Should the Mantel test be used in spatial analysis?
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Bibliographic record
Abstract
Summary The Mantel test is widely used in biology, including landscape ecology and genetics, to detect spatial structures in data or control for spatial correlation in the relationship between two data sets, for example community composition and environment. The study demonstrates that this is an incorrect use of that test. The null hypothesis of the Mantel test differs from that of correlation analysis; the statistics computed in the two types of analyses differ. We examined the basic assumptions of the Mantel test in spatial analysis and showed that they are not verified in most studies. We showed the consequences, in terms of power, of the mismatch between these assumptions and the Mantel testing procedure. The Mantel test H 0 is the absence of relationship between values in two dissimilarity matrices, not the independence between two random variables or data tables. The Mantel R 2 differs from the R 2 of correlation, regression and canonical analysis; these two statistics cannot be reduced to one another. Using simulated data, we show that in spatial analysis, the assumptions of linearity and homoscedasticity of the Mantel test (H 1 : small values of D 1 correspond to small values of D 2 and large values of D 1 to large values of D 2 ) do not hold in most cases, except when spatial correlation extends over the whole study area. Using extensive simulations of spatially correlated data involving different representations of geographic relationships, we show that the power of the Mantel test is always lower than that of distance‐based Moran's eigenvector map (dbMEM) analysis and that the Mantel R 2 is always smaller than in dbMEM analysis, and uninterpretable. These simulation results are novel contributions to the Mantel debate. We also show that regression on a geographic distance matrix does not remove the spatial structure from response data and does not produce spatially uncorrelated residuals. Our main conclusion is that Mantel tests should be restricted to questions that, in the domain of application, only concern dissimilarity matrices, and are not derived from questions that can be formulated as the analysis of the vectors and matrices from which one can compute dissimilarity matrices.
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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 | 0.004 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| 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