Analyzing lognormal data: A nonmathematical practical guide
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Bibliographic record
Abstract
Lognormal distributions are pervasive in pharmacology and elsewhere in biomedical science, arising naturally when biological effects multiply rather than add. Despite their ubiquity in pharmacological parameters (eg, EC50, IC50, Kd, and Km), lognormal distributions are often overlooked or misunderstood, leading to flawed data analysis. This largely nonmathematical review explains why lognormal distributions are common, how to recognize them, and how to analyze them appropriately. We show that many measured variables are lognormal. So are many derived parameters, particularly those defined as ratios of lognormal variables. Through examples and simulations accessible to working scientists, we demonstrate how misidentifying lognormal distributions as normal leads to reduced statistical power, unnecessarily large sample sizes, false identification of outliers, and inappropriate reporting of effects as differences rather than ratios. We challenge the common practice of using normality tests to decide how to analyze data, showing that many data sets pass both normality and lognormality tests, especially with small sample sizes. Instead, we advocate for assuming lognormality based on the nature of the variable. This review provides practical guidance on recognizing and presenting lognormal data, and comparing data sets sampled from lognormal distributions. Based on Monte Carlo simulations, we recommend the lognormal Welch's t test or nonparametric Brunner-Munzel test for comparing 2 unpaired groups, the lognormal ratio paired t test for paired comparisons, and lognormal ANOVA for ≥3 groups. By recognizing and properly handling lognormal distributions, pharmacologists can design more efficient experiments, obtain more reliable statistical inferences, and communicate their results more effectively. SIGNIFICANCE STATEMENT: Lognormal distributions are common in pharmacology and many scientific fields, but they are often misunderstood or overlooked. This review provides a detailed guide to recognizing and analyzing lognormal data, aiming to help pharmacologists perform more appropriate and more powerful statistical analyses, draw more meaningful conclusions from their data, and communicate their results more effectively.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.007 | 0.056 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.007 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it