me: As soon as you’re trying to read someone else’s code, you will be grateful if they tried to be clear and consistent.

4.2.3 Safety

It is only human to make occasonal errors. To make sure that errors are not too costly, a good habit is to occasionally save intermediate steps. As we have seen, R allows us to create a copy y of some object x as simply as y <- x. This motivates:

  • Principle 3: Make copies (and copies of copies) of your data.

Making copies (or spanning some similar safety net) is useful for your objects, data files, and your scripts for analyzing them. Although it also is a good idea to always keep a “current master version” of a data file, it is advisable to occasionally copy your current data and then work on the copy (e.g., before trying out some unfamiliar analysis or command). As creating copies and then working on them is so easy, it can even save you from remembering and repeatedly typing complicated object names (e.g., plotting some variables of df rather than posPsy_p_info).

Copies of data

During a long and complicated analysis, it is advisable to save an external copy of your current data when having reached an important intermediate step. While there are many different formats in which data files can be stored, a good option for most files is csv (comma-separated-values), which can easily be read by most humans and machines. Importantly, always verify that the external copy preserves the key information contained in your current original:

Note that we will cover additional details of file paths and how to import more exotic file types when introducing the readr package (Wickham, Hester, & Francois, 2018) in the chapter on Importing data (Chapter 6).

4.2.4 Data screening

Screening data involves checking the dimensions of data, the types of variables, missing or atypical values, and the validity of observations.

Basics

What do we want to know immediately after loading a data file? Well, ideally everything, which we can set in stone as:

  • Principle 4: Know your data (variables and observations).

Realistically, the principle implies that there are some essential commands that will quickly propel us from a state of complete ignorance to a position that allows for productive exploration. Directly after loading a new file, we typically want to know:

  • the dimensions of the data (number of rows and columns),
  • the types of variables (columns) contained, and
  • the semantics of the observations (rows).

To gain an initial understanding of new data, we typically inspect its codebook (if available). For a well-documented dataset, inspecting its R documentation provides us with a description of the variables and values. The codebook of the table posPsy_AHI_CESD of the ds4psy package can be viewed as follows:

Here, we first read this data into an object AHI_CESD, create a copy df (to simplify subsequent commands without changing the data) and inspect it with some basic R commands:

We note that AHI_CESD is quite large (or rather long): The data contains 992 observations (rows) and 50 variables (columns). Most of the variables were read in as integers and — judging from their names — many belong together (in blocks). Their names and ranges suggest that they stem from questionnaires or scales with fixed answer categories (e.g., from 1 to 5 for ahi__, and from 1 to 4 for cesd__). Overall, an observation (or row of data) is a measurement of one participant (characterised by its id and an intervention value) at one occasion (characterised by the value of occasion and elapsed.days) on 2 different scales (ahi and cesd).

Unusual values

  • Principle 5: Know and deal with unusual values.

Unusual values include:

  • missing values (NA or -77, etc.),
  • extreme values (outliers),
  • other unexpected values (e.g., erroneous and impossible values).

Missing values

What are missing values? In R, missing values are identified by NA. Note that NA is different from NULL: NULL represents the null object (i.e., something is undefined). By contrast, NA means that some value is absent.

Both NA and NULL are yet to be distinguished from NaN values.

Missing data values require attention and special treatment. They should be identified, counted and/or visualized, and often removed or recoded (e.g., replaced by other values).

Counting NA values:

This shows that df does not contain any missing (NA) values.

Practice

Since we just verified that df does not contain any NA values, we create a tibble tb with NA values for practice purposes:

The following code illustrates how we can count and recode NA values:

More frequently, special values (like -66, -77 and -99) indicate missing values. To deal with them in R, we recode all instances of these values in tb as NA:

For more sophisticated ways of dealing with (and visualising) NA values, see the R packages mice (Multivariate Imputation by Chained Equations), VIM (Visualization and Imputation of Missing Values) and Amelia II.

