Editing Effect size (section)

==Interpretation==

The interpretation of an effect size of being ''small'', ''medium'', or ''large'' depends on its substantive context and its operational definition. Jacob Cohen<ref name="CohenJ1988Statistical"/> suggested interpretation guidelines that are near ubiquitous across many fields. However, Cohen also cautioned:

<blockquote>"The terms 'small,' 'medium,' and 'large' are relative, not only to each other, but to the area of behavioral science or even more particularly to the specific content and research method being employed in any given investigation... In the face of this relativity, there is a certain risk inherent in offering conventional operational definitions for these terms for use in power analysis in as diverse a field of inquiry as behavioral science. This risk is nevertheless accepted in the belief that more is to be gained than lost by supplying a common conventional frame of reference which is recommended for use only when no better basis for estimating the ES index is available." (p. 25)</blockquote>

Sawilowsky<ref name="Sawilowsky2009">{{cite journal | last=Sawilowsky | first=S | year=2009 | title=New effect size rules of thumb| journal=Journal of Modern Applied Statistical Methods | volume=8 | pages=467–474 | doi= 10.22237/jmasm/1257035100| issue=2| doi-access=free }} http://digitalcommons.wayne.edu/jmasm/vol8/iss2/26/</ref> recommended that the rules of thumb for effect sizes should be revised, and expanded the descriptions to include ''very small'', ''very large'', and ''huge''. Funder and Ozer <ref name="Funder&Ozer2019"/> suggested that effect sizes should be interpreted based on benchmarks and consequences of findings, resulting in adjustment of guideline recommendations.

{{Proper name|Lenth}}<ref>{{Cite web | author = Russell V. Lenth | title = Java applets for power and sample size | url = http://www.stat.uiowa.edu/~rlenth/Power/ | publisher = Division of Mathematical Sciences, the College of Liberal Arts or The University of Iowa | access-date = 2008-10-08}}</ref> noted for a ''medium'' effect size, "you'll choose the same ''n'' regardless of the accuracy or reliability of your instrument, or the narrowness or diversity of your subjects. Clearly, important considerations are being ignored here. Researchers should interpret the substantive significance of their results by grounding them in a meaningful context or by quantifying their contribution to knowledge, and Cohen's effect size descriptions can be helpful as a starting point."<ref name="Ellis2010"/> Similarly, a U.S. Dept of Education sponsored report  argued that the widespread indiscriminate use of Cohen's interpretation guidelines can be inappropriate and misleading.<ref name="Lipsey">{{Cite book | author = Lipsey, M.W.  | title = Translating the Statistical Representation of the Effects of Education Interventions Into More Readily Interpretable Forms | publisher = U.S. Dept of Education, National Center for Special Education Research, Institute of Education Sciences, NCSER 2013–3000  | location = United States | url=http://ies.ed.gov/ncser/pubs/20133000/pdf/20133000.pdf  | year = 2012 |display-authors=etal}}</ref> They instead suggested that norms should be based on distributions of effect sizes from comparable studies. Thus a small effect (in absolute numbers) could be considered ''large'' if the effect is larger than similar studies in the field. See [[Abelson's paradox]] and Sawilowsky's paradox for related points.<ref>{{cite journal |last=Sawilowsky |first=S. S. |year=2005 |title=Abelson's paradox and the Michelson-Morley experiment |journal=Journal of Modern Applied Statistical Methods |volume=4 |issue=1 |pages=352 |url=http://digitalcommons.wayne.edu/coe_tbf/13 |doi=10.22237/jmasm/1114907520 |doi-access=free }}</ref><ref>{{cite book |first1=S. |last1=Sawilowsky |first2=J. |last2=Sawilowsky |first3=R. J. |last3=Grissom |year=2010 |chapter=Effect Size |editor-first=M. |editor-last=Lovric |title=International Encyclopedia of Statistical Science |publisher=Springer }}</ref><ref>{{cite journal |first=S. |last=Sawilowsky |year=2003 |title=Deconstructing Arguments from the Case Against Hypothesis Testing |journal=Journal of Modern Applied Statistical Methods |volume=2 |issue=2 |pages=467–474 |url=http://digitalcommons.wayne.edu/coe_tbf/17 |doi=10.22237/jmasm/1067645940 |doi-access=free }}</ref>

The table below contains descriptors for various magnitudes of ''d'', ''r'', ''f'' and ''omega'', as initially suggested by Jacob Cohen,<ref name="CohenJ1988Statistical"/> and later expanded by Sawilowsky,<ref name="Sawilowsky2009"/> and by Funder & Ozer.<ref name="Funder&Ozer2019">{{cite journal | last1=Funder| first1=D.C. | last2=Ozer| first2=D.J. |year=2019 | title=Evaluating effect size in psychological research: Sense and nonsense | journal=Advances in Methods and Practices in Psychological Science | volume=2 | pages=156–168 | doi=10.1177/2515245919847202 | issue=2}}</ref>

{| class="wikitable"
! Effect size !! ''d'' !! ''r'' !! ''f'' !! ''omega''
|-
| Very small ||  0.01<ref name="Sawilowsky2009"/> || 0.005<ref name="Sawilowsky2009"/> || 0.005<ref name="Sawilowsky2009"/> || 
|-
| Small ||  0.20<ref name="CohenJ1988Statistical"/><ref name="Sawilowsky2009"/> || 0.10<ref name="CohenJ1988Statistical"/><ref name="Sawilowsky2009"/> || 0.10<ref name="CohenJ1988Statistical"/><ref name="Sawilowsky2009"/> || 0.10<ref name="CohenJ1988Statistical"/>
|-
| Medium ||  0.41,<ref name="Funder&Ozer2019"/> 0.50<ref name="CohenJ1988Statistical"/> || 0.20,<ref name="Funder&Ozer2019"/> 0.24<ref name="CohenJ1988Statistical"/> || 0.20,<ref name="Funder&Ozer2019"/> 0.31<ref name="CohenJ1988Statistical"/> || 0.30<ref name="CohenJ1988Statistical"/>
|-
| Large ||  0.63,<ref name="Funder&Ozer2019"/> 0.80<ref name="CohenJ1988Statistical"/> || 0.30,<ref name="Funder&Ozer2019"/> 0.37<ref name="CohenJ1988Statistical"/> || 0.32,<ref name="Funder&Ozer2019"/> 0.40<ref name="CohenJ1988Statistical"/> || 0.50<ref name="CohenJ1988Statistical"/>
|-
| Very large ||  0.87,<ref name="Funder&Ozer2019"/> 1.20<ref name="Sawilowsky2009"/>  ||0.40,<ref name="Funder&Ozer2019"/> 0.51<ref name="Sawilowsky2009"/>|| 0.44,<ref name="Sawilowsky2009"/>  0.60<ref name="Funder&Ozer2019"/> || 
|-
| Huge ||  2.0<ref name="Sawilowsky2009"/> || 0.71<ref name="Sawilowsky2009"/> || 1.0<ref name="Sawilowsky2009"/> || 
|-
|}