Editing Effect size (section)

===Population and sample effect sizes===
As in [[statistical estimation]], the true effect size is distinguished from the observed effect size. For example, to measure the risk of disease in a population (the population effect size) one can measure the risk within a sample of that population (the sample effect size). Conventions for describing true and observed effect sizes follow standard statistical practices—one common approach is to use Greek letters like ρ [rho] to denote population parameters and Latin letters like ''r'' to denote the corresponding statistic. Alternatively, a "hat" can be placed over the population parameter to denote the statistic, e.g. with <math>\hat\rho</math> being the estimate of the parameter <math>\rho</math>.

As in any statistical setting, effect sizes are estimated with [[sampling error]], and may be biased unless the effect size estimator that is used is appropriate for the manner in which the data were [[sampling (statistics)|sampled]] and the manner in which the measurements were made.  An example of this is [[publication bias]], which occurs when scientists report results only when the estimated effect sizes are large or are statistically significant.  As a result, if many researchers carry out studies with low statistical power, the reported effect sizes will tend to be larger than the true (population) effects, if any.<ref name="Brand2008">{{Cite journal | vauthors = Brand A, Bradley MT, Best LA, Stoica G | year = 2008 | title = Accuracy of effect size estimates from published psychological research | journal = [[Perceptual and Motor Skills]] | volume = 106 | issue = 2 | pages = 645–649 | doi = 10.2466/PMS.106.2.645-649 | url = http://mtbradley.com/brandbradelybeststoicapdf.pdf | pmid = 18556917 | s2cid = 14340449 | access-date = 2008-10-31 | archive-url = https://web.archive.org/web/20081217175012/http://mtbradley.com/brandbradelybeststoicapdf.pdf | archive-date = 2008-12-17 | url-status=dead }}</ref> Another example where effect sizes may be distorted is in a multiple-trial experiment, where the effect size calculation is based on the averaged or aggregated response across the trials.<ref name="Brand2011">{{Cite journal |vauthors=Brand A, Bradley MT, Best LA, Stoica G | year = 2011 | title = Multiple trials may yield exaggerated effect size estimates | journal = [[The Journal of General Psychology]] | volume = 138 | issue = 1 | pages = 1–11 | doi=10.1080/00221309.2010.520360 | pmid = 21404946 | s2cid = 932324 | url = http://www.ipsychexpts.com/brand_et_al_(2011).pdf| archive-url = https://web.archive.org/web/20110713053244/http://www.ipsychexpts.com/brand_et_al_(2011).pdf| url-status = usurped| archive-date = July 13, 2011}}</ref>

Smaller studies sometimes show different, often larger, effect sizes than larger studies. This phenomenon is known as the small-study effect, which may signal publication bias.<ref>{{Cite journal |last1=Sterne |first1=Jonathan A. C. |last2=Gavaghan |first2=David |last3=Egger |first3=Matthias |date=2000-11-01 |title=Publication and related bias in meta-analysis: Power of statistical tests and prevalence in the literature |url=https://www.jclinepi.com/article/S0895-4356(00)00242-0/abstract |journal=Journal of Clinical Epidemiology |language=English |volume=53 |issue=11 |pages=1119–1129 |doi=10.1016/S0895-4356(00)00242-0 |issn=0895-4356 |pmid=11106885|url-access=subscription }}</ref>