The Application of Canonical Correlation to Two-Dimensional Contingency Tables
Bibliographic record
Abstract
This paper re-introduces and demonstrates the use of Mickey's (1970) canonical correlation method in analyzing large two-dimensional contingency tables.This method of analysis supplements the traditional analysis using the Pearson chi-square.Examples and a MATLAB source listing are provided.Almost every elementary statistics textbook has some coverage of the chi-square test (e.g., Comrey & Lee, 2007, Kirk, 2007, Howell, 2002).In particular, the chi-square test is presented in the analysis of categorical data.Most of these textbooks will take the reader up to the contingency table that involves the cross tabulation of two categorical variables.With contingency tables, there are two modes of analyses (Kennedy, 1983): (1) Symmetric and (2) Asymmetric.In the symmetrical case, no distinction is made between the two variables as to which is the dependent variable and which is the independent variable.The primary interest is in whether the two variables are related.In the asymmetric case one of the categorical variables is identified as the independent variable and the other categorical variable is the dependent variable.Here the interest is in The authors wish to thank the editor and an anonymous reviewer for clarifying the different variations that exist in canonical correlation analysis.They point out two major aspects to canonical correlation.The first is the nature of the input data and the second is the algorithm used to extract the canonical coefficients and correlation.The editor also wrote in SPSS a program to create a dummy data set from a contingency table suitable for analysis using the Mickey method [available on the journal's web site].
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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 | 0.020 | 0.161 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.007 | 0.013 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.005 | 0.004 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.009 | 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; 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".