Errors of Measurement

Random Error of Measurement and the Impact

The most common random error involves attenuated measurement. Attenuation takes place when the reliability of the measurement instrument is less than perfect. One feature of a random error is that the sum of the errors for any sample sum to zero. One feature of the impact of random error is [Page 428]that the mean of the sample does not change but the individual scores should not be considered entirely accurate. Essentially, what happens with a random error is that the population estimate does not change; however, the larger the degree of random error, the less accurate any estimation of that parameter.

One implication of random error of measurement becomes an increase in the variance of the distribution of scores. A set of scores that are normally distributed (bell curve) will maintain the shape of that curve, even with a large amount of random error. However, the shape of the curve becomes impacted by increasing the standard deviation and variance of the distribution. The spread or estimate for any score simply becomes reduced in accuracy.

Systematic Error of Measurement and the Impact

Systematic error takes place when the error in the individual observations occurs consistently across all the measurements for the sample. For example, suppose a measure inflates each score by 3 units, the true score for each observation should be considered 3 less units than the observed or reported score. A systematic error indicates only that the error is predictable from some known entity but not that the amount of error is consistent for each score.

For example, suppose the impact of the error is to add 30% to any given true score. A true score of 10 would mean a measured score of 13, whereas a true score of 20 would mean a measured score becomes 26. The level of error is not the same for each participant score, but the impact of the error is systematic for each participant score.

There are a variety of different systems that could be developed that impact scores. The impact of the error of measurement could reduce the validity of the particular index. For example, a blood pressure gauge that inaccurately adds about 50 points to everyone’s blood pressure would create problems in assessing the existence of high blood pressure in a sample of participants. When there exists a metric for comparison, any error of measurement, especially a systematic error, may create misclassification problems when scores are used to provide an assessment. Similarly, a cognitive test of some ability, such as mathematics, may prove problematic if a test (e.g., quantitative reasoning on a standardized test) has different versions and some can be considered more or less difficult.

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