Theoretically defined test reliability computable from a single administration via parallel-half vector lengths and angle exceeds split-half reliability but falls below Cronbach alpha¶

Claim · All claims
Evidence · 1 study (2 entries) · theoretical r2 · q2
Currency · newest study 2021 · not yet checked against its sources · not reviewed by a person

Subclaims¶

Reading the evidence codes

q is the design tier, i the impact, n the sample, and the kind with its r the rigour judged within that kind: what each code means.

This claim: no standardized effect is recorded in observations/ for it yet, so no benchmark reading is possible.

q2 i? Using an iterative parallel-half split and the lengths of the two subtest score vectors and the angle between them, error variance and theoretically defined reliability (rtt = ST²/SX²) can be estimated from a single administration. → 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 the 50-item test split into parallel halves by the iterative process (equal means 10.25; SDs 66.70 vs 67.11). With ‖Xg‖ = 315.6169, ‖Xh‖ = 315.6058 and Cosθgh = 0.975479, theoretical reliability was 0.551577, SE² = 5.362239, true score variance = 6.595749.

"Theoretical reliability of the test 𝑟𝑡𝑡 = 1 - ‖𝑋𝑔‖2+ ‖𝑋ℎ‖2− 2 ‖𝑋𝑔‖‖𝑋ℎ‖𝑐𝑜𝑠𝜃𝑔ℎ 𝑛.𝑆𝑋 2 = 0.551577"

Chakrabartty 2021 (2)¶

q2 · i? · theoretical · r2

Comparison of reliability estimates on the same data: split-half reliability rgh was 0.380813, theoretical reliability 0.551577, and Cronbach alpha 0.78. The article reports the theoretical value fell between the two.

"Theoretical reliability of the test was higher than the Split-half reliability but lower than Cronbach 𝛼(0.78)"

Discussion¶

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 — related
No statistically significant differences among the four Knowledge/Judgment item scores (ANOVA p=.549), confirming similar rank scores — related
A pilot study (N = 10) established timed-administration parameters, showing high internal consistency and minimal speededness for the SCS1 12-item subset — related
Adding items to a knowledge test can increase reliability without requiring the added items to be redundant with existing items — related
Cronbach's alpha equals the reliability of the scale score under classical test theory, domain sampling, and generalizability theory, and should be interpreted as a reliability coefficient — related

Page metadata

Field	Value
`type`	`claim`
`id`	`single-administration-theoretical-reliability-vectors`
`title`	`Theoretically defined test reliability computable from a single administration via parallel-half vector lengths and angle exceeds split-half reliability but falls below Cronbach alpha`
`description`	`Theoretically defined test reliability computable from a single administration via parallel-half vector lengths and angle exceeds split-half reliability but falls below Cronbach alpha`
`status`	`review`
`evidence_strength`	`moderate`
`newest_evidence`	`2021`
`generated`	by `process:wiki-ingest` on `2026-09-25`
`trust`	unverified — no one has confirmed this page's content
`sources`	2 — `chakrabartty-2021`, `chakrabartty-2021-2`

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