Systematic sampling of discrete and continuous populations: sample selection and the choice of estimator
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Systematic sampling is easy, efficient, and widely used, though it is not generally recognized that a systematic sample may be drawn from the population of interest with or without restrictions on randomization. The restrictions or the lack of them determine which estimators are unbiased, when using the sampling design as the basis for inference. We describe the selection of a systematic sample, with and without restriction, from populations of discrete elements and from linear and areal continuums (continuous populations). We also provide unbiased estimators for both restricted and unrestricted selection. When the population size is known at the outset, systematic sampling with unrestricted selection is most likely the best choice. Restricted selection affords estimation of attribute totals for a population when the population size — for example, the area of an areal continuum — is unknown. Ratio estimation, however, is most likely a more precise option when the selection is restricted and the population size becomes known at the end of the sampling. There is no difference between restricted and unrestricted selection if the sampling interval or grid tessellates the frame in such a way that all samples contain an equal number of measurements. Moreover, all the estimators are unbiased and identical in this situation.
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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 | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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