Classical Test Theory
The goal of reliability theory is to estimate errors in measurement and to suggest ways of improving tests so that errors are minimized.
The central assumption of reliability theory is that measurement errors are essentially random. This does not mean that errors arise from random processes. For any individual, an error in measurement is not a completely random event. However, across a large number of individuals, the causes of measurement error are assumed to be so varied that measure errors act as random variables.
If errors have the essential characteristics of random variables, then it is reasonable to assume that errors are equally likely to be positive or negative, and that they are no correlated with true scores or with errors on other tests.
It is assumed that:
1. Mean error of measurement = 0
2. True scores and errors are uncorrelated
3. Errors on different measures are uncorrelated
Reliability theory shows that the variance of obtained scores is simply the sum of the variance of true scores plus the variance of errors of measurement.
This equation suggests that test scores vary as the result of two factors:
1. Variability in true scores
2. Variability due to errors of measurement.
The reliability coefficient provides an index of the relative influence of true and error scores on attained test scores. In its general form, the reliability coefficient is defined as the ratio of true score variance to the total variance of test scores. Or, equivalently, one minus the ratio of the variation of the error score and the variation of the observed score:
Unfortunately, there is no way to directly observe or calculate the true score, so a variety of methods are used to estimate the reliability of a test.
Some examples of the methods to estimate reliability include test-retest reliability, internal consistency reliability, and parallel-test reliability. Each method comes at the problem of figuring out the source of error in the test somewhat differently.
Read more about this topic: Reliability (psychometrics)
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