Other unusual values: Counting cases, dropouts, outliers, and unexpected values

While dealing with missing values is a routine task, finding other unusual values involves some effort. However, discovering unusual values can also be fun, as it requires the state of mind of a detective who gradually uncovers facts — and aims to ultimately reveal the truth – by questioning a case’s circumstances or its suspects. In principle, we can detect atypical values and outliers (remember Exercise 3 of Chapter 3, for different definitions) by counting values, computing descriptive statistics, or by checking the distributions of raw values. To illustrate this, let’s inspect the data of AHI_CESD further. Since participants in this study were measured repeatedly over a range of several months, 2 good questions to start with are:

  1. How many participants were measured at each occasion?

  2. How many measurement occasions are there for each participant?

ad 1.: The first question (about participants per occasion) concerns a trend (i.e., development over time) that also addresses the issue of dropouts (observations present at some, but absent at other occasions). The number of participants per occaion can easily be computed by using dplyr or plotted by using ggplot2:

Note the similarities and differences between the 2 bar plots. Although they look almost the same (except for the automatic label on the y-axis and their title), they use completely different data as inputs. Whereas the 1st bar plot is based on the full raw data df, the 2nd one uses the summary table id_by_occ as its input data.

Practice

  • Which of the 2 plot versions would make it easier to add additional information (like error bars, a line indicating mean counts of participants, or text labels showing the count values for each category)?

ad 2.: To address the 2nd question (about the number of measurements per participant), we could try to count them in a bar plot (which automatically counts the number of cases for each value on the x-axis):

This does the trick, but the graph looks messy (as the instances on the x-axis are sorted by particpant id). A cleaner solution could use 2 steps: First compute a summary table that contains the number of cases (rows) per id, and then plot this summary table:

Note our use of the aesthetic y = n and stat = "identity" when using geom_bar: As our summary table occ_by_id already contained the counts (in n), we needed to prevent the default behavior of geom_count. If we had not done so, the resulting bar plot would have been rather boring, as it would have counted the number of n values for every id.

Practice

  • Check out the graph resulting from the following command (and explain why it looks the way it does):

Back to our bar plot (2a): The resulting graph was identical to the previous one (except for some labels) and looked just as messy. We can clean it up by changing the order of id numbers on the x-axis:

A simpler way of doing this would consist in rearranging the cases in our summary table occ_by_id and saving it as occ_by_id_2. And as showing hundreds of id values as x-axis labels makes little sense, we add a variable that simply provides the current row number to occ_by_id_2 and then plot n by row:

Our exploration shows that every participant was measured on at least 1 and at most 6 occasions (check range(occ_by_id$n) to verify this). This raises two additional questions:

  • Was every participant measured on occasion 0 (i.e., the pre-test)?

  • Was every participant measured only once per occasion?

The first question may seem a bit picky, but do we really know that nobody showed up late (i.e., missed occasion 0) for the study? Actually, we do already know this, since we counted the number of participants and the number of participants per occasion above:

  • the study sample contains 295 participants (check nrow(posPsy_p_info)), and

  • the count of participants per occasion showed a value of 295 for occasion 0 in id_by_occ.

For the record, we testify that:

To answer the second question, we can count the number of lines in df per id and occasion and then check whether any unexpected values (different from 1, i.e., n != 1) occur:

Importantly, 2 participants (8 and 64) are counted twice for an occasion (2 and 4, respectively).

Compare our counts of id_by_occ with Table 1 (on p. 4, of Woodworth et al., 2018), which also shows the number of participants who responded on each of the 6 measurement occasions): As the counts in this table correspond to ours, the repeated instances for some measurement occasions (which could indicate data entry errors, but also be due to large variability in the time inteval between measurements) were not reported in the original analysis (i.e., Table 1). This suggests that the 2 participants with repeated occasions were simply counted and measured twice on one occasion and missing from another one.

Our exploration so far motivates at least 2 related questions:

  • Are the dropouts (i.e., people present at first, but absent at one or more later measurements) random or systematic?

  • How does the number of elapsed.days correspond to the measurement occasions?

We’ll save the 1st of these questions for practice purposes (see Exercise 2 in Section 4.4.2 below). The 2nd question directs our attention to the temporal features of measurements and motivates a general principle and corresponding practice that motivates different ways of viewing the distributions of values.

