Reference interval establishment reference

Reference interval establishment calculates new reference limits from your own healthy subjects: a two-sided reference interval or a one-sided lower or upper limit, for each partition. Each limit has a two-sided confidence interval showing how precisely it is estimated.

• Independent healthy subjects who meet your eligibility rules. Each subject counts once. Repeat draws are averaged and flagged.
• Optionally partitions, for example female and male, each with its own limits. Without a partition column, all subjects are in partition 1.
• The counts to collect are in the collection plan under Run this study.

• Automatic for each partition (default): uses nonparametric limits at 120 or more eligible subjects. With 20 to 119, it checks the original values with Shapiro–Wilk at a 0.05 threshold, then the log10 values when every measurement is positive. A supported Gaussian model selects parametric limits; a supported log-Gaussian model selects log-normal limits within its supported coverage and confidence settings. Otherwise it uses nonparametric limits where estimable. With fewer than 20 subjects the diagnostic is recorded and no distribution model is selected, so the nonparametric minimum for the selected coverage and sidedness applies. At the default 95% two-sided coverage, that minimum is 39 and no limits are printed. The saved result identifies the chosen method and diagnostic, and the report prints them beside the limits on page 1.
• Nonparametric percentiles: limits at rank p(n + 1) with exact confidence intervals.
• Parametric (normal theory): assumes a normal distribution.
• Log-normal (approximate CIs): assumes the log10 values are normal. It needs two-sided limits, coverage 0.95, confidence 90 %, 95 % or 99 %, and positive values. Limit CIs are approximate.

Data transformation is selected separately for each partition in automatic mode. For a manual estimator it is shown beside the estimator and set by it: None, or Base-10 logarithm for log-normal. Results are reported in the study unit.

Why the method matters is in Choosing an estimator.

Other coverage and confidence settings need other counts. The result gives the number.

Day and Run can be imported but aren't shown in the grid. See Importing and mapping and Column reference.

The calculation stops until these are fixed:

• a missing analyte or unit;
• a subject entered in two partitions;
• a cohort with no eligible subjects;
• rows marked with errors.

Too few subjects does not stop the calculation. The result gives the count and explains why the limits weren't calculated.

The dialog is in Set acceptance limits. For this study:

• A limit applies to the Lower reference limit or the Upper reference limit, with a Lower limit, an Upper limit or both.
• The limit is compared with the reference limit itself, in the study unit. The CI width doesn't enter.
• A reference limit that wasn't calculated gives Undecided.

See About acceptance decisions.

The summary and overview show every partition. With several, Partition details chooses the partition whose supporting details are shown.

• Reference limits by partition gives each partition's subjects, the method with its Shapiro–Wilk p value under automatic selection, and each limit with its two-sided CI.
• Subject values and limit CIs by partition adds the mean, SD, observed range and the CI ranks. Automatic selection also shows the method and normality diagnostic used for each partition. The reason for any "Not estimated" is below the table.
• Estimator details · partition under Detailed statistics holds the estimator, assumptions, sample-size and tail checks, exclusions and CI ranks.
• The plot shows a histogram of each partition with lines at the limits and brackets for their CIs. It switches between Histogram and Raw points.
• Review values outside 1.5·IQR whiskers lists values beyond the Tukey fences, with View row links. Flagged values stay in the result.
• Including excluded rows (for information only) appears when a partition has excluded rows. It shows what the exclusions changed.

Distribution diagnostics · partition needs at least 3 subjects whose values are not all the same:

• Normal Q–Q: a straight line suggests a roughly normal shape, a curve suggests skew, and isolated end points are tail values.
• Box and raw-point strip: the box runs from Q1 to Q3 with the median, whiskers reach the most extreme values within 1.5 × IQR, and the strip shows every subject.

reference_establish_120.csv: 240 example white blood cell counts (10^9/L), 120 subjects each in female and male, one draw each.

Setup: two-sided, coverage 0.95, Nonparametric percentiles, 90 % confidence. One acceptance limit: Upper reference limit at most 12.5 10^9/L.

The study status is Criteria met.

