An Information Manifold Perspective for Analyzing Test Data
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
Modifications of current psychometric models for analyzing test data are proposed that produce an additive scale measure of information. This information measure is a one-dimensional space curve or curved surface manifold that is invariant across varying manifold indexing systems. The arc length along a curve manifold is used as it is an additive metric having a defined zero and a version of the bit as a unit. This property, referred to here as the scope of the test or an item, facilitates the evaluation of graphs and numerical summaries. The measurement power of the test is defined by the length of the manifold, and the performance or experiential level of a person by a position along the curve. In this study, we also use all information from the items including the information from the distractors. Test data from a large-scale college admissions test are used to illustrate the test information manifold perspective and to compare it with the well-known item response theory nominal model. It is illustrated that the use of information theory opens a vista of new ways of assessing item performance and inter-item dependency, as well as test takers' knowledge.
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.
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 | 0.018 | 0.035 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 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