PerspectiveSTATISTICS

Measurement error and the replication crisis

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Science  10 Feb 2017:
Vol. 355, Issue 6325, pp. 584-585
DOI: 10.1126/science.aal3618

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  • Correcting Measurement Error to Build Scientific Knowledge
    • Brenton M. Wiernik, Postdoctoral Fellow, Ghent University
    • Other Contributors:
      • Deniz S. Ones, Professor, University of Minnesota

    Loken and Gelman (1) describe problems of null-hypothesis significance testing, selective publishing, and imperfect measures distorting the scientific literature. They raise questions about the validity of widely-accepted, well-understood methods for statistically correcting measurement error (2) and the studies that have applied them. Relationships and effects under study are affected by “noise.” But fortunately, the “noise” can be separated into two types, and there are well-known solutions for each. The first type is systematic error in measurements, which predictably biases observed relations downward. The second type is random (sampling) error, which unpredictably obscures true relations, unsystematically making observed relations smaller or larger. On average, random error is zero, but it can be large in small samples (3). Both types of error obscure true relations and must be corrected to draw accurate conclusions. Systematic error can be addressed in single samples using well-known statistical corrections (2). Random error cannot be corrected in single samples because the direction and size of the error is unknown. However, random error asymptotes to zero as sample size increases. Its impact can be mitigated either by gathering much larger samples or, more practically, by combining results from smaller studies using meta-analysis (4). When studies are meta-analytically pooled, their random errors cancel out. Furthermore, their systematic errors can be statistically...

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    Competing Interests: None declared.
  • RE: Measurement error and the replication crisis

    As noted in a personal email from the lead author, the article could have made a clearer distinction between sampling error and random measurement error. We show that random measurement error always attenuates population effect sizes and statistical power, which reduces the chance of obtaining a significant result.

    If sampling error (due to luck or questionable research practices) inflates observed effect sizes enough to produce a significant result, the median amount of inflation is inversely related to power of a study. Thus, conditional on selection for significance, random measurement error leads to more inflation, but the estimated effect sizes are never larger than the effect sizes that would have been obtained with a more reliable measure. In sum, consistent with statistical theories, random measurement error always attenuates observed effect sizes, even when studies are selected for significance.

    For a detailed comment that could not be published in Science, you can read the commentary on my blog.

    Ulrich Schimmack & Rickard Carlsson

    replicationindex.wordpress.com/2017/02/23/random-measurement-error-and-the-replication-crisis-a-statistical-analysis/

    Competing Interests: None declared.