Describe › Reference intervals

Parametric reference interval

A parametric reference interval covers the central fraction of a Gaussian distribution as mean ± z·SD, defaulting to 95% — the 2.5th to the 97.5th percentile.

What is Parametric reference interval?

A clinical reference interval is the range where 95% of a healthy reference population fall — anything outside is a flag for further investigation. Under approximate normality, the limits are mean ± 1.96·SD; in our reporting we use 90% CIs on each limit to convey uncertainty.

The Gaussian framing is the simpler / older approach but only valid when the analyte is normal. For positively-skewed lab values (most analytes), either log-transform first or switch to the non-parametric (percentile) interval.

For covariate-adjusted reference intervals (analyte depends on age, sex, etc.) use reference_interval_covariate instead — it fits a regression rather than a single interval.

When should I use Parametric reference interval?

Establishing a normal range for a clinical assay.
When the analyte is approximately normal (check with Q-Q / Shapiro before).

What data does it need?

One numeric column + coverage (90 / 95 / 99 %).

What does it report?

Lower and upper limits + t-based 90% CIs for each limit.

What does it assume?

Reference population is approximately normal.
Sample is representative of the healthy reference population.
n ≥ 40 for reasonable precision; ≥ 120 is the CLSI guideline.

Formula

Lower = mean − z · SD;  Upper = mean + z · SD;  SE(limit) = SD · √(1/n + z² / (2(n − 1)))

How do I interpret the result?

Compare CI widths on the limits to the magnitude of the interval — if the CIs are wide relative to the interval, the interval is poorly estimated and you need a bigger reference sample.

References

Bland (2015). Estimating reference ranges. BMJ Stats Note.