GPTomics/bio-data-visualization-distribution-plots

Version Compatibility

Reference examples tested with: ggplot2 3.5+, ggbeeswarm 0.7+, ggdist 3.3+, gghalves 0.1.4+, seaborn 0.13+, matplotlib 3.8+, ptitprince 0.3+ (Python raincloud).

Before using code patterns, verify installed versions match. If versions differ:

• Python: pip show <package> then help(module.function) to check signatures
• R: packageVersion('<pkg>') then ?function_name to verify parameters

If code throws ImportError, AttributeError, or TypeError, introspect the installed package and adapt the example to match the actual API rather than retrying.

Distribution Plots

"Plot the distribution per group" -> Render boxplot, violin, beeswarm, or raincloud calibrated to N per group, the underlying distribution shape, and the audience's ability to read each encoding. The default geom_bar(stat='summary') is the canonical misleading choice — Weissgerber 2015 PLOS Biol documented that 703 top physiology papers use bar-of-mean despite multiple distinct distributions producing identical bars.

• R: ggplot2::geom_boxplot, ggplot2::geom_violin, ggbeeswarm::geom_quasirandom, ggdist::stat_halfeye, gghalves::geom_half_violin
• Python: seaborn.boxplot/violinplot/swarmplot/stripplot, ptitprince.RainCloud

The Single Most Important Modern Insight -- Bars of Means Lie

Weissgerber, Milic, Winham & Garovic 2015 PLOS Biol 13:e1002128 surveyed 703 papers in top physiology journals and found that bar-and-line graphs of means dominate, despite many distinct distributions producing identical bar plots. Bimodal data, skewed data, and data with outliers all collapse to the same bar height and error bar. The bar plot is a hypothesis test result rendered as visualization; the visualization should show the data.

The modern alternative is to show every point for n < 30, layer summary on top, and reserve summary-only plots for large N where points would overplot.

Decision Tree by N per Group

| N per group | Recommended | Avoid | |-------------|-------------|-------| | 3-10 | Dot plot or jittered raw points + median bar | Bar of mean | | 10-30 | Beeswarm OR quasirandom + box overlay | Bare boxplot (hides bimodality) | | 30-200 | Raincloud (Allen 2019) OR box + jitter | Bare violin (default KDE bandwidth oversmooths) | | 200-1000 | Letter-value plot (Hofmann 2017) OR violin with explicit bandwidth | Box alone (collapses tails) | | >1000 | Density (KDE) or histogram + summary stats | Individual points (overplot) |

Always annotate N somewhere on the plot (caption, x-axis tick label, or stratum count).

Box, Violin, Beeswarm, Raincloud -- The Four Standard Encodings

Boxplot (Tukey 1977) -- summary only

ggplot(df, aes(group, value, fill = group)) +
    geom_boxplot(outlier.shape = NA, alpha = 0.7, width = 0.5) +
    geom_jitter(width = 0.2, alpha = 0.5, size = 1) +
    scale_fill_manual(values = c('#0072B2', '#D55E00')) +
    labs(x = NULL, y = 'Expression') +
    theme_classic()

Box shows: median, IQR, 1.5×IQR whiskers, outliers. Hides: bimodality, sample size, density.

Notched boxplot (notch = TRUE): notches show 95% CI for median (±1.58·IQR/√n); non-overlapping notches roughly indicate distinct medians. Use with N ≥ 15.

Violin -- density + summary

ggplot(df, aes(group, value, fill = group)) +
    geom_violin(alpha = 0.7, trim = FALSE,
                bw = 'SJ') +                            # Sheather-Jones bandwidth
    geom_boxplot(width = 0.1, fill = 'white', outlier.shape = NA) +
    scale_fill_manual(values = c('#0072B2', '#D55E00'))

KDE bandwidth pitfall: ggplot's default is Silverman's rule of thumb, which oversmooths bimodal data into a single mode. Use bw = 'SJ' (Sheather-Jones plug-in) for honest representation of multimodality.

trim = TRUE (default) cuts the violin at the data range — visually misleading because the violin's tails imply density extending beyond the data. trim = FALSE lets the KDE extend.

Beeswarm / quasirandom -- every point shown deterministically

library(ggbeeswarm)
ggplot(df, aes(group, value, color = group)) +
    geom_quasirandom(method = 'quasirandom', width = 0.3, alpha = 0.7) +
    scale_color_manual(values = c('#0072B2', '#D55E00')) +
    stat_summary(fun = median, geom = 'crossbar', width = 0.5, color = 'black')

Quasirandom (van der Corput sequence; Bostock implementation) gives reproducible jitter that fills space without random scatter. Beeswarm is similar but with collision avoidance. Both are deterministic — reruns produce identical layouts.

