Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1301.1034

How many of the digits in a mean of 12.3456789012 are worth reporting?

R. S. Clymo
View original source ↗Read source document ↗Export metadata ↓

Abstract

OBJECTIVE. A computer program tells me that a mean value is 12.3456789012, but how many of these digits are significant (the rest being random junk)? Should I report: 12.3?, 12.3456?, or even 10 (if only the first digit is significant)? There are several rules-of-thumb but, surprisingly (given that the problem is so common in science), none seem to be evidence-based. RESULTS. Here I show how the significance of a digit in a particular decade of a mean depends on the standard error of the mean (SEM). I define an index, DM that can be plotted in graphs. From these a simple evidence-based rule for the number of significant digits ("sigdigs") is distilled: the last sigdig in the mean is in the same decade as the first or second non-zero digit in the SEM. As example, for mean 34.63 (SEM 25.62), with n = 17, the reported value should be 35 (SEM 26). Digits beyond these contain little or no useful information, and should not be reported lest they damage your credibility.

Explore related subjects

q-bio.OTstat.AP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

R. S. Clymo. 2021-05-06. How many of the digits in a mean of 12.3456789012 are worth reporting?. https://doi.org/10.1186/s13104-019-4175-6

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

MarkerScout: A Disease-Agnostic Machine Learning Framework for Biomarker Prediction from Multi-Scale Mechanistic Models

We demonstrate the framework on three infectious diseases derived from a companion mechanistic immune-simulation platform: SARS-CoV-2, Influenza A Virus, and Plasmodium falciparum. Each disease was evaluated across hospitalization and intensive care unit cohorts, yielding six cohorts in total. Best-pipeline cross-validated macro F1 ranged from 0.82 for IAV-HOSP to 0.99 for COV-ICU, and the framework produced tiered, direction-aware biomarker lists for each disease and phase. Interleukin-18 (IL-18) reached the strongest tier in both SARS-CoV-2 phases with consistent direction. When benchmarked against three separate, independently collected clinical ICU datasets, MarkerScout's top-ranked features outperformed 94.4% of randomly selected feature sets of equivalent size for SARS-CoV-2, with a weaker but directionally consistent advantage for Influenza A Virus (66.7%) and Plasmodium falciparum (60.7%).

q-bio.OT↗
arXiv2026

Enhancing Clinical Decision Support and Differential Diagnosis with Knowledge Graphs, and Retrieval Augmented Generation in Generative AI

Diagnostic error carries a burden, while unconstrained large language models (LLMs) remain vulnerable to hallucination and weak integration of quantitative laboratory dynamics. We developed a decision-support pipeline combining disease-specific biomarker correlation graphs, ordinary differential equations (ODEs), deep sequence classification, and retrieval-augmented generation (RAG). For 103 disease classes from a full blood count (FBC) repository, biomarker networks were used as coupling matrices to generate 30 trajectories per disease (3,090 total). A one-dimensional convolutional neural network (CNN) and long short-term memory (LSTM) network classified disease trajectories and six dynamical clusters. A constrained GPT-4o-mini RAG layer used a 19-pattern BMJ Best Practice/NICE corpus to generate differential diagnoses evaluated for diagnostic suitability, evidential grounding, and clinical plausibility. Across five random-seed runs, disease-level accuracy was $0.940 \pm 0.006$ for the CNN (95\% CI 0.933--0.948) and $0.852 \pm 0.019$ for the LSTM (95\% CI 0.828--0.875); the CNN advantage was 8.87 percentage points (95\% CI 6.47--11.27; $t(4)=10.26$, $p=5.1\times10^{-4}$; Hedges' $g=3.67$). Among 100 sampled RAG cases, 96 parsed successfully; evidence was cited in 97.9\%, the true diagnosis was mentioned in 71.9\%, and the composite score was 3.82/5 with a 47.9\% strict pass rate. The central finding was a decoupling between grounding and diagnostic correctness: classifier-correct versus classifier-wrong outputs differed in diagnostic suitability but not evidential grounding. Post-hoc analysis confirmed a 1.02-point diagnostic-score difference (Mann--Whitney $p=0.0024$; Hedges' $g=0.72$), whereas grounding differed by only $-0.02$ points ($p=0.839$; $g=-0.04$).

q-bio.OT↗
arXiv2026

Expanding the Human Ancestry Ontology to include under-represented populations and ethnicities for broader utility in annotations

Successful discovery, integration and reuse of data relies on the availability of rich, well-structured and machine-readable metadata to describe every aspect of the data, from sample sources to collection processes to experimental protocols. The use of standardised terminologies to express concepts in a harmonised fashion lies at the core of high-quality data annotation, increasing the FAIRness of the data, facilitating data integration and promoting reproducibility. Here, we describe the Human Ancestry Ontology (HANCESTRO), originally developed to improve standardised reporting of genetic ancestry genomic resources such as the NHGRI-EBI GWAS Catalog and the Human Cell Atlas through high-level population descriptors, and more recently expanded to include diverse and previously under-represented populations in genomics and genetics research. HANCESTRO provides a framework for population descriptors that includes both ancestry based on the analysis of genetic information and self-reported ethnicity, which is based on social and cultural factors that don't necessarily align with genetic populations. By enabling the accurate and interoperable representation of population-related data, it promotes inclusive, representative and reproducible science.

q-bio.OT↗