Data Visualization — MSMB Chapter 3 (summary)

Own-words summary of an external source (see frontmatter for license/attribution). Not a substitute for the original chapter.

1. Scope

This chapter equips a reader to choose and construct data visualizations for exploratory analysis and for publication, with emphasis on visual displays of distributions and relationships in biological measurement data. It covers a small set of canonical plot types for one and two variables, a compositional framework (the grammar of graphics) for reasoning about and assembling plots, techniques for showing more than two dimensions, principled use of color, axis/scale transformations, and displays organized along genomic coordinates. The recurring concern is honesty: which displays faithfully convey the structure of a sample (its modes, skew, tails, density) and which create artifacts or hide information, so that a reader picks an effective, non-misleading display rather than defaulting blindly.

2. Concepts & Methods

Two graphics paradigms. Procedural / canvas-based plotting (base R graphics) draws specialized plots directly onto a canvas; simple for quick exploration but hard to compose or modify. Grammar of graphics (implemented in ggplot2, after Wilkinson) instead describes a plot as a declarative object built from modular pieces, which can be assembled, stored partially, and refined incrementally (via the + operator). The latter is the chapter’s main tool.
Grammar-of-graphics components. A plot is specified by: (1) one or more datasets (expected in a tidy dataframe/tibble, one row per observation); (2) geometric objects (geoms — points, lines, bars, rectangles, contours) that visually represent data; (3) aesthetic mappings from variables to visual properties (position on $x$ / $y$ , color, fill, shape, size, transparency $\alpha$ ), each with an associated scale (e.g. linear, logarithmic, rank); (4) a coordinate system (Cartesian by default; alternatives include polar); (5) statistical summarization rules (stats — identity, count/binning, mean, smoothing); (6) a facet specification; (7) layout/theme parameters. Items (1)–(3) are required; (4)–(7) default sensibly. Geoms carry default stats (a histogram geom bins; a smooth geom fits and draws a curve). The same component type may be used repeatedly as layers, overlaying e.g. points, a smoother, and a confidence band on the same data.
One-dimensional distribution displays, ordered roughly from least to most informative:
- Barplot of a summary (e.g. mean): reduces a whole sample to one number; loses shape information.
- Boxplot: compact five-number-style summary (median, quartiles, whiskers, outliers); shows location, spread, and skew via the position of the median within the box.
- Dot plot / beeswarm plot: shows individual points, perturbed to avoid overlap (dot plots bin one axis and stack; beeswarm shifts overlapping points sideways).
- Density plot: a smoothed estimate of the underlying data-generating density.
- Violin plot: a density estimate drawn as a symmetric shape, arranged like a boxplot for comparing several groups.
- Ridgeline plot: stacked density curves, suited to comparing many ( $\sim$ dozens of) distributions.
- ECDF plot: the empirical cumulative distribution function.
CDF and ECDF. The cumulative distribution function of a one-dimensional random variable is $F(x)=P(X\le x)$ ; the density is its derivative where it exists. The finite-sample analogue is the ECDF, $F_n(x)=\frac{1}{n}\sum_{i=1}^{n}\mathbb{1}(x_i\le x)$ , i.e. the fraction of observed values $\le x$ , where $\mathbb{1}$ is the indicator function. Equivalently, plotting sorted values against their ranks traces the ECDF.
Two-dimensional displays (scatterplots and density). A plain scatterplot maps two variables to the two screen axes. For large samples, dense regions overplot; remedies are point transparency ( $\alpha$ ), a 2D kernel density estimate shown as contours or filled polygons (controlled by a smoothing bandwidth and binning), or hexagonal binning (counts of points per hexagonal cell, mapped to color) — the last avoids smoothing-induced loss of isolated points.
More than two dimensions. Extra variables can map to additional aesthetics (color, shape, size, $\alpha$ ) — in principle up to several, but legibility collapses quickly. Faceting (a.k.a. trellis/lattice) instead splits the data by one or two variables into a grid of small multiples, each panel sharing a common construction, enabling 4–5 dimensions to be read by comparison. Continuous variables can be faceted after discretizing (equal-width bins via cutting, or equal-count bins via quantiles/ranks). Using a factor on an axis is a form of implicit faceting.
Color. Color perception is three-dimensional. Two parameterizations appear: RGB (three channels in $[0,1]$ , a point in a unit cube; hex triplets are this in base-256), and HCL (hue $H\in[0,360]$ , chroma $C\ge 0$ , luminance $L\in[0,100]$ ; polar coordinates in a perceptual CIE-LUV space, with the maximum $C$ depending on $H$ and $L$ ). Palettes (e.g. RColorBrewer) fall into three kinds matched to data type: qualitative (unordered categories), sequential (low→high), diverging (a meaningful midpoint with deviations both ways). Color-wheel constructions (complementary, triadic, tetradic, analogous, split-complementary, warm/cool) give harmonious sets.
Heatmaps. Display a large matrix as a grid of colored cells; rows/columns are typically reordered by hierarchical clustering, with the resulting dendrograms drawn at the margins. Often shown on centered/relative values (each row minus its mean) with a diverging palette centered at zero.
Data transformations of scales. The logarithm maps multiplicative change to additive distance ( $\log(ax)=\log a+\log x$ ), spreading out data huddled near zero with a long tail. The rank transformation replaces values by their order statistics, equalizing density along an axis. Both can be applied to position aesthetics and to color scales.
Genomic / along-sequence displays. Genomic data carry coordinates (sequence name, interval, strand), a natural integrating axis. Displays include ideograms, karyograms, and read pile-ups; the challenge is the range of scales from whole genome to nucleotide. Coordinate-associated data are held in interval/range structures (e.g. a GRanges-style object).

