Classical Test theory and Assumptions Flashcards
What is psychometrics?
The field of study concerned with measurement of psychological attributes and characteristics.
e.g. personality traits, attitudes, abilities etc.
What is the purpose of psychometrics?
To design and evaluate reliable and valid psychological measures.
Underlying ideas of CTT
Everything with latent variables is based on CTT, trying to infer something about latent variables (measurement is an inference)
Rests on the notion of TRUE SCORES: an individual’ test score measured without error (T)
True scores
TRUE SCORES: an individual’ test score measured without error (T).
As psychological attributes cannot be measured directly, this is a hypothetical value.
We are not interested in the data, but what it implies.
CTT assumes T is randomly distributed on a normal distribution (if someone took a test an infinite number of times, T would be the mean of these normally distributed scores)
How do we infer true scores?
We infer the values of true scores by administering appropriate test stimuli and calculating an observed score (X)
What is measurement error?
Measurement error (e) is the discrepancy between the true and observed score.
On any given occasion, the observed score will be an imperfect measure of the true score- not an error, it is temporally bound (reflects that exact time)
Measurement error assumption 1:
X= T+e
observed score= True score + error
Measurement error assumption 2 (random):
e(X)= T, so e(e)= 0
Error variance is expected to be random with a mean of 0 (the expected value of error is 0, over infinite tests).
This means that error is essentially 0, so the observed score essentially = true score
You have complete faith that what you are recording (observed score) is actually the true score
Measurement error assumption 3 (correlation1):
Error is expected to be uncorrelated with the true score- there is no systematic relationship between the true score and error (i.e. correlation between T and e=0)
There is no systematic error (the observed score systematically biased away from the true score)
Measurement error assumption 4 (correlation2):
Errors are uncorrelated across 2 tests, or 2 pairs of tests.
Random errors are uncorrelated with each other.
Measurement error assumption 5 (correlation3):
Errors on one test are uncorrelated with the true score on a second test.
E.g. true score of depression doesn’t influence error on anxiety.
What is the expected variance of the observed score?
Expected variance of the observed scores is variance of true score + error variance.
This implies that if we reduce error variance, the observed score variance will be closer to the true score.
other assumptions or CTT
1) all items contribute equally to the overall score
2) response options (in a ration scale) are at equal intervals
3) error applies equally to all scores across the measurement continuum (same error for people scoring high as more people scoring low)
SEM (standard error of measurement)
The standard deviation (SD) or random errors around the true score for an individual
i.e. if someone took the test an infinite number of times, SEM would be the SD of the collected scores
SEM is the intra-individual index of the precision of the test.
