IRT Precision

Unlike classical reliability, IRT measurement precision varies across the latent trait continuum

In IRT, measurement precision is not constant — it depends on where a person falls on the latent trait. The Test Information Function I(θ) determines the local Standard Error: $SE(\theta) = 1/\sqrt{I(\theta)}$. A test can be highly reliable at one trait level and nearly useless at another.

Number of items: 10

θ (person's trait): 0.0

Avg discrimination (a): 1.5

Avg difficulty (b): 0.0

SE(θ)

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68% CI width

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95% CI width

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Test information function

$I(\theta) = \sum a_i^2 P_i(\theta) Q_i(\theta)$ (2PL). $SE(\theta) = 1 / \sqrt{I(\theta)}$. Local reliability $\rho(\theta) = 1 - 1/I(\theta)$ when $\sigma^2 = 1$.

The key insight: Unlike Cronbach's $\alpha$, IRT precision varies across the trait continuum. A test is most precise where information peaks — and can be nearly useless at the extremes, which is exactly where clinical decisions are often made. Move θ to the tails to see this for yourself.

Citation

Persson, B. N. (2026). IRT Precision: How Test Information Shapes Measurement Error [Interactive visualization]. https://bjorn-persson.github.io/visualizations/irt-precision/

@misc{Persson2026irtprecision,
  author = {Björn N. Persson},
  year = {2026},
  title = {IRT Precision: How Test Information Shapes Measurement Error},
  note = {Interactive visualization},
  url = {https://bjorn-persson.github.io/visualizations/irt-precision/}}