4.2.5 Viewing distributions

  • Principle 6: Inspect the distributions of variables.

A simple way to get an initial idea about the range of a variable x is to compute summary(x). However, plotting the distribution of individual variables (e.g., with histograms or frequency polygons) provides a more informative overview over the distributions of values present in the data (e.g., whether the assumptions of statistical tests are met) and can provide valuable hints regarding unusual or unexpected values.

Histograms

A histogram provides a cumulative overview of a variable’s values along one dimension (see our examples in Chapter 2). Here, we use a histogram of elapsed.days to address the question:

  • How are the measurement times (elapsed.days) distributed overall (and relative to the stated times of each occasion)?

To compare the actual measurement times with our expectations, we first use summary() to get a descriptive overview of elapsed.days and plot a corresponding histogram:

This shows that the measurement times (denoted by elapsed.days) were not distributed homogeneously, but rather clustered around certain days. It seems plausible that the clusters should be located at the stated times of each occasion. To verify this, we create a vector occ_days that contains the values of our expectations regarding these occasions (based on Table 1 of Woodworth et al., 2018):

Now we can plot the distribution of elapsed.days and use the additional vector occ_days to mark our corresponding expectations by vertical lines:

Interestingly, the first three occasions are as expected, but Occasions 4 to 6 appear shifted to the left (i.e., the measurements according to elapsed.days seem to have happened about 7 days earlier than stated).

4.2.6 Filtering cases

Once we have detected something noteworthy or strange, we may want to mark or exclude some cases (rows) or variables (columns). As we can easily select rows and filter cases (see dplyr::select and dplyr::filter in the last session), it is helpful to add some dedicated filter variables to our data. Let’s use the participant data posPsy_p_info to illustrate how we can create and use filter variables:

In previous exercises —
Exercise 5 of Chapter 2) and Exercise 4 of Chapter 3) — we asked and answered the question:

  • What is the age range of participants (overall and by intervention)?

by using dplyr pipes and ggplot2 calls. For instance, we can visualize the distribution of age values by plotting histograms:

For practice purposes, suppose we only wanted to include participants up to an age of 70 years in some analysis. Rather than dropping these participants from the file, we can introduce a filter variable that is TRUE when some criterion (here: age > 70) is satisfied, and otherwise FALSE:

  • Principle 7: Use filter variables to identify and select sub-sets of observations.

The above histograms showed that our data contained cases of people whose age is over 70. We can use base R commands to count and identify those people in p_info:

Alternatively, we can use dplyr to filter the data by this criterion age > 70:

If this age criterion is important for future analyses, we could create a dedicated filter variable and add it to p_info:

In the present case, filter(over_70) is about as long and complicated as filter(age > 70) and thus not really necessary. However, defining explicit filter variables can pay off when constructing more complex filter conditions or when needing several sub-sets of the data (e.g., for cross-validation purposes). Given an explicit filter variable, we can later filter any analysis (or plot) on the fly. For instance, if we wanted to check the age distribution of participants up to 70 years:

Filter variables also allow us to quickly create sub-sets of the data:

The convenience of using filter in a dplyr pipe often renders it unnecessary to create dedicated filter variables. However, if a dataset is reduced to some subset of cases (e.g., by excluding some survey participants from an analysis, as they failed attention checks or stated that their data cannot be trusted) it is good practice to explicitly distinguish between valid and invalid cases, rather than just deleting the invalid ones.

4.2.7 Viewing relationships

Relationships are inherently interesting, even when just considering those between variables. Actually, most research hypotheses involve relationships or measures of correspondence between two or more (continuous or categorical) variables. This motivates another principle:

  • Principle 8: Inspect relationships between variables.

In practice, we can inspect relationships between variables by various types of plots that show the values of some variable(s) as a function of values or levels of others. Our choice of plots depend on the point we intend to make, but also on the types of variables that are being considered.

4.2.8 Trends and developments

A special relationship often of interest in psychology and other sciences are trends or developments: A trend shows how some variable changes over time. When studying trends or developments, the time variable is not always explicitly expressed in units of time (e.g., days, weeks, months), but often encoded implicitly (e.g., as repeated measurements).

