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Biology Skills

Uncertainty estimates and statistical inference

Summary

Error bars, confidence intervals, and other uncertainty depictions must be chosen to match the analysis. The plot’s annotations should state what the uncertainty represents (SD, SEM, 95% CI, credible interval, etc.). If n is small (<10), prefer showing raw data or IQR over misleading “standard error” bars. Avoid implying statistical significance: e.g., overlapping error bars do not always mean non-significance. For model-based inference plots (regression lines, ROC curves), annotate uncertainty (shading or error ribbons) only if sample size and model assumptions are appropriate.

Core rules

  • Annotation: Label error bars/intervals clearly (e.g. “mean ± SD” or “95% CI”) in caption or legend.
  • Match data: Use SD bars for sample variability, SE/CI when making inference. Don’t use SE bars for describing distribution with small n.
  • Sample size: With small n, emphasize raw data or use bootstrapped CI.
  • Statistical lines: When adding fitted lines (e.g. trend lines), also add a shaded CI or bootstrap band if claiming predictive power.
  • Avoid inferential claims: In plots, do not use “*” to denote significance unless a statistical test was done and described. Instead, describe differences in text or use annotated p-values separately.

Required context

  • Clarify if visual is exploratory or inferential.
  • Know the number of replicates and data distribution (to choose parametric vs nonparametric error estimates).
  • If a statistical model is implied, know its assumptions.

AI behaviour

  • Pick proper bars: Suggest SD bars for experimental variability or 95% CIs for treatment effects, depending on use-case.
  • Explain error: Always include notes on what error bars mean in the caption.
  • Check interpretation: Do not allow error bars to be interpreted as significance markers; add clarifying text if needed.

Common failure modes

  • Ambiguous bars: Plot with error bars unlabeled; reader cannot tell if they are SD, SE, or CI.
  • Small-n overconfidence: Showing SE bars for n=3 gives false precision.
  • Misleading intervals: Plotting mean±CI to judge individual data spread (CI narrows as n grows, not a measure of variability).

Authoritative standards

  • Statistical visualization: Recommend labeling and transparency (American Statistician guidelines on effect sizes and CIs).

Examples

Example: Group mean comparison

  • Data: Two group means, n=5 each.
  • Check: Prefer show individual points or boxplot + points instead of only mean±SE. If bars used, caption “mean ± SD (n=5)”.
  • Good outcome: Plot shows points and error bars labeled “SD” in legend.

Example: Regression line

  • Data: Scatter of x vs y (n=100).
  • Check: Fit linear regression with shaded 95% confidence band. Label line “best-fit ± 95% CI”.
  • Good outcome: Plot includes dashed line for fit and shaded region for confidence (caption notes CI).