A confidence interval is not decoration inside the parentheses: it is built from the estimate and its standard error. It has to contain the estimate, and unless it is a ratio, it has to be centered on it.
A Wald interval — the default in almost every package — is built as estimate ± z · SE. The estimate sits at the center by construction, not by accident.
So if the midpoint of the two limits is not the estimate, one of two things is true: the interval is not a Wald interval (it may be a percentile bootstrap or a profile-likelihood interval, in which case the asymmetry is legitimate and must be declared), or the numbers come from different models.
The second happens more often than it sounds in papers with several tables: the estimate from Table 3 paired with the interval from Table 2, after a covariate was added.
An odds ratio of 2.5 with interval [1.2, 5.2] looks asymmetric, and it is on the original scale: 1.3 below and 2.7 above. But on the log scale it is perfectly centered, which is where it was built.
The correct check is the geometric mean: √(1.2 × 5.2) = 2.50. It matches. Applying the arithmetic mean here — 3.2 — and declaring an error is the commonest mistake made by people auditing these tables.
The same holds for risk ratios, hazard ratios, and anything whose null value is 1 rather than 0.
The width yields the standard error: SE = (upper − lower) / (2 · z), with z = 1.96 for 95 %. It is the figure hardly any paper reports and the one needed to include it in a meta-analysis.
It also works as a cross-check: if the paper gives the t and the estimate, the standard error must be estimate/t, and that has to agree with the one implied by the interval. Two routes to the same number.
And there is a third reading, the one that matters: a very wide interval says the study lacks the power to tell a small effect from a large one, however far below .05 the p value fell. That is covered in how to report confidence intervals.
Then asymmetry is expected and correct, because percentiles need not fall symmetrically. What you must do is say in the text that it is a bootstrap interval, with how many replications and of what type (percentile, BCa). Without that sentence a reviewer reads it as an error.
Not under any standard method. If it happens, there is a typo or two analyses have been mixed. It is one of the very few checks on this axis that admits no legitimate explanation.
For Cohen's d, in practice yes, although its exact intervals are built from the noncentral t and are slightly asymmetric. The containment check always applies; the centering one applies with some slack.
That is a genuine contradiction: for a difference, the 95 % interval excludes zero exactly when p < .05. If they disagree, they were computed from different models or different standard errors.