  • Principle 9: Inspect trends over time or repeated measurements.

Trends can be assessed and expressed in many ways. Any data that measures some variable more than once and uses some unit of time (e.g., in AHI_CESD we have a choice between occasion vs. elapsed.days) can be used to address the question:

  • How do the values of a variable (or scores on some scale) change over time?

Practice

The line graph just shown used a tiny summary table (id_by_occ) as its data input.

  • Can you draw the same line plot from the AHI_CESD raw data? If yes, try imitating the following look (but remember that — irrespective of appearances — these plots are unrelated to Ikea):

4.2.10 Values by category

A measure of correspondence that is common in psychology asks whether the values of some continuous variable vary as a function of the levels of a categorical variable. With regard to our data in AHI_CESD we may wonder:

  • Do the happiness scores (ahiTotal) vary by intervention?

To visualize the relationship, we cannot use a scatterplot with the mapping x = intervention and y = ahiTotal, as there would only be 4 distinct values for x (go ahead plotting it, if you want to see it). Fortunately, there’s a range of alternatives that allow plotting the raw values and distributions of a continuous variable as a function of a categorical one:

Combinations

Sometimes combining 2 or more geoms can be more informative than just using one:

When using multiple geoms in one plot, their order matters, as later geoms are printed on top of earlier ones. In addition, combining geoms typically requires playing with aesthetics. Incidentally, note how the last plot moved some redundant aesthetic mappings (i.e., x, y, and color) from the geoms to the 1st line of the command (i.e., from the mapping argument of the geoms to the general mapping argument).

Tile plots

We already discovered that bar plots can either count cases or show some pre-computed values (when using stat = "identity", see Section 2.4.2). In the following, we show that we can also compute summary tables and then map their values to the color fill gradient of tiles, or to the size of points:

occasion n ahiTotal_mn cesdTotal_mn
0 295 69.70508 15.06441
1 147 72.35374 12.96599
2 157 73.04459 12.36943
3 139 74.55396 11.74101
4 134 75.19403 11.70896
5 120 75.83333 12.83333
occasion intervention n ahiTotal_mn cesdTotal_mn
0 1 72 68.38889 15.05556
0 2 76 68.75000 16.21053
0 3 74 70.18919 16.08108
0 4 73 71.50685 12.84932
1 1 30 69.53333 15.30000
1 2 48 71.58333 14.58333

The abrupt color change from Occasion 0 to Occasion 1 (from a brighter to darker hue of blue) illustrates the sharp drop of participant numbers in all 4 treatment conditions. The proportion of dropouts is particularly high in Intervention 3, where only 24 of 74 participants (32.4%) are present at Occasion 1. By contrast, the participant numbers per group from Occasions 1 to 5 appear to be fairly stable. (Exercise 2 — in Section 4.4.2 — addresses the issue of potentially selective dropouts.)

Let’s create a corresponding plot that maps a dependent measure (here: mean happiness scores ahiTotal_mn) to the fill color of tiles:

To facilitate the interpretation of this plot, we changed the color gradient (by using scale_fill_gradient() with two colors for low and high): The lowest average scores of happiness (or ahiTotal_mn) are shown in the color Bordeaux, the highest ones in "gold". As the scores vary on a continuous scale, using a continuous color scale is appropriate here. And assigning high happiness to “gold” hopefully makes the plot easier to interpret. The plot shows that all intervention conditions score higher happiness values as the number of occasions increase. Whereas Interventions 2 to 4 show a marked increase from Occasion 0 to 1, Intervention 1 makes its biggest step from Occasion 2 to 3.

Note that our previous line plot (called plot_ahi_by_occ_iv above) showed the same trends as this tile plot. But whereas the line plot (by mapping happiness to height y) makes it easy to see differences in the upward trends between groups, the tile plot (by mapping happiness to fill) facilitates row- and column-wise comparisons on the same dimension (color hue). Thus, informationally equivalent plots can suggest and support different interpretations and it is important to choose the right plot from a variety of options.

Practice

Create a tile plot that shows the developments of mean depression scores cesdTotal by measurement occasion and intervention. Choose a color scale that you find appropriate and easy to interpret. What do you see?