Raincloud (Allen 2019) -- distribution + summary + raw

Goal: Show distribution (half-violin), summary (boxplot), and raw observations (jittered points) in a single per-group panel without occlusion.

Approach: Place a half-violin on one side, a thin boxplot in the middle, and jittered points on the other side via gghalves::geom_half_violin + geom_boxplot + geom_half_point with position_nudge offsets; flip to horizontal so the visual reads as a literal raincloud.

library(gghalves)
ggplot(df, aes(group, value, fill = group, color = group)) +
    geom_half_violin(side = 'r', alpha = 0.7, position = position_nudge(x = 0.15)) +
    geom_boxplot(width = 0.15, outlier.shape = NA, alpha = 0.7,
                 position = position_nudge(x = -0.05)) +
    geom_half_point(side = 'l', alpha = 0.5, size = 1.5, range_scale = 0.4,
                    position = position_nudge(x = -0.2)) +
    scale_fill_manual(values = c('#0072B2', '#D55E00')) +
    scale_color_manual(values = c('#0072B2', '#D55E00')) +
    coord_flip()                                          # horizontal "raincloud"

import ptitprince as pt
import seaborn as sns
pt.RainCloud(x='group', y='value', data=df,
             palette=['#0072B2', '#D55E00'],
             bw='scott', cut=0,                          # bandwidth + trim
             width_viol=0.6, orient='h')

Raincloud = half-violin (distribution) + boxplot (summary) + jittered raw points. Allen 2019 Wellcome Open Res 4:63 — modern publication default for N 30-200.

Letter-value plot (Hofmann-Wickham 2017)

library(lvplot)
ggplot(df, aes(group, value, fill = group)) +
    geom_lv(k = 5, alpha = 0.7) +
    scale_fill_manual(values = c('#0072B2', '#D55E00'))

Extends Tukey's boxplot via additional letter-value quantiles (Hofmann, Wickham, Kafadar 2017 J Comput Graph Stat 26:469). For large N, the standard boxplot collapses tail structure; letter-value preserves it.

sns.boxenplot(x='group', y='value', data=df,
              palette=['#0072B2', '#D55E00'])             # seaborn calls it boxenplot

Stacked / split violin (paired comparisons)

library(introdataviz)               # split-violin geom
ggplot(df, aes(group, value, fill = condition)) +
    geom_split_violin(alpha = 0.7) +
    geom_boxplot(width = 0.15, position = position_dodge(0.5), outlier.shape = NA)

For 2-condition comparison within each group, split-violin shows both densities back-to-back. More compact than dodged violins.

Per-Method Failure Modes

Bar of mean with SEM

Trigger: geom_bar(stat = 'summary') + geom_errorbar(stat = 'summary', fun.data = mean_se).

Mechanism: Mean ± SEM collapses all distributional information; reader cannot assess bimodality, skew, or N.

Symptom: Reviewer asks to "show the data"; the figure must be redone.

Fix: Replace with raincloud, beeswarm, or boxplot+jitter. Show points for N < 30.

Violin with default Silverman bandwidth oversmooths bimodality

Trigger: geom_violin() without specifying bw.

Mechanism: Silverman's rule of thumb assumes unimodal Gaussian; oversmooths bimodal data into a single peak.

Symptom: Single-cell expression bimodality (off / on) renders as a unimodal violin; biologically false.

Fix: bw = 'SJ' (Sheather-Jones plug-in) for honest bimodality. Note: nrd0 IS Silverman; nrd (Scott) oversmooths less than Silverman but Sheather-Jones is preferred.

Notched boxplot with too-small N

Trigger: notch = TRUE with N < 15 per group.

Mechanism: Notch can extend beyond Q1/Q3, producing visually-misleading "inside-out" notches.

Symptom: ggplot warning ("notch went outside hinges"); notches look weird.

Fix: Use notches only with N ≥ 15. For smaller N, show raw points instead.

Boxplot hides outliers when jittered points are overlaid

Trigger: geom_boxplot() + geom_jitter() with default outlier.shape = 19.

Mechanism: Outliers render twice — once from boxplot (large dots), once from jitter (smaller dots) — visually duplicated.

Symptom: Some points appear bigger than others without reason.

Fix: geom_boxplot(outlier.shape = NA) when overlaying raw points.

Trim = TRUE on violin misleads about tails

Trigger: geom_violin() default trim = TRUE.

Mechanism: Default trims violin at the data range; the visual still shows narrowing "tails" implying density extends slightly beyond the data.

