Attenuation correction

The attenuation correction or reduction correction ( Engl. Correction for attenuation ) estimates two variables such as strong  x and  y correlate would if they did not measurement error would be tainted if they so perfect reliability would have.

One differentiates:

• the simple mitigation correction; it only corrects the lack of reliability of one of the two measured values:

${\displaystyle r_{x'y'}={\frac {r_{xy}}{\sqrt {r_{xx}}}}}$ or ${\displaystyle r_{x'y'}={\frac {r_{xy}}{\sqrt {r_{yy}}}}}$

• the double reduction correction; With it, the lack of reliability of both measured values ​​is corrected, which should be related:

${\displaystyle r_{x'y'}={\frac {r_{xy}}{\sqrt {r_{xx}\cdot r_{yy}}}}}$

With

• the corrected correlation r _{x'y '} or the correlation of the true values
• the uncorrected correlation r _xy
• the reliability r _{xx of} the measurement x
• the reliability r _{yy of} the measurement y.

Practical use

The simple reduction correction can e.g. Use it well, for example, if you want to know whether it is worthwhile to improve a measuring instrument that is intended to predict a criterion. It could e.g. For example, you want to use an intelligence test in elementary school (measuring instrument) to predict school grades in secondary school (criterion). The intelligence test could be improved by extending it (see Spearman-Brown formula ). The school grades, on the other hand, already represent a measured value that one also wants to predict in real terms. Now, if the predictive accuracy (i.e. the correlation) of the intelligence test for the grade were low, one might wonder whether it would be worthwhile to improve the measurement accuracy of the intelligence test. On the other hand, the assumption of a perfectly accurate school grade and thus also the correction of the second variable is nonsensical, because it can be assumed that the currently relatively imprecise determination of the grades will not change in the school system in the foreseeable future.

The double reduction correction is z. This is useful, for example, when the relationship between two constructs that can not be observed directly is sought for which only an estimate is available using an indicator prone to measurement errors . For example, intelligence cannot be observed directly; it can only be measured using an intelligence test which, however , is influenced by many random disturbances . It is important that the reduction correction only corrects the random interference influences on the measurement, but not the systematic ones. The same measurement error could apply to a variable that is not directly observable and which one wants to check whether it is related to intelligence. The double reduction correction is therefore of particular interest for research , since it cannot be assumed that both measurements will be carried out perfectly (reliably) without errors.

Problem: dilution paradox

The dilution paradox says: With a reduction correction, the higher the corrected relationship , the lower the accuracy of the individual measurements.

In technical terms, this means: the lower the reliabilities of the measurements that you want to correlate with each other, the more drastic the correction of the correlation, since the reliabilities in the denominator are included in the formula. At the same time, however, the confidence interval of the corrected correlation increases, which ultimately takes account of the reliability-related lower estimation precision and resolves the paradox.

Individual evidence

1. ↑ ^{a b} Amelang, M. & Schmidt-Atzert, L. (2006). Psychological diagnosis and intervention (pp. 39–44). Springer: Heidelberg, ISBN 978-3-540-28462-8 , doi : 10.1007 / 3-540-28507-5 .
2. ^ JE Hunter, FL Schmidt: Methods of meta-analysis: Correcting error and bias in research findings . 2nd Edition. SAGE, London 2004, ISBN 978-1-4129-0479-7 .