Hint: Your result could look like the following plot:

Point size plots

Another way of expressing the value of a continuous variable — like a frequency n or an average score ahiTotal_mn — as a function of 2 categorical variables is by mapping it to the size dimension of a point. In the following, we illustrate this by creating the same plot twice. First, we use the raw data (AHI_CESD) in combination with geom_count() to show the frequency of cases by occasion for each intervention:

Alternatively, we could use the data from our summary table (tab_scores_by_occ_iv, created above), and geom_point with its size aesthetic mapped to our frequency count n:

Note that — in both versions — we added two scale functions to adjust features that ggplot2 would otherwise set automatically. Specifically, we used the scale_size_area function of ggplot2 to increase the maximal size of points and the scale_y_continuous function to slightly increase the range of y-axis values.

Practice

4.2.11 Tuning plots

As the examples above have shown, most default plots can be modified — and ideally improved — by fine-tuning their visual appearance. In ggplot2, this means setting different aesthetics (or aes() arguments) and scale options (which take different arguments, depending on the type of aesthetic involved). Popular levers for prettifying your plots include:

  • colors: can be set by the color or fill arguments of geoms (variable when inside aes(...), fixed outside), or by choosing or designing specific color scales (with scale_color);

  • labels: labs(...) allows setting titles, captions, axis and legend labels, etc.;

  • legends: can be (re-)moved or edited;

  • themes: can be selected or modified.

Mixing geoms and aesthetics

In Chapter 2 (Section 2.3), we have learned that ggplot2 allows combining multiple geoms into the layers of one plot. Importantly, different geoms can use different aesthetic mappings. For instance, if we wanted to express 2 different dependent variables in one plot, we could use common mappings for the general layout of the plot (i.e., its x- and y-dimensions), but set other aesthetics (like fill colors or text labels) of 2 geoms to different variables.

For instance, we could add text labels to the geom_tile() and geom_point() plots from above. By adding geom_text() and setting its label aesthetic to a different variable (e.g., the frequency count n) we could simultaneously express 2 different continuous variables on 2 different dimensions (here fill color or size vs. the value shown by a label of text):

Similarly, adding geom_text() with the aesthetic label = n to our previous point size plot would allow expressing mean happiness scores (ahiTotal_mn) by point size and the frequency of corresponding data points (n) as text labels on the points:

Beware that mixing multiple dimensions on different geoms can quickly get confusing, even for ggplot enthusiasts. Realizing this motivates another principle and lets us conclude on a cautionary note.

Plotting with a purpose

Our last examples have shown that we should create 2 separate graphics when making multiple points or expressing more than a single relationship in a plot. This brings us to:

  • Principle 10: Create graphs that convey their messages as clearly as possible.

So go ahead and use the awesome ggplot2 machine to combine multiple geoms and adjust their aesthetics for as long as this makes your plot prettier. However, rather than getting carried away by the plethora of options, always keep in mind the message that you want to convey. If additional fiddling with aesthetics does not help to clarify your point, you are probably wasting your time by trying to do too much.

References

Müller, K. (2017). here: A simpler way to find your files. Retrieved from https://CRAN.R-project.org/package=here

Wickham, H., Hester, J., & Francois, R. (2018). readr: Read rectangular text data. Retrieved from https://CRAN.R-project.org/package=readr

Woodworth, R. J., O’Brien-Malone, A., Diamond, M. R., & Schüz, B. (2018). Data from “Web-based positive psychology interventions: A reexamination of effectiveness”. Journal of Open Psychology Data, 6(1). https://doi.org/10.5334/jopd.35


  1. Actually, listing everything required to execute a file can get quite excessive (check out sessionInfo() or the session_info and package_info functions of devtools, in case you’re interested, and consider using the packrat package in case you want to preserve or share your current setup). Hence, most people only explicitly list and load non-standard packages (in their currently installed version).

  2. RStudio helps with writing well-structured and clean code by providing foldable sections (by typing repeated characters, like ----) or automatic shortcuts (e.g., see the keyboard shortcuts for automatic indenting and un-/commenting).