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Data Quality Confidence Interval Calculator

This calculator estimates a confidence interval around the observed percentage of records that pass a defined data quality check. Instead of treating the sample pass rate as the exact population rate, it shows a plausible range for the underlying quality level based on sample size and confidence level. It is useful for data stewards, analytics engineers, and QA teams auditing completeness, validity, uniqueness, or another binary pass/fail rule. A narrower interval supports more precise reporting, while a wide interval signals that additional reviewed records may be needed before making a firm quality claim.

Audit sample

records
records
Result
—
Estimated data quality pass rate
Lower confidence bound—
Upper confidence bound—
Approx. half-width—
Records failing check—

1. Define one pass/fail rule
Use a consistent quality criterion for every record in the sample, such as a required field being valid.

2. Enter the reviewed sample
Provide the total number of records that were independently checked.

3. Enter the passing count
Count only records that satisfy the stated criterion; the passing count cannot exceed the reviewed count.

4. Choose confidence
Use the confidence level that matches the uncertainty you want to report.

5. Read the interval
Review the observed pass rate together with the lower and upper bounds; a tighter range means greater precision.

Formula:

p̂ = x / n; center = (p̂ + z²/(2n)) / (1 + z²/n); half-width = z × √((p̂(1−p̂) + z²/(4n))/n) / (1 + z²/n)

Where:

  • p̂ — observed proportion of reviewed records that pass
  • x — number of passing records
  • n — number of reviewed records
  • z — standard-normal critical value for the selected confidence level

Assumptions: The calculator uses the Wilson score interval for a binomial proportion. The sample should reasonably represent the records or events to which you want to generalize, and each record should be classified with the same rule.

What the result means

The displayed range expresses sampling uncertainty around the observed quality pass rate. For example, a 95% interval is a procedure that would capture the true population proportion in about 95% of repeated samples under the model assumptions.

The interval does not account for biased sampling, inconsistent reviewers, changing source systems, or correlated records; those issues can make a mathematically narrow interval misleading.

Given: 400 records are reviewed, 372 pass the quality check, and a 95% confidence level is selected.

Calculation: p̂ = 372 ÷ 400 = 0.93. With z = 1.96, the Wilson center is about 0.926 and the half-width is about 0.025. The interval is approximately 0.901 to 0.951.

Result: Observed pass rate = 93.0%; 95% confidence interval ≈ 90.1% to 95.1%.

Interpretation: The audit supports a high pass rate, but the population quality level should be reported as a range rather than as exactly 93%.

Why use an interval instead of only the pass rate?

A sample pass rate is one estimate and will vary from sample to sample. The interval adds a practical measure of sampling uncertainty around that estimate.

What counts as a passing record?

A pass should be defined before sampling and applied consistently. If you are checking several rules at once, decide whether a record must pass all rules or whether each rule will be analyzed separately.

Why does a larger sample usually narrow the interval?

More observations provide more information about the underlying proportion. Holding the observed rate and confidence level roughly constant, uncertainty generally decreases as sample size increases.

Can I use this when zero records fail?

Yes. The Wilson method still produces a nonzero uncertainty range even when every sampled record passes, avoiding the unrealistic conclusion that the population pass rate is known to be exactly 100%.

Does this measure all dimensions of data quality?

No. It estimates uncertainty for one binary quality criterion at a time. Completeness, accuracy, timeliness, consistency, and other dimensions may need separate checks and intervals.