Credible Interval Width Calculator

Estimate credible interval width using variance and confidence.

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Quick Facts

Variance
Spread
Variance drives width
Confidence
Level
Level sets z value
Sample
Size
Size tightens interval
Decision Metric
Width
Interval width

Your Results

Calculated
Interval Width
-
Credible interval width
Half Width
-
Half-width precision
Effective Sample
-
Sample with design effect
Signal Score
-
Effect vs width

Interval Plan

Your defaults create a clear credible interval.

What This Calculator Measures

Estimate credible interval width using posterior variance, confidence, and sample size.

By combining practical inputs into a structured model, this calculator helps you move from vague estimation to clear planning actions you can execute consistently.

This calculator estimates credible interval width based on posterior variance.

How to Use This Well

  1. Enter posterior std dev and confidence.
  2. Add sample size and prior weight.
  3. Set effect size and design effect.
  4. Review interval width.
  5. Adjust sample size if needed.

Formula Breakdown

Width = 2 x z x std / sqrt(n)
Half-width: width / 2.
Effective n: n / design effect.
Signal: effect / width.

Worked Example

  • Std dev 1.8 with 95% confidence.
  • Width around 0.57.
  • Signal score about 1.1.

Interpretation Guide

RangeMeaningAction
Width under 0.5Tight.High precision.
0.5-1.0Moderate.Standard precision.
1.0-1.5Wide.Increase sample.
1.5+Very wide.Refine model.

Optimization Playbook

  • Increase sample: tighten interval.
  • Reduce variance: improve data quality.
  • Adjust design effect: reflect sampling plan.
  • Compare effect: check signal score.

Scenario Planning

  • Baseline: current std dev.
  • Higher sample: add 50 samples.
  • Higher confidence: increase to 99%.
  • Decision rule: keep width under 1.

Common Mistakes to Avoid

  • Ignoring design effects.
  • Using low sample size.
  • Misreading standard deviation.
  • Skipping prior adjustments.

Implementation Checklist

  1. Estimate variance.
  2. Pick confidence level.
  3. Set sample size.
  4. Review width.

Measurement Notes

Treat this calculator as a directional planning instrument. Output quality improves when your inputs are anchored to recent real data instead of one-off assumptions.

Run multiple scenarios, document what changed, and keep the decision tied to trends, not a single result snapshot.

FAQ

What confidence level should I use?

95% is common for credible intervals.

How does prior weight affect width?

Stronger priors can tighten intervals.

What is design effect?

It adjusts for complex sampling.

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