3. When It Applies

Exploration vs. presentation: fast, low-ceremony plotting fits interactive exploration; the compositional grammar fits building refined, reproducible, publication figures and trying alternatives cheaply.
Choosing a 1D display by sample size and distribution shape: boxplots suit unimodal samples and compact side-by-side comparison; when the distribution may be multimodal, long-tailed, or skewed, or has large outliers, prefer displays that show the data or full density (dot/beeswarm, density, violin, ridgeline, ECDF). Show individual points when the count is small enough; use beeswarm/violin/ridgeline as counts and number of groups grow.
ECDF is the recommended choice when a faithful, assumption-light view of a distribution is wanted, especially comparing several samples or differing sample sizes.
2D dense data: as point count rises, move from raw points → transparency → 2D density contours/fills → hexagonal binning; add back individual points to recover sparse-region outliers.
Encoding extra dimensions: prefer one or two added aesthetics, or faceting, over piling on many aesthetics.
Color kind must match variable kind: qualitative palette for unordered categories, sequential for ordered magnitudes, diverging for signed deviations about a midpoint (e.g. fold changes about zero).
Transform a scale when points are huddled with sparse remaining space (sharp peak, long tail): log for multiplicative/positive data; rank when even log leaves the distribution very uneven or when a monotone but density-equalizing view is wanted.
Aspect ratio matters: use equal data-to-space mapping when both axes share units (e.g. log-expression vs. log-expression, or PCA components after an orthonormal rotation); banking (setting the aspect so typical line slopes are near $\pm 1$ ) reveals fine line-shape structure that an unbanked plot hides.

4. Assumptions & Validity Conditions

Grammar-of-graphics input shape: functions expect tidy dataframe input (one observation per row, variables in columns); other layouts (matrices, separate vectors) must be reshaped first.
Mean as a summary (barplot of means, normal-theory error bars) presupposes the mean is an appropriate summary — i.e. roughly unimodal, not highly skewed, without large outliers.
Density estimation depends on a chosen smoothing window/bandwidth; the estimate is only as trustworthy as that choice (see failure modes). A density curve also presumes enough data to support it, and silently does not encode how much.
2D density contours/fills likewise rest on bandwidth and binning choices.
ECDF assumes only that the ordering of values matters and their sequence/index does not; under that, it is essentially assumption-free and lossless.
Heatmap row/column order by clustering assumes a chosen clustering method and distance; the ordering is not unique.
Log transform requires strictly positive values (zeros/negatives break it).
Banking presumes the data approximately follow a line whose slope is informative.

