Test difficulty value defined as ratio of observed to maximum score vector length times cosine of their angle equals test mean divided by number of items¶

Claim · All claims
Evidence · 1 study · theoretical r2 · q2
Currency · newest study 2021 · not yet checked against its sources · not reviewed by a person · overdue for a recheck since 2024: tool and model accuracy changes quickly

Subclaims¶

q2 i? Difficulty value of a test (DiffT) equals the ratio of the length of the observed score vector to the length of the ideal vector multiplied by cos∅, which equals the test mean divided by m, with higher values indicating an easier test. → Chakrabartty 2021

Evidence¶

Chakrabartty 2021¶

Chakrabartty, S. N. (2021). Assessment of item and test parameters: Cosine similarity approach. International Journal of Psychology and Educational Studies, 8(3), 28-38. https://dx.doi.org/10.52380/ijpes.2021.8.3.190

q2 · i? · theoretical · r2

Empirical verification on a 50-item Selection Test administered to 911 candidates (n=911, m=50). Applying the cosine definition, the article reports DiffT = 0.409901, concluding the "Test was moderately difficult".

"By (1.3), 𝐷𝑖𝑓𝑓𝑇 = ‖𝑋‖ ‖𝐼‖ cos ∅ = 𝑋̅ 𝑚 = 0.409901⇒ Test was moderately difficult"

Discussion¶

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