Specialty › Precision & CI width

Regression-based reference limits

Precision-based sizing finds the n a regression-based reference limit needs for a target half-width, from Bland's (2015) SE = σ · √(1/n + z² / (2(n − 2))).

What is Regression-based reference limits?

The SE of a reference limit (mean + z·σ) combines uncertainty in both the mean and σ. The second term in the SE formula reflects the σ uncertainty and grows as z grows — making 99% reference limits (z = 2.58) much harder to pin down than 95% (z = 1.96).

When should I use Regression-based reference limits?

Designing a reference-interval study with a target precision per limit.

What data does it need?

Residual SD σ + target half-width + coverage z.

What does it report?

Required n (or achieved half-width if n given).

How do I interpret the result?

99% reference limits need substantially more n than 95% — for the same half-width, plan for ~70% more subjects when going from z = 1.96 to z = 2.58.