Percentile-based grain size distribution analysis tools (GSDtools) – estimating confidence limits and hypothesis tests for comparing two samples
Bibliographic record
Abstract
Abstract. Most studies of gravel bed rivers present at least one bed surface grain size distribution, but there is almost never any information provided about the uncertainty of the percentile estimates. We present a simple method for estimating the confidence intervals about the grain size percentiles derived from standard Wolman or pebble count samples of bed surface texture. Our approach uses binomial probability theory to generate confidence intervals for all grain sizes in the distribution. We find that the standard sample size of 100 observations is associated with errors ranging from about ±15 % to ±30 %, which may be unacceptably large for many applications. In comparison, a sample of 500 stones produces an uncertainty ranging from about ±9 % to ±18 %. In order to help workers develop appropriate sampling approaches that produce the desired level of precision, we present simple equations that approximate the proportional uncertainty associated with the median size and the 84th percentile of the distribution as a function of the sample size and the standard deviation of the distribution, assuming that the underlying distribution is log-normal. However, the true uncertainty of any sample can only be accurately estimated once the sample has been collected, so these simple equations complement – but do not replace – the basic uncertainty analysis using binomial probability theory.
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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 | 0.032 | 0.183 |
| Meta-epidemiology (narrow) | 0.004 | 0.003 |
| Meta-epidemiology (broad) | 0.003 | 0.005 |
| Bibliometrics | 0.009 | 0.004 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.005 | 0.005 |
| Open science | 0.007 | 0.007 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.069 | 0.019 |
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".