Editing Confidence interval (section)

==== Confidence procedure for ''ω''<sup>2</sup> ====
Steiger<ref>{{cite journal |last= Steiger|first=J. H. |date= 2004|title= Beyond the F test: Effect size confidence intervals and tests of close fit in the analysis of variance and contrast analysis|journal= Psychological Methods|volume= 9|issue= 2|pages= 164–182|doi= 10.1037/1082-989x.9.2.164|pmid=15137887 }}</ref> suggested a number of confidence procedures for common [[Effect size#Omega-squared (ω2)|effect size]] measures in [[Analysis of variance|ANOVA]]. Morey et al.<ref name=Morey /> point out that several of these confidence procedures, including the one for ''ω''<sup>2</sup>, have the property that as the ''F'' statistic becomes increasingly small—indicating misfit with all possible values of ''ω''<sup>2</sup>—the confidence interval shrinks and can even contain only the single value ''ω''<sup>2</sup>&nbsp;=&nbsp;0; that is, the CI is infinitesimally narrow (this occurs when <math>p\geq1-\alpha/2</math> for a <math>100(1-\alpha)\%</math> CI).

This behavior is consistent with the relationship between the confidence procedure and [[Statistical hypothesis testing|significance testing]]: as ''F'' becomes so small that the group means are much closer together than we would expect by chance, a significance test might indicate rejection for most or all values of ''ω''<sup>2</sup>. Hence the interval will be very narrow or even empty (or, by a convention suggested by Steiger, containing only 0). However, this does ''not'' indicate that the estimate of ''ω''<sup>2</sup> is very precise. In a sense, it indicates the opposite: that the trustworthiness of the results themselves may be in doubt. This is contrary to the common interpretation of confidence intervals that they reveal the precision of the estimate.