The Importance of Type II Error in Hypothesis Testing
Bibliographic record
Abstract
Statistical tests of significance theoretically deal with two mutually exclusive hypotheses: the null and the alternative. However, at least in biomedical assays, only the null hypothesis is taken into account through type I error evaluation. But, basing these tests solely on type I error has two drawbacks: first, the probability limits (5%, 1% and 0.1%) arbitrarily set to the significance levels have no scientific justification. Second, acceptation of the null hypothesis is just a matter of chance, as it is mainly conditioned by the sample size due to its direct effect on the power of the test. In this sense, while the alternative hypothesis should be accepted due to its higher likelihood, the inference based on type I error alone would lead erroneously to accepting the null one. A numerical example illustrates how considering type I error alone, a same difference was declared non-significant first but turned out to significant thereafter when the sample size was increased. Therefore, the same null hypothesis was initially accepted and rejected afterwards. However when type II error was included in the test, the same decision was adopted no matter what the sample size was. This was possible through a reformulation of the alternative hypothesis. On the other hand, type II error may, in many cases have more far-reaching consequences than type I, and then should never be ignored, especially in assays dealing with human health, food, toxicity, etc.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.589 | 0.797 |
| Meta-epidemiology (narrow) | 0.004 | 0.002 |
| Meta-epidemiology (broad) | 0.012 | 0.007 |
| Bibliometrics | 0.007 | 0.009 |
| Science and technology studies | 0.004 | 0.033 |
| Scholarly communication | 0.015 | 0.013 |
| Open science | 0.010 | 0.008 |
| Research integrity | 0.015 | 0.023 |
| Insufficient payload (model declined to judge) | 0.007 | 0.002 |
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; the direct Gemma label and the distilled Codex classifier agree on what is shown here.
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".