5. Failure Modes & Invalidity Patterns

Barplots of means hide the distribution. Warning sign: a bar (optionally with error bars) standing in for a whole sample. Consequence: skew, multimodality, outliers, and sample size are invisible; when the mean is not a fair summary the plot is outright misleading. Fix: show the data or the full distribution.
Density-plot bandwidth trap. A window too small yields unstable, “wiggly” spurious peaks in sparse regions; too large smooths away real sharp peaks. Consequence: apparent modes that are artifacts of smoothing, or real features erased. The empirical density of a finite sample is, unsmoothed, a sum of Dirac spikes — far from any smooth truth — and smoothing’s distortion is hard to control. Detection/mitigation: prefer the ECDF (converges to the true CDF as $n$ grows, with small finite-sample gap, and needs no bandwidth); vary the bandwidth and check stability.
Multimodality is not transformation-invariant. Reading a histogram/density for bimodality as evidence of an underlying mechanism is fragile: the number and location of modes depend on the scale the data are plotted on. Under a nonlinear monotone transform $f$ the density transforms by the chain rule, $\tilde p(x)=p(f(x))\,f'(x)$ , and a mode of one variable is generally not a mode of the transformed variable (the two coincide only when $f$ is affine, $f''\equiv 0$ ). Consequence: a “biological” bimodality may be an artifact of working in, say, raw vs. log units. Detection: check whether the modal structure survives plausible rescalings.
Overplotting hides density. A dense scatter cloud reads as a featureless mass; outskirts are interpretable but interior structure is not. Even with transparency, dense regions saturate to black while isolated points fade. Density/contour/hex methods cure the interior but can drop sparse-region outliers — a complementary information loss. Remedy: combine (e.g. density fill plus added points).
Density-vs-coordinate visual artifact. An apparent trend in $y$ versus $x$ — e.g. variance of one quantity seeming to depend on another — can be a pure consequence of uneven point density along $x$ (more points where $x$ is small), not a real dependence. Detection: re-plot against the rank of $x$ (which equalizes density); if the apparent trend vanishes, it was an artifact. (Density-/bin-based displays can also mitigate it.)
Dendrogram ordering is arbitrary. Heatmap impressions depend heavily on row/column order, yet clustering order is one of many valid choices, and at every internal branch the two children can be flipped without changing the tree’s topology. Consequence: “patterns” may be artifacts of arbitrary layout decisions rather than real structure. (Assessing whether clusters are real is deferred to later material.)
Regression/smoother lines can mislead. Overlaying a fitted line/smoother on a scatterplot is not always meaningful (the chapter flags this as a question to consider), e.g. when the relationship or the line’s assumptions don’t fit the data.
Faceting with adaptive axes trades detail for comparability: per-panel free scales reveal within-panel detail but make panels not directly comparable.
Default laziness and over-decoration. Two opposite failures: using software defaults unthinkingly (e.g. legacy palettes, lexicographic category order, default aspect), and adding “visual candy” that clutters without conveying a message.

6. Empirical Checks & Calibration

Simulate under a known truth to expose artifacts. The chapter’s diagnostic for the density-vs-coordinate trap is to pair a real variable with a simulated response drawn independently (so the truth is “no dependence”); the raw scatter still looks dependent, and re-plotting against rank confirms the apparent trend was a density artifact. This is the central simulate-under-known-truth check: generate data with the property you want to test for absent, and verify the display does not invent it.
ECDF as a calibration-friendly reference. Because $F_n$ converges to the true $F$ and stays close even at modest $n$ , comparing an ECDF to a hypothesized CDF — or comparing several ECDFs — gives an assumption-light read on distributional differences; pass = curves track the reference / each other, fail = systematic separation.
Bandwidth sensitivity check. Vary the smoothing bandwidth (and binning) of density/contour estimates; features that appear or vanish across reasonable settings are not trustworthy.
Scale-transform sensitivity check. Re-examine modality and apparent relationships under log and under rank transforms; conclusions that flip are scale artifacts, not findings.
Aspect-ratio (banking) check. Compute a target aspect (e.g. so the median absolute slope is $1$ ) and compare to the default; structure that only emerges at the banked aspect was being hidden.
Color palette suitability check. Palette metadata flags which palettes are colorblind-safe; choosing by data kind (qualitative/sequential/diverging) and by colorblind-safety is a calibration of the display to its readers and its variable type.

