Measurement models

Question 1

Standard error of measurement

Answer 1

Represents the average size of the error scores. The larger, the greater the average difference between observed scores and true scores. The less reliable the test. Closely related to reliability; Rxx = 1 means SEm =0

Question 2

Psychometric models

Answer 2

Because true scores can’t be obtained, they’re estimated. 4 models were created to do this, all adding restrictions and assumptions.
Most strict to least strict:
- parallel model
- Tau equivalent
- Essentially tau equivalent
- congeneric

Question 3

Key assumptions

Answer 3

1. Test measurement error is random
2. True scores and error scores are uncorrelated

Question 4

Parallel test

Answer 4

1. a=0, b=1 meaning the test scores are equal, the means are equal and the variance is equal.

The correlation between observed scores in a parallel tests is equal to reliability
Used in eg test-retest, split half and alternate forms

Question 5

Tau-equivalent test

Answer 5

a=0 and b=1, so again same scores. This one does not assume that two test have the same error variance. So true score mean AND observed score mean are equal.

2 tests don’t need to have same reliability, meaning the correlation between test does not equal reliability

Question 6

Essentially tau equivalent

Answer 6

Assumes b=1, so only the slope. True score means are equal, observed score means are not

2 tests don’t need to have same reliability, meaning the correlation between test does not equal reliability

Question 7

Congeneric test

Answer 7

No further assumptions. True scores are linearly related, but may differ on intercept (a) and slope (b)