Showing uncertainty

An estimate without its uncertainty invites the reader to treat it as exact. An interval without a label is worse: SD and SE differ by a factor of √n, and a 95% CI is about ±2 SE (1.96 for a normal approximation), so the same data can give three very different bars and the reader cannot tell which they are looking at.

Rule 1: every interval states five things

1. Kind: standard deviation, standard error, confidence interval, credible interval, prediction interval, min–max, or quantile range.
2. Level: 50%, 80%, 95%; or "±1 SD".
3. n and the unit of replication: 5 training seeds; 212 orders; 14 weeks. Not "n = 3 runs" when the runs share a seed.
4. Method: normal approximation, Wilson, bootstrap (percentile, stratified), posterior from model X.
5. What it is about: the mean, a single future week, the difference.

Caption pattern: "Shaded: 80% prediction interval for weekly orders from forecast model v3 (trained to 28 Sep 2026). Points: observed."

Rule 2: uncertainty is computed by analysis, never by the figure

The plotting layer draws intervals it is given. It does not widen, symmetrise, smooth or invent them. If no interval exists, the figure says "no uncertainty estimate available" rather than drawing a decorative band.

Rule 3: pick the display for the reader

Reader and question	Display
Analyst comparing a few estimates	point + interval (error bar), raw points if n is small
Time series with forecast	line + band, widening with horizon; fan chart for several levels
Non-technical decision maker ("how likely are we to exceed 250 orders?")	quantile dotplot or a stated probability; frequencies ("in 8 of 10 simulated Septembers")
Many plausible trajectories	ensemble of thin lines, or hypothetical outcome plots (animated draws)
Distribution of a model metric across seeds	dots for each seed, with the summary marked

Research on lay readers (Kay et al. 2016; Fernandes et al. 2018; Hullman et al. 2015) found frequency-framed displays such as quantile dotplots and hypothetical outcome plots support better probability judgements than error bars alone. Use them where a decision depends on a probability.

Rule 4: comparisons need the interval of the difference

• Two SE bars that do not overlap do not establish a significant difference; two 95% CIs that overlap slightly do not establish its absence. For paired data (same eval items, same weeks) overlap says almost nothing.
• If the claim is "B beats A", compute and show the interval of B − A, paired where the design is paired.

Rule 5: respect the bounds of the quantity

A rate cannot leave 0–100%; a count cannot go negative. Symmetric ±1.96·SE bars on 2 of 10 cancellations give −5% to 45%. Use an interval that respects the bounds: Wilson 95% for 2/10 is about 5.7% to 51.0%. Report it, and question whether a rate on n = 10 belongs in the chart at all.

Rule 6: precision follows uncertainty

Round the estimate to the interval's precision: "conversion 24% (95% CI 20–28%)", not "24.37%". See numbers-style.

ieeVisualizer: what exists and what is planned

• Intervals (spec 1.0): a band mark (y_lower/y_upper along x), an errorbar mark (with the point y when encoded), and y_lower/y_upper on line (drawn as a band), scatter and vertical bar marks (error bars). Every interval needs interval_kind (confidence / credible / prediction / quantile / min-max / standard-error / standard-deviation) and interval_level as a fraction (0.95) for the first four, or interval_multiplier (1 = ±1 SE) for SE/SD bars; a quantile level is central (0.8 = 10th-90th percentile), interval_quantiles [0.05, 0.75] states a non-central one; validate refuses one without (missing_interval_kind, missing_interval_level), and lower above upper (interval_inverted) or a bound in another unit (interval_unit_mismatch). The renderer writes "95 % prediction interval" in the legend (or the caption when the legend is hidden) and draws bounds as given; a null bound is a gap.
• Templates: timeseries 2.0.0 takes intervals (several levels make a fan chart); fan_chart draws nested quantile bands from an ensemble's paths (empirical quantiles, a level refused when its tail is thinner than one path) or from given quantile columns; estimate_comparison draws estimates with intervals across groups; distribution shades "central 90% of the distribution (P5–P95)" of a named distribution (a discrete one also says what it really covers); sample_distribution draws a histogram with a KDE whose bandwidth is stated, an ECDF, or a quantile dotplot. timeseries 1.0.0's lower_column/upper_column still draw two unlabelled dotted lines: state the kind and level in the caption there.
• Simulated ensembles: ieeVisualizer.stochastic (random_walk, gbm) records the seed and marks the data synthetic; fan_chart says so in the caption. Say how many paths and which model.
• Still yours to state: n, the unit of replication and the method (Rule 1, items 3-5) have no field; put them in the caption.
• Planned (ROADMAP "Phase 2 onward"): an ensemble mark for many trajectories (thin lines per path).

Good / bad

Bad: "Model B: 71.3% ± 1.2" (which ±? over what?). Good: "Model B: 71.3% (mean of 5 seeds; 95% bootstrap CI 70.1–72.4%)".

Bad: forecast line extending three months with no band and a solid style. Good: dashed forecast with 50% and 80% prediction bands, caption naming the model and training cut-off.

Bad: grey band on the orders chart labelled "uncertainty". Good: "Band: 90% range of weekly orders in 2023–2025 for the same week" (a historical range, labelled as such, not a confidence interval).

Checklist

• Every interval names kind, level, n (unit of replication), method, and target.
• Intervals come from the analysis; nothing widened or invented in plotting.
• Display matches the reader (frequency framing for lay decisions).
• Comparative claims use the interval of the difference (paired if paired).
• Bounded quantities use bounded intervals.
• Reported precision matches the interval width.
• If no estimate of uncertainty exists, the figure says so.

Adapted in part from ieeVisualizer's own docs (MIT), K-Dense scientific-visualization and uncertainty-and-units (MIT) and Hullman et al. 2015 (CC BY 4.0); changed: rewritten and condensed, examples replaced. Sources and licences: SOURCES.md.