7. Interpretation, Guidance & Trade-offs

Match the display to the message and to the data’s shape. The plot type (geom), the proportions/aspect ratio, and the colors are the main levers; choose them deliberately rather than by default.
Prefer showing data or full distributions over single-number summaries when space allows; a boxplot is strictly more informative than a bar-of-means in the same footprint, and point/density/ECDF displays more still.
Read distribution displays honestly: a median’s position in a box indicates skew direction; a density curve does not tell you how much data backs it (so curves from very different sample sizes are not equally reliable); an ECDF is lossless up to ordering and is the safest default for comparison.
Treat modes, trends, and clusters as hypotheses, not conclusions until checked against scale transforms (modes/trends), density/rank re-plots (trends), and clustering validity (heatmap blocks).
Transform trade-offs: the log scale has a clean interpretation (equal steps = equal multiplicative change) but fails on non-positive data; rank equalizes density and removes density artifacts but discards the magnitude metric.
Aspect ratio: keep equal data-to-space mapping when axes share units; for line-like data consider banking; PCA plots are usually wider than tall because later components carry no more variance than earlier ones.
Color guidance: use dark, high-contrast colors (low luminance) for lines/points against a light background, and lighter, low-to-moderate-chroma pastels for area fills; holding chroma and luminance fixed while varying hue yields balanced palettes and avoids irradiation illusions where light areas look larger; favor colorblind-safe palettes.
Vector vs. raster output: prefer vector formats (e.g. PDF) for plots — they rescale without pixelation and can always be rasterized later, whereas the reverse is hard.
Interactivity trade-off: browser-/server-backed interactive plots add expressivity but some require a live computing session behind them, whereas a static or self-contained file needs none — a portability cost to weigh.
Report/hold fixed for trustworthiness: the smoothing bandwidth, binning, scale transformation, aspect ratio, and clustering/ordering choices all materially shape what a reader sees and should be deliberate (and, implicitly, disclosed).

8. Connections & Key Terms

Builds on: the notion of a random variable and its distribution (CDF, density), summary statistics (mean, median, quartiles), and the idea of estimating a population quantity from a finite sample. Sets up: clustering and assessment of cluster significance (foreshadowed by dendrogram caveats); dimension reduction such as principal component analysis (aspect-ratio discussion); count-data and fold-change analyses (log scales, MA-style displays); and downstream work on data representation/tidying and on genomic-coordinate data structures. The deeper through-line is that visualization is an inferential act whose choices must be checked empirically, not trusted by default.

Key terms:

Grammar of graphics — a compositional framework that describes a plot as data + geoms + aesthetic-to-scale mappings (+ coordinates, stats, facets, theme), enabling modular construction.
Geom (geometric object) — the visual mark representing data (point, line, bar, contour, polygon, …).
Aesthetic — a mapping from a data variable to a visual property (position, color, shape, size, transparency).
Scale — the rule converting data values to an aesthetic’s units (linear, logarithmic, rank).
Stat (statistic) — any function of the data computed for display (identity, count/bin, mean, smooth).
Layer — one geom+stat combination; multiple layers overlay on shared data.
Facet (trellis/lattice) — small multiples obtained by splitting data on one or more variables.
CDF — $F(x)=P(X\le x)$ , the probability of being at most $x$ .
ECDF — $F_n(x)$ , the sample fraction of values $\le x$ ; converges to $F$ and is lossless up to ordering.
Density estimate — a smoothed approximation of the data-generating density; depends on a bandwidth.
Bandwidth / smoothing window — the tuning parameter controlling how much a density (or 2D contour) is smoothed.
Overplotting — loss of visible structure when many marks coincide in dense regions.
Hexagonal binning — counting points in hexagonal cells and color-mapping the counts, an unsmoothed density display.
Boxplot / violin / ridgeline / beeswarm — distribution displays trading off compactness against how directly they show data and shape.
Banking — choosing the aspect ratio so typical line slopes are near $\pm 1$ , revealing line-shape detail.
RGB / HCL color models — coordinate systems for the three-dimensional space of color (channel intensities vs. hue–chroma–luminance).
Qualitative / sequential / diverging palette — palette families matched to unordered, ordered, and signed-about-a-midpoint variables.
Dendrogram — the tree from hierarchical clustering used to order heatmap rows/columns; its branch flips and method choice make the order non-unique.
Rank transformation — replacing values by their order positions, equalizing density along an axis and exposing density-driven artifacts.
Genomic coordinates / range object — sequence-name + interval + strand annotation that serves as the organizing axis for along-genome displays.