Symptom: Reader infers density beyond observed range.

Fix: trim = FALSE to let KDE extend, OR explicitly cap with coord_cartesian. Document the choice.

No N annotation

Trigger: Boxplot with no N per group reported.

Mechanism: Reader cannot assess statistical power; tiny N looks identical to large N at this encoding.

Symptom: Reviewer requests "show N per group."

Fix: Add N to x-axis tick label (Control (n=12)) or use stat_summary(geom='text', fun.data = function(x) data.frame(label = paste('n=', length(x)))).

Wide raincloud at small N

Trigger: Raincloud applied with N = 5 per group.

Mechanism: KDE with N=5 is meaningless; violin shape is artifact of bandwidth.

Symptom: Smooth violin from 5 points; misleads about underlying distribution.

Fix: For N < 30, drop the violin half; use box + raw points only.

Reconciliation: When Encodings Disagree

| Pattern | Cause | Action | |---------|-------|--------| | Bar of mean shows clear separation; raincloud shows overlapping distributions | Bars hide overlap | Use raincloud; bars exaggerate effect | | Violin shows unimodal; histogram shows bimodal | Default Silverman bandwidth oversmooths | Re-render with bw = 'SJ' | | Boxplot medians look distinct; t-test n.s. | Boxplot of small N is unreliable | Show raw points; rerun with appropriate non-parametric test | | Notched boxplot notches non-overlap; rank test n.s. | Notch is an approximation, not a hypothesis test | Notches are heuristic only; use formal test |

Operational rule: for N < 30, show every point. For N 30-200, raincloud. For N > 200, letter-value or violin with explicit bandwidth. Always annotate N.

Quantitative Thresholds

| Threshold | Value | Source | |-----------|-------|--------| | N for valid notched boxplot | ≥15 | Common practice | | N to show raw points | <30 | Weissgerber 2015 | | N where violin > box | >30 (with explicit bandwidth) | Visualization guidance | | Whisker length (Tukey) | 1.5 × IQR | Tukey 1977 | | Notch length (McGill 1978) | ±1.58 × IQR / sqrt(N) | McGill 1978 | | KDE bandwidth (Sheather-Jones) | plug-in selector | Sheather-Jones 1991 |

Common Errors

| Error / symptom | Cause | Solution | |-----------------|-------|----------| | Bimodal data shown as unimodal violin | Default Silverman bandwidth | bw = 'SJ' | | Duplicate large points on box + jitter | outlier.shape not suppressed | geom_boxplot(outlier.shape = NA) | | Notches "inside-out" | N too small | Show raw points; remove notch | | Raincloud looks smooth at N=5 | KDE meaningless at small N | Drop violin half; box + points only | | No N visible | Default boxplot | Add n=... to x label or stat_summary text | | Violin tails extend beyond data | trim = TRUE default + KDE bandwidth | trim = FALSE and cap with coord_cartesian | | Bar of mean criticized in review | Weissgerber 2015 default failure | Replace with raincloud or box+jitter |

References

• Allen M, Poggiali D, Whitaker K, Marshall TR, van Langen J, Kievit RA. 2019. Raincloud plots: a multi-platform tool for robust data visualization. Wellcome Open Res 4:63. doi:10.12688/wellcomeopenres.15191.1
• Hofmann H, Wickham H, Kafadar K. 2017. Letter-value plots: boxplots for large data. J Comput Graph Stat 26(3):469-477. doi:10.1080/10618600.2017.1305277
• McGill R, Tukey JW, Larsen WA. 1978. Variations of box plots. Am Stat 32(1):12-16.
• Sheather SJ, Jones MC. 1991. A reliable data-based bandwidth selection method for kernel density estimation. J R Stat Soc B 53(3):683-690.
• Streit M, Gehlenborg N. 2014. Points of view: Bar charts and box plots. Nat Methods 11(2):117.
• Tukey JW. 1977. Exploratory Data Analysis. Addison-Wesley.
• Weissgerber TL, Milic NM, Winham SJ, Garovic VD. 2015. Beyond bar and line graphs: time for a new data presentation paradigm. PLOS Biol 13(4):e1002128. doi:10.1371/journal.pbio.1002128

Related Skills

• data-visualization/statistical-annotation - Add p-value brackets to distribution plots
• data-visualization/color-palettes - CVD-safe categorical palettes
• data-visualization/ggplot2-fundamentals - Grammar of graphics base
• single-cell/markers-annotation - Stacked / split violin for scRNA gene-by-cluster
• clinical-biostatistics/effect-measures - Effect size to accompany distribution