Medical Edition

Reference interval software for clinical laboratories Five quantile methods including robust and bootstrap approaches, a full range of transformations and partitioning by sex, age or ethnicity. Outlier screening and normality assessment before the limits are estimated.

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Microsoft Excel with the Analyse-it tab selected, showing a reference interval report for calcium in females: the frequency histogram with the reference limits and their 90% confidence intervals, the dot plot, descriptive statistics, the Reference Limits table, the Estimate Limits menu open on the ribbon listing the quantile, Harrell-Davis, bootstrap, biweight and normal estimators, and the Reference Interval task pane open on Reference Limits. Handwritten notes: Runs inside Excel: every analysis is on the Analyse-it tab; Quantile, robust, Harrell-Davis, bootstrap: the estimators under one menu; Histogram with the reference limits and their 90% CIs; Descriptive statistics for the partition; Partitions by factor: one report per group; The report is an ordinary Excel worksheet: share it, archive it, open it on any PC with Excel.

Establish the reference ranges clinicians depend on

Excel’s PERCENTILE function returns a quantile and stops. No confidence interval on the limit, no choice of quantile method for the sample size, no transformation for skewed data, no partition by sex or age. Every laboratory result a clinician sees is interpreted against a reference interval. Normal patients are flagged and abnormal patients are missed when the interval is wrong. Wrong can mean too wide, too narrow, from the wrong population or not partitioned where it should be.

Which quantile method suits this sample size and distribution? Should the interval be partitioned by sex or age? Establishing intervals from your own population is one of the most consequential statistical tasks a laboratory performs.

Parametric, non-parametric, robust, bootstrap and Harrell-Davis quantiles

The quantile method should match the sample size and the shape of the data. Parametric quantiles when the distribution is Gaussian. Non-parametric with three computation approaches — (N+1)p, Np+½ and (N+⅓)p+⅓ — when there are 120 or more observations. Robust bi-weight for small or moderately skewed samples, bootstrap for distribution-free estimation, Harrell-Davis for a smooth quantile estimate. Every reference limit has a confidence interval, and the frequency histogram shows the limits against the data.

  • Normal (parametric) quantile, Z (MVUE) or t-based
  • Non-parametric quantile: (N+1)p, Np+½, (N+⅓)p+⅓
  • Harrell-Davis quantile
  • Bootstrap quantile
  • Robust bi-weight quantile for symmetric and skewed small samples
  • Confidence intervals on all reference limits
  • Two-sided reference interval or one-sided reference limit
  • Frequency distribution histogram with normal overlay and reference limits
Microsoft Excel showing a reference interval report for a 20-sample calcium set: the histogram with robust bi-weight reference limits, and the Reference Limits table with bootstrap 90% confidence intervals, with the task pane open on the estimator options. Handwritten notes: Reference limits from a sample of 20; Robust bi-weight limits with bootstrap 90% CIs; Quantile estimator, and its CI method.
Robust bi-weight reference limits for a calcium sample of 20, each with a bootstrap 90% confidence interval, and the histogram with the limits marked above.

Partition by sex, age group, ethnicity or any combination of factors

Where a reference interval differs between subgroups, one interval for everyone misclassifies patients in both. Partition by sex, age group, ethnicity or any combination of factors within a single analysis. Separate calcium intervals for males and females, for example, or age-stratified alkaline phosphatase ranges for paediatric populations. Outlier screening and normality assessment run independently for each subgroup.

  • Partition by factor(s)

Log, Box-Cox, Manly exponential and two-stage modulus transformations

Non-normal data forced through a parametric calculation gives limits that do not fit the population. Log, square root, cube root, reciprocal, Box-Cox, Manly exponential and two-stage exponential/modulus transformations bring skewed data closer to normal. Choose the transformation that achieves the best fit, compute parametric reference limits on the transformed scale and back-transform to the original units.

  • Log transformation
  • Square and cube root
  • Reciprocal transformation
  • Box-Cox
  • Manly exponential
  • Two-stage exponential / modulus
Microsoft Excel showing a reference interval report for ALT in females: the raw histogram with its reference limits, and beneath it the Transformed histogram of ln ALT with a normal curve overlaid, with the task pane open on the Transform section. Handwritten notes: Raw ALT: skewed, with its reference limits; The same data after a log transform, normal curve overlaid; Transform: log, Box-Cox, Manly or two-stage modulus.
ALT in females: the raw histogram with its reference limits, and beneath it the same data after a natural log transformation with the normal curve overlaid.

Tukey outlier box plot, Shapiro-Wilk, Anderson-Darling and normal Q-Q plot

An extreme value or a wrong assumption about the distribution distorts the limits, so screen the data before establishing them. The Tukey box plot identifies outliers. Normality is assessed with the Shapiro-Wilk and Anderson-Darling tests, the frequency histogram with normal overlay and the normal Q-Q plot with Lilliefors confidence band. Run them on the raw data, and again after a transformation.

  • Tukey outlier box plot
  • Shapiro-Wilk test
  • Anderson-Darling test
  • Normal Q-Q plot with Lilliefors confidence band
Microsoft Excel showing the Transformed section of a reference interval report: the ln ALT histogram with a normal curve, the Tukey outlier box plot beneath it with near outliers marked, descriptive statistics and the Reference Limits table in U/L. Handwritten notes: Normal curve overlaid on the transformed data; Tukey box plot: near outliers flagged; Reference limits, back in U/L.
The log-transformed ALT data with the normal curve overlaid, and the Tukey outlier box plot beneath it with the near outliers marked.

Example analyses

See reference interval results in detail — partitioned intervals, histograms with reference limits and outlier screening — using example datasets you can download and follow along with.

EP28 A3 Example 1 2 pages EP28-A3c — Table 4
Calcium reference intervals by sex. 120 observations per sex, reported separately. Distribution with descriptive statistics, and nonparametric reference limits from the (N+1)p quantile with 90% CIs.

Part of the Medical edition

Reference intervals are one part of the Medical edition, alongside diagnostic accuracy, Bland-Altman agreement and survival analysis. The edition also includes the full Standard edition for hypothesis testing, regression and descriptive statistics.

Related guides in the Learn section: choosing a reference interval method, transferring and verifying an interval, when to partition and handling outliers and skew.

For the rest of a method validation programme — precision, linearity, detection limits, bias at clinical decision points, regression-based method comparison and reference-interval transference — see the Method Validation edition.

Software you can trust

Validated calculations you can defend at peer review Every calculation is performed by Analyse-it — no Excel formulas, no third-party functions. Results are validated against published datasets and thousands of internal test cases before every release. How Analyse-it is developed and validated →
Patient data stays on your PC Analyse-it runs entirely within Microsoft Excel on your PC. No cloud processing, no data transmission. Patient data and research data stay within your facility under your own data governance controls.
Standard Excel workbooks anyone can open Every analysis is an ordinary .xlsx workbook. Share with co-authors, attach to a manuscript submission, archive for publication queries. No proprietary format, no licence required to view results. Co-authors and reviewers see exactly what you see.
Results that cannot be accidentally broken Analysis output contains computed values, not formulas. Nothing to accidentally overwrite, no cell references to break, no formula errors to introduce. The results you published are exactly what you will find when you reopen the workbook months or years later, when a reviewer asks.

Free trial and pricing

Try it on your own data first. The 15-day trial is every feature from all five editions — install it and start straight away.

Download 15-day trial See pricing or get a quote →

Medical edition: US$ 340 per year or US$ 815 for a perpetual licence. Every purchase carries a 30-day money-back guarantee. Need a quote for purchasing? Add the licence to the cart and save it as a PDF quote.