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Validation

Statistical rigor, stated plainly.

Every number here is measured on public data and reported as-is. None is a claim of state of the art.

§ 01 / Results

Predictive accuracy on public benchmarks.

Predictive accuracy — AUC
0.835
ASSISTments-2009 · p<.005
MethodBKT + IRT ensemble
DataPublic knowledge-tracing
ComparisonBeats every reproducible baseline

AHCOS's measurement engine was evaluated on public knowledge-tracing datasets. On ASSISTments-2009 it reaches an AUC of 0.835 (p<.005). Across these benchmarks, the ensemble beats every reproducible baseline we tested.

Every figure on this page is measured on public data and reported as-is. None is a claim of state of the art.

ASSISTments-2009 · AUC
0.835
Statics-2011 · AUC
0.824
ASSISTments-2015 · AUC
0.706

Note On Statics-2011 (0.824) and ASSISTments-2015 (0.706), results sit within the range reported in the field.

0.0586
Expected Calibration Error (ECE) — predicted confidence closely matches observed accuracy
0.750.813
Ability recovery — correlation between recovered and true latent ability, across conditions
§ 02 / Method

How is capability inferred?

Component

Bayesian Knowledge Tracing (BKT)

Models the probability that a latent skill has been mastered, updating that belief as a learner produces correct and incorrect responses.

Component

Item Response Theory (IRT)

Models ability as a latent trait, separating how able a person is from how hard or discriminating each item is.

Together

The ensemble

Combining the two yields estimates that are both responsive and stable — and, critically, each estimate carries a confidence band rather than a bare number.

§ 03 / Interpretation

What it means — and what it does not.

An AUC of 0.835 means the model reliably ranks correct outcomes above incorrect ones on a recognized public benchmark. The low Expected Calibration Error (0.0586) means its stated confidence can be trusted — it backs our principle of confidence, not false certainty.

What it is not: a claim of state of the art, or a claim about anything beyond the measurement layer. These results validate the tracing and estimation engine — not other parts of the platform. Real-world outcome studies, run with pilot partners, are how this validation deepens next.

§ 04 / References

Sources and methods.

  • DatasetsASSISTments 2009 & 2015; Statics 2011 — public knowledge-tracing benchmarks.
  • MethodBayesian Knowledge Tracing (Corbett & Anderson, 1994); Item Response Theory.
  • BaselinesDeep Knowledge Tracing (DKT) and successor models, used as reproducible comparison points.
  • StandardW3C Verifiable Credentials; Open Badges 3.0.