Classical Test Theory

Question 1

What are the seven assumptions of classical test theory?

Answer 1

1. X = T + E
2. E[X] = T
3. þ_ET = 0
4. þ_E1E2 = 0
5. þ_E1T2 = 0
6. If two tests have observed scores X and X’ that satisfy Assumptions 1 through 5, and if, for every population of examinees,

T = T’ and σ_E2 = σ_E’2

     then they are parallel tests​

7. If two tests have observed scores X1 and X2 that satisfy Assumptions 1through 5, and if, for every population of examinees,T₁ = T₂ + c₁₂where c₁₂ is a constant, then the tests are called essentially τ-equivalent tests

Question 2

Is measurement theory under classical test theory systematic or unsystematic?

Answer 2

Unsystematic

Question 3

What is the difference between systematic and unsystematic measurement error?

Answer 3

Unsystematic = occurs due to random chance

Systematic = occurs due to issues with the measurement instrument itself (e.g., it consistently over or under estimates)

Question 4

What is the greek symbol for the an individual’s true score?

Answer 4

tau, or τ

Question 5

When are two tests essentially τ-equivalent tests?

Answer 5

When both have the same true score (τ), but different error variances (σ_E²).

E.g., three people take two tests and score 10, 11, 12 on one and then 12,13,14 on the other

Question 6

Are parallel tests also essentially τ-equivalent?

Answer 6

Yes

Question 7

Are essentially τ-equivalent tests parallel tests?

Answer 7

It depends. They are parallel if they have their error variances (σ_E²) are equivalents.

Question 8

What is a true score?

Answer 8

An average score taken over repeated independent testings with the same test