Measurement errors and reliability

1st axiom of the classical test theory The first axiom of the test theory says that a measured value is always composed of the true value and a measurement error. X = W + ex Only with perfect reliability would the measurement error = 0, and the measured value be the true value. In practice, however, this almost never occurs! Since the measurement error is unknown, one does not know the true value of the measurement.

Standard measurement error

If the reliability of a measurement method is known, the so-called standard measurement error can be determined: The standard measurement error: ex = ±s x ?1-rrel 68% of the errors occur in this interval. Even larger errors can only be expected for 32%. To obtain more significant data, the reliability should be increased.

The phenomenon of regression of the center

In test procedures, some values may turn out particularly good or particularly bad. For these values a high true value can be associated with a false high measurement error or a true low value with false low measurement error. The fact that this phenomenon occurs again with a measurement repetition is very small.

The regression to the middle therefore means that false-high and false-low measurements tend to be in the middle during a measurement repetition. These change values are useless for evaluating the change caused by training.

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