It is a range of plausible values
The interval gives you a range compatible with the data, at the stated level of confidence. A wide interval means the study could not pin the effect down; a narrow one means it could.
That is a statement about precision, and precision is mostly a function of sample size. Two studies can report the same effect with very different intervals and mean quite different things by it.
Whether it crosses the null matters, and not only that
An interval for a difference that includes zero, or for a ratio that includes one, corresponds to a non-significant result. That is the connection to the p value and it is where most readers stop.
But an interval running from a trivial effect to a large one is a different situation from one running from a small effect to a slightly smaller one, even though both may be non-significant. The first says the study was uninformative; the second says the effect is probably small.
Read the ends, not the middle
The point estimate is the single most likely value and it is not the finding. What matters for practice is whether the lower end is still large enough to be worth acting on, and whether the upper end is large enough to be worth worrying about.
If the entire interval sits above what you would consider a meaningful difference, the result is useful regardless of where the point estimate falls within it.
Significance is not importance
A very large study can produce a statistically significant difference that nobody would act on, because with enough participants a trivial effect becomes detectable. The interval makes that visible immediately where the p value hides it.
This is worth stating explicitly in your own writing when it applies, because a paper that reports significance without commenting on magnitude leaves the reader to assume the effect was substantial.
Non-significant does not mean no effect
It means the data are compatible with no effect, along with everything else inside the interval. A study reporting no significant difference with an interval running from a large benefit to a large harm has found nothing at all, and should be described that way.
Writing no effect was found when the study was simply too small to detect one is among the most common misreadings in student literature reviews.
How to write it up
Report the effect with its interval rather than the p value alone, and say what the interval means in the units a reader cares about. Where the interval is wide, say so, because acknowledging imprecision is what a careful reader is looking for.
That habit also protects you in a viva. An examiner asking how confident you are in a finding is asking about the interval, and having already written about it means you have already answered.
A short way to describe a result
Give the effect, give the interval, and say what the ends mean in the units that matter. Three clauses, and the reader knows both what was found and how firmly.
Compare that with reporting significance alone, which tells a reader that something was detected while leaving the size of it entirely unstated. The longer version is barely longer and it is far harder to misread.
Questions this raises.
What does ninety-five percent confidence actually mean?
That if the study were repeated many times, intervals constructed the same way would contain the true value in ninety-five percent of those repetitions. It is a statement about the procedure rather than about this particular interval, which is a subtlety worth knowing and rarely worth spelling out in a paper.
Should I report the interval or the p value?
Both where your field expects both, and the interval is the more informative of the two. Most reporting standards now ask for effect sizes with intervals precisely because a p value alone tells a reader whether something was detected and nothing about how large it was.
What makes an interval wide?
Mostly a small sample, and also high variability in what was measured. A wide interval is not a flaw in the analysis, it is an accurate report of how much the study could establish. Treating a wide interval as though it pinned something down is the error.
Can I compare intervals between studies?
Informally and with considerable care. Overlapping intervals do not necessarily mean two studies agree, and non-overlapping ones do not automatically mean they disagree, because the comparison depends on more than the ranges. Where that comparison matters to your argument, a meta-analysis that has done it formally is a far stronger citation than your own reading of two forest plots side by side.
Does this apply to odds ratios?
Yes, with the null value at one rather than zero, and with the additional care that odds ratios overstate risk differences when an outcome is common. Where a paper reports an odds ratio for a frequent outcome, that is worth noting rather than translating it directly into a statement about risk.
Warren Cobbett
PhD, Biostatistics, on the statistics and analysis side of the hall. Writes for The Footnote and coaches the students who bring this work to the desk. The rest of the specialists.
Elsewhere in the hall.
Send the assignment and the deadline.
A specialist credentialed in your own field reads what you actually have and replies within two hours with a plan and a price. The reading costs nothing, and if the honest answer is that we are not the right hall for it, you will get that instead.
