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Uncertainty and models

Error-bar chart

Shows estimates with uncertainty or variability intervals.

  • Plot
  • Uncertainty
  • Comparison

What it answers

How uncertain or variable is each estimate?

Shape
Points or bars with interval whiskers
What it shows
Estimate differences and interval overlap.

Example

The question

How sure are we about each region’s average satisfaction?

Average satisfaction by region with 95% confidence intervals (score out of 10)

Average satisfaction by region with 95% confidence intervals (score out of 10)Dots are averages, whiskers 95% confidence intervals. North 7.8 (7.5 to 8.1); South 7.2 (6.7 to 7.7); East 8.1 (7.2 to 9); West 7.5 (7.2 to 7.8); Central 6.9 (6.3 to 7.5). East is highest but its interval is wide (small sample).Average score (out of 10)5678910NorthSouthEastWestCentral7.87.28.17.56.9
Average satisfaction by region with 95% confidence intervals (score out of 10)Dots are averages, whiskers 95% confidence intervals. North 7.8 (7.5 to 8.1); South 7.2 (6.7 to 7.7); East 8.1 (7.2 to 9); West 7.5 (7.2 to 7.8); Central 6.9 (6.3 to 7.5). East is highest but its interval is wide (small sample).Average score (out of 10)5678910NorthSouthEastWestCentral
Dots are averages, whiskers 95% confidence intervals. North 7.8 (7.5 to 8.1); South 7.2 (6.7 to 7.7); East 8.1 (7.2 to 9); West 7.5 (7.2 to 7.8); Central 6.9 (6.3 to 7.5). East is highest but its interval is wide (small sample).

Illustrative data. It belongs to no company.

When to use it

Use it when

Comparing estimates with explicit uncertainty or variability.

Avoid it when

Unlabelled interval types or interpreting all whiskers as confidence limits.

How to read it

Read estimate and interval endpoints; check the interval definition.

Note

Label standard deviation, standard error or interval coverage explicitly.

The data you need

Layout
Wide interval summary
Fields
Item: text; Estimate,Lower,Upper: numbers
One row is
One estimate and its lower and upper interval bounds. What is the grain?
Rules
Require Lower <= Upper. Explain interval type, units and coverage. Asymmetric intervals are allowed.
Optional
Alternative Estimate,LowerError,UpperError distances. Distinguish bounds from distances.
Preparation
Fit or obtain a suitable model/estimate first, then pair estimates with correctly labelled bounds or standard errors. Preserve coverage and scale information.
Units
Estimates and interval endpoints share an effect/measurement unit unless transformed. Coverage such as 95% is a model-based probability statement, not a data-share denominator.
Example of the input layout: Wide interval summaryA wide table: one row per item, with a separate column for each measure or period.ItemEstimateLowerUpper…ABC
A wide table: one row per item, with a separate column for each measure or period.

Worked example

A estimate 10 with bounds 8-12; B15 with 11-19. B's estimate is higher and its interval wider; overlap alone is not a complete test.

ItemEstimateLowerUpper
A10812
B151119
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