Lecture 3

Question 1

Measurement precision has two different aspects

Answer 1

1. Information; this concept applies to the test score of a single person, thus the within-person aspect of measurement precision
2. Reliability, this concept applies to a population of persons, thus the between-person aspect of measurement precision

Question 2

How can we compute the information concept for a single observed test score?

Answer 2

Inf = 1 / (Var(Ej))

–> the info on test taker j’s true score is the reciprocal of his within person error variance

Question 3

What does a small amount of info means?

Answer 3

A small amount of info (large within-person error variance) means that the test taker j’s observed score vary widely around j’s true score across repeated test administrations

Question 4

Definition and formula for reliability

Answer 4

Def: the reliability of the observed test scores is the squared product moment correlation between observed and true test scores in a population of persons

Formula: REL(S) = cor(S,T)^2
However, since you have no information about the true score, this cannot be computed.

Question 5

What are the two approaches to estimate the reliability?

Answer 5

• parallel tests

- lower bound reliability

Question 6

Name three requirements of parallel tests

Answer 6

Parallel tests are tests that have:

1. True scores are equal
2. Equal error variances
3. Cov(Ej, E’j) = 0

Question 7

Definition and formula for the standard error of measurement of a test

Answer 7

Def = the standard error of measurement of a test is the square root of the error variance in the population of persons

Formula = SEM = wortel(Var(s)*(1-Rel(s))

Question 8

How can you compute alpha

Answer 8

Use the covariance matrix

1. Add all the elements in the diagonal
2. Divide by the sum of all the elements in the matrix
3. 1 - outcome of step 2
4. Compute N/(n-1)
5. Outcome 3 * outcome 4

Question 9

How is the correlation corrected for attenuation calculated?

Answer 9

The correlation between two tests corrected for attenuation is the product moment correlation between the true scores of the two tests in a population of persons

1. Compute the correlation between the two tests
2. Multiply the reliabilities of the tests and take the square root
3. Divide 1 by 2

Question 10

What is the signal to noise ratio?

Answer 10

The signal to noise ratio of a test is the ratio of the true score variance and the error variance of the test in a population of persons.

F = Rel(S)/1-Rel(S)

Question 11

How can we calculate the correlation between two items?

Answer 11

N-1

1. For all persons: compute the differences between the personal score on an item and the item mean score
2. Multiply those outcomes and sum up for all the persons
3. Divide by N minus 1