Determination of Confidence Intervals in Non-normal Data: Application of the Bootstrap to Cocaine Concentration in Femoral Blood
Bibliographic record
Abstract
Calculating the confidence interval is a common procedure in data analysis and is readily obtained from normally distributed populations with the familiar [Formula: see text] formula. However, when working with non-normally distributed data, determining the confidence interval is not as obvious. For this type of data, there are fewer references in the literature, and they are much less accessible. We describe, in simple language, the percentile and bias-corrected and accelerated variations of the bootstrap method to calculate confidence intervals. This method can be applied to a wide variety of parameters (mean, median, slope of a calibration curve, etc.) and is appropriate for normal and non-normal data sets. As a worked example, the confidence interval around the median concentration of cocaine in femoral blood is calculated using bootstrap techniques. The median of the non-toxic concentrations was 46.7 ng/mL with a 95% confidence interval of 23.9-85.8 ng/mL in the non-normally distributed set of 45 postmortem cases. This method should be used to lead to more statistically sound and accurate confidence intervals for non-normally distributed populations, such as reference values of therapeutic and toxic drug concentration, as well as situations of truncated concentration values near the limit of quantification or cutoff of a method.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.040 | 0.218 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.004 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".