---
title: "Meta-analysis"
chunk: 5/7
source: "https://en.wikipedia.org/wiki/Meta-analysis"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T04:26:08.077779+00:00"
instance: "kb-cron"
---

=== Validation of meta-analysis results ===
The meta-analysis estimate represents a weighted average across studies and when there is heterogeneity this may result in the summary estimate not being representative of individual studies. Qualitative appraisal of the primary studies using established tools can uncover potential biases, but does not quantify the aggregate effect of these biases on the summary estimate. Although the meta-analysis result could be compared with an independent prospective primary study, such external validation is often impractical. This has led to the development of methods that exploit a form of leave-one-out cross validation, sometimes referred to as internal-external cross validation (IOCV). Here each of the k included studies in turn is omitted and compared with the summary estimate derived from aggregating the remaining k- 1 studies.  A general validation statistic, Vn based on IOCV has been developed to measure the statistical validity of meta-analysis results. For test accuracy and prediction, particularly when there are multivariate effects, other approaches which seek to estimate the prediction error have also been proposed.

== Challenges ==
A meta-analysis of several small studies does not always predict the results of a single large study. Some have argued that a weakness of the method is that sources of bias are not controlled by the method: a good meta-analysis cannot correct for poor design or bias in the original studies. This would mean that only methodologically sound studies should be included in a meta-analysis, a practice called 'best evidence synthesis'. Other meta-analysts would include weaker studies, and add a study-level predictor variable that reflects the methodological quality of the studies to examine the effect of study quality on the effect size. However, others have argued that a better approach is to preserve information about the variance in the study sample, casting as wide a net as possible, and that methodological selection criteria introduce unwanted subjectivity, defeating the purpose of the approach. More recently, and under the influence of a push for open practices in science, tools to develop "crowd-sourced" living meta-analyses that are updated by communities of scientists  in hopes of making all the subjective choices more explicit.

=== Publication bias: the file drawer problem ===

Another potential pitfall is the reliance on the available body of published studies, which may create exaggerated outcomes due to publication bias, as studies which show negative results or insignificant results are less likely to be published. For example, pharmaceutical companies have been known to hide negative studies and researchers may have overlooked unpublished studies such as dissertation studies or conference abstracts that did not reach publication. This is not easily solved, as one cannot know how many studies have gone unreported.
This file drawer problem characterized by negative or non-significant results being tucked away in a cabinet, can result in a biased distribution of effect sizes thus creating a serious base rate fallacy, in which the significance of the published studies is overestimated, as other studies were either not submitted for publication or were rejected. This should be seriously considered when interpreting the outcomes of a meta-analysis.
The distribution of effect sizes can be visualized with a funnel plot which (in its most common version) is a scatter plot of standard error versus the effect size. It makes use of the fact that the smaller studies (thus larger standard errors) have more scatter of the magnitude of effect (being less precise) while the larger studies have less scatter and form the tip of the funnel. If many negative studies were not published, the remaining positive studies give rise to a funnel plot in which the base is skewed to one side (asymmetry of the funnel plot). In contrast, when there is no publication bias, the effect of the smaller studies has no reason to be skewed to one side and so a symmetric funnel plot results. This also means that if no publication bias is present, there would be no relationship between standard error and effect size. A negative or positive relation between standard error and effect size would imply that smaller studies that found effects in one direction only were more likely to be published and/or to be submitted for publication.
Apart from the visual funnel plot, statistical methods for detecting publication bias have also been proposed. These are controversial because they typically have low power for detection of bias, but also may make false positives under some circumstances. For instance small study effects (biased smaller studies), wherein methodological differences between smaller and larger studies exist, may cause asymmetry in effect sizes that resembles publication bias. However, small study effects may be just as problematic for the interpretation of meta-analyses, and the imperative is on meta-analytic authors to investigate potential sources of bias.
The problem of publication bias is not trivial as it is suggested that 25% of meta-analyses in the psychological sciences may have suffered from publication bias. However, low power of existing tests and problems with the visual appearance of the funnel plot remain an issue, and estimates of publication bias may remain lower than what truly exists.
Most discussions of publication bias focus on journal practices favoring publication of statistically significant findings. However, questionable research practices, such as reworking statistical models until significance is achieved, may also favor statistically significant findings in support of researchers' hypotheses.

=== Problems related to studies not reporting non-statistically significant effects ===
Studies often do not report the effects when they do not reach statistical significance. For example, they may simply say that the groups did not show statistically significant differences, without reporting any other information (e.g. a statistic or p-value). Exclusion of these studies would lead to a situation similar to publication bias, but their inclusion (assuming null effects) would also bias the meta-analysis.