• CI on estimated limits: the lower limit's CI uses order statistics 1 and 7, the upper's 114 and 120. Because ranks are whole numbers, achieved coverage is 92 % against the nominal 90 %.
• The female upper CI, 10.3 to 14, runs to the largest value.
• Tail estimates: 6 of 120 female values fall outside the limits, against about 6 expected. Male: 5 of 120.
• The review list flagged 3 female values (F080 11.5, F001 11.8, F112 14; upper fence 11.250) and 1 male value (M033 11.5; upper fence 11.263). They stay in the result.

In a second study, row F112 (14.0) was excluded with a reason. Female result:

The upper 90 % CI became 10.00 to 11.80.

On the 120-subject file, a one-sided upper limit at 90 % confidence gave female 10.40, CI 9.60–11.80, and male 10.48, CI 9.70–11.00. Each had 6 of 120 values above.

reference_establish.csv has 41 rows: 20 female subjects (F019 has two draws, averaged) and 20 male. With the nonparametric estimator, every limit and CI shows —, and the note gives the reason: two-sided limits need 39 subjects. Parametric (normal theory) gives, for example, female 3.232 to 10.763 10^9/L, with 90 % CIs of 1.940–4.523 on the lower limit and 9.472–12.055 on the upper.

When you calculate WBC · reference interval establishment by sex in the example project, LabRuns records these methods:

1. Automatic reference method choice is per partition: at least 120 eligible subjects uses nonparametric limits. With 20 to 119 subjects, Shapiro–Wilk p ≥ 0.05 supports normal-theory limits; otherwise positive values with Shapiro–Wilk p ≥ 0.05 after log10 transformation support log-normal limits, within their supported settings. If neither model is supported, or there are fewer than 20 subjects, nonparametric calculation minima apply. A normality test does not establish normality.
2. Nonparametric limits are the values at rank p(n+1) (Hyndman–Fan type 6, linear interpolation) for p = (1−coverage)/2 and 1−(1−coverage)/2. At 95% coverage they need at least 39 subjects. Each limit has an exact binomial order-statistic CI.
3. Parametric limits are mean ± z·s and assume a Gaussian reference distribution. Limit CIs use SE = s·√(1/n + z²/(2(n−1))) with a t(n−1) multiplier.
4. Repeat draws from one subject are averaged into one value. The distribution histogram uses ceil(√n) equal-width bins, at most 40.
5. At least 120 eligible subjects per partition are recommended. Each partition is analyzed on its own.
6. Distribution diagnostics: ordered values plotted against standard-normal quantiles at Blom positions pᵢ = (i − 3/8)/(n + 1/4).
7. Box: type-7 quartiles, IQR = Q3 − Q1. Whiskers end at the most extreme values within Q1 − 1.5 IQR and Q3 + 1.5 IQR. Values beyond the whiskers stay in the analysis.
8. Q–Q and box plots need at least 3 values that are not all identical. The strip plot shows every included value.
9. Reference review: Tukey 1.5·IQR screening using the type-7 quartiles. Values outside Q1 − 1.5·IQR or Q3 + 1.5·IQR are flagged for review. Values equal to a fence are not flagged.

• Nonparametric one-sided limits use p = coverage (upper) or p = 1 − coverage (lower). Two-sided limits need n ≥ 1/p − 1.
• Limit CI: ranks r and s with each tail at most α/2, achieved coverage P(r ≤ B ≤ s − 1), B ~ Binomial(n, p). If a rank falls outside 1…n, there is no CI. Horowitz 2008 gives ranks 1–7 and 114–120 at n = 120, 90 %.
• Parametric limits use z = Φ⁻¹((1 + coverage)/2) two-sided or Φ⁻¹(coverage) one-sided (Bland). Identical values put both limits at that value and withhold both limit confidence intervals.
• Log-normal limits: m ± z·s on the log10 scale with z = Φ⁻¹(0.975), back-transformed as 10^x. Each limit CI has log-scale half-width Φ⁻¹((1 + confidence)/2) · s · √((1 + z²/2)/n). Achieved coverage is unknown. Values at or below zero, or identical log values, stop the analysis.

See Study reference.

Evidence references: CAP COM.40605, COM.40615 (9 December 2025). In a binder, the CAP evidence index lists the report sections behind each requirement and the laboratory records that go with them.