how to read CI

Note from reading 'Inference by Eye'. The interpretation of CI figures does not only require the knowledge of what are plotted (SE vs SD vs CI) but alos require the knowledge of experiement design / analysis context (whether it shows group means of independent samples vs pre-post means of repeated measures vs meta analysis). It is important to understand what effect or comparison is the major interest.

CI is just one from an infinite sequence: if the experiment ware repeated many times and a CI calculated for each, in the long run 95% of the CI will include the true mean. Equivalentlyl, a research who routinely reports 95% CI can expect over a lifetime that about 95% of those intervals will catpure the true mean. To interpret CI: CI is a range of plausible values for mean; values outside the CI are relatively implausible.

The width of CI is the largest error of estimation we are likely to make.

for a comparison of two independent means, p<=0.05 when the overlap of the 95%CI is no more than about half the average width of CI, that is, when proportion overlap is about half. In addition, p<=.01 when the two CI do not overlap. If we see SE, and consider the relationship between SE and 95% CI, P<=0.05 when the gap between the SE bars is at lease about the size of the average SE(of the 2 groups). This rule does not work at all for paired data, because the width of CI for the difference is sensitive to the correlation between the pairs; positive correlation will reduce the width of CI for the mean difference.