The theory of measurement introduced here has been called the classical test theory because it was developed from simple assumptions made by test theorists since the inception of testing.
The approach is also called the theory of true and error scores. The basic starting point of the classical theory of measurement is the idea that test scores result from the influence of two factors;
Factors that contribute to consistency.
Factors that contribute to inconsistency.
The first factor is desirable because it represents the true amount of the attribute in question, while the second factor represents the unavoidable nuisance of error factors that contribute to inaccuracies of breakdown as simple equation; X=T+e
Where X=obtained score, T=True score, e=Errors of measurement.
Errors in measurement thus represent discrepancies between the obtained score and the corresponding true scores: e=X-T
e can be either positive or negative.
It is important to stress that true score is never known. We can obtain a probability that true score resides within a certain interval and we can also derive a best estimate of the true score.
Although it is impossible to eliminate all measurement error, test developers do strive to minimize the psychometric nuisance through careful attention to the sources of measurement error.
Sources of measurement error:
• Item selection
• Test Administration
• test scoring
• Systematic measurement error.
Measurement error and reliability:
Measurement errors are random
Mean error of measurement=0
True score and errors are uncorrelated: r=0
Errors on different test are uncorrelated: r=0
The variance of obtained scores is simply the variance of true scores plus the variance of errors of measurement.
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