Distributions, summaries and sample size

Summary

Visualising distributions requires choosing methods suited to data scale and sample size. For small n, plot raw observations (e.g. jittered dots or stripcharts). For larger n, summarise with histograms, density plots, or boxplots. Explore multiple binwidths in histograms to reveal different patterns. Show variability: include individual points or error bars (with clear notation). Avoid plotting mean±SE when n is tiny, as it hides distribution. When data are skewed, consider log-transform or nonparametric summaries.

Core rules

• Show raw data if small: If n<20, prefer dot plots (with jitter) or strip charts. Avoid smooth curves (density) unless annotated that n is small.
• Histogram binning: Try several bin widths; a too-large bin can hide structure. Label axes (count/frequency) clearly.
• Bar vs histogram: Do not use bar charts for continuous data or distribution summary (except binned frequency as histogram).
• Summary plots: Boxplots/violin plots should be supplemented by raw data points if groups are small. Label what ‘whiskers’ represent.
• Scale awareness: If using log scales, note that this compresses skewness.
• Sample size annotation: Report the number of observations or replicates on the figure (e.g. “n = 8” in subtitle or caption).

Required context

• Actual sample size in each group or category.
• Nature of distribution (normality, skewness) if known.
• Whether values represent counts, proportions, or continuous measurements.

AI behaviour

• Check n: Before choosing a plot, examine sample size. If n is low, prioritize raw-data plots.
• Bin selection: If using histograms, suggest at least two binning schemes.
• Label statistics: When summarising, annotate precisely (e.g. “median ± IQR with all data overlaid”).
• Compare appropriately: Do not overlay or compare distributions with vastly different n without adjusting scales or normalization.

Common failure modes

• Too few data: Using a violin plot on n=3 yields a misleading continuous shape.
• Large bars instead of density: Making a bar chart to show a single continuous variable’s spread.
• Hidden sample size: Showing means with error bars but omitting “n=”.
• Assuming normality: Using symmetric error bars on clearly skewed data without mention.

Authoritative standards

• R4DS guidance: “Always explore a variety of binwidths when working with histograms”.
• Statistical best practices: Align with recommendations to plot raw data points where possible (e.g. Weissgerber et al. on transparent reporting).

Examples

Example: Histogram binning

• Data: Enzyme activity levels (n=100).
• Check: Create histograms with different binwidths (e.g. 5 vs 20). Label y-axis “Frequency” and describe in caption if needed.
• Good outcome: Two side-by-side histograms showing fine vs coarse bins, illustrating stable unimodal shape.

Example: Small group dot plot

• Data: Survival fractions for 5 mice per group.
• Check: Use a dot-stripchart or beeswarm, not just group means. Add jitter to distinguish points.
• Good outcome: A plot showing individual values for each mouse; group median lines optional, but raw points visible.

Sources

• R4DS: recommendation to explore multiple binwidths in histograms.
• Data visualization best practices (Cleveland/McGill).