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?