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I know the recommendation to report effect sizes is often accompanied by that to also report confidence intervals. However I'm not sure if the two refer to the same variables.

If I want to ascertain the statistical significance and effect size of the difference in some variable X between population A and population B, I might report a t- & a p-value and an effect size measure (e.g. Cohen's d). The CIs would presumably apply to the population estimates (or is it more meaningful for it to apply to the effect size itself?).

But then would the CIs (at 95%) not simply be mean+-1.96SEM, i.e. be graphically identical to an error bar (assuming it defined by the 95%-CI?)? If so, then I don't understand how reporting CIs complements reporting effect sizes, since essentially both could, at a first approximation, be eye-balled from the plot with error bars. Or?

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  • $\begingroup$ Plot with errorbars is one way to report confidence intervals. Do you want to test if effect for pop A differs from the same effect for pop B, and looking for suitable test/plot? $\endgroup$ – Ott Toomet Aug 11 '16 at 18:40
  • $\begingroup$ Well the test would just be a t-test, and the error bars can use either CIs or SEMs. My question was really more conceptual. $\endgroup$ – z8080 Aug 11 '16 at 21:29

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