A results section should show each important estimate together with its 95% confidence interval, and it should show the p-value only after the estimate and interval. A p-value alone tells readers whether a result passed a threshold. It does not tell them how large the effect might be or which effect sizes the data are compatible with. The interval does. It cannot, however, repair a biased study, a weak design, or selective reporting, and it is only as useful as the way it is written up.
The order that reporting guidance asks for
Several major reporting standards converge on the same sequence. AHA/ASA author guidance states that quantitative results should be presented in this order: the estimated effect size (the point estimate), then the confidence interval (typically 95%), then the associated actual p-value. The JAMA Network’s author instructions ask authors to quantify findings with appropriate uncertainty indicators, such as confidence intervals, and caution against relying solely on hypothesis testing.
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The reason for this order is that the estimate and its interval belong to a single statement about magnitude and precision. When the p-value comes first, or appears alone, readers tend to treat “significant” as the finding and skip the size of the effect.
A reporting pattern you can adapt
A workable sentence for most two-group comparisons follows this form:
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Estimated [effect measure] was [point estimate] (95% CI [lower, upper]; p = [actual p-value]).
The sentence is only half the job. The surrounding text or the table note should also name the contrast and reference group, the units, the analysis population, and the model or method used to produce the interval. If the confidence level is not 95%, say so in the same sentence. The null value depends on the effect measure, and readers need it to interpret the interval:
| Effect measure | Null value (no effect) | How to read the interval |
|---|---|---|
| Ratios (for example, risk ratio, odds ratio, hazard ratio) | 1 | An interval that lies entirely above 1 is compatible only with an increase in the outcome across the stated range; one entirely below 1 is compatible only with a decrease. |
| Differences (for example, mean difference, risk difference) | 0 | The same logic applies around 0, with the sign of the interval indicating the direction of the difference. |
Match the interval method to the estimand and the design. Clustered, stratified, or weighted data, and models with several random effects, may need interval methods that reflect that structure. Do not present an interval as if it captured every source of uncertainty unless the analysis actually does that. If the interval reflects only sampling variability, say so.
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What an interval says, and what it does not
A confidence interval conveys precision and uncertainty. It does not express the probability that the true value is inside this particular interval.
The repeated-sampling meaning
The American Physiological Society’s 2004 reporting guidance explains the idea through repeated sampling. Its illustration uses 200 hypothetical samples drawn from the same population: the interval method is designed so that, across repeated samples, about 95% of the intervals it produces would contain the fixed population mean. That is a property of the procedure. It is an explanatory device, not a published empirical result.
The probability-of-this-interval misreading
The most common error is to say that there is a 95% chance the parameter lies between the two numbers printed in a paper. Once computed, a particular interval either contains the fixed value or it does not. The 95% describes how often the method succeeds over many repetitions under its assumptions. Those assumptions include the model, the sampling scheme, and the absence of bias, and an interval cannot check them.
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Reading width: precision and imprecision
A narrower interval generally indicates a more precise estimate, because the data constrain the effect more tightly. A wide interval can leave a clinically important benefit, no effect, or a harm all plausible at once. Width should therefore be read against the outcome scale and against the decision the result is meant to inform. An interval of plus or minus two percentage points means something different for a rare adverse event than for blood pressure in millimetres of mercury.
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1Clear out junk files and repair common Windows errors2Scan for outdated or missing drivers - takes under a minute3Repair Windows errors before they cause bigger problemsA wide interval is best described as imprecision. It should not automatically be reported as evidence that the effect is absent. Limited information can produce a wide interval even when an effect exists.
Null values and “no difference” language
An interval that includes the null value is not proof of no effect or of equality. The U.S. Census Bureau’s Statistical Quality Standard E2 asks that nonsignificant comparisons be explicitly identified and that authors not claim population equality merely because an interval includes the null. The same caution applies in any field: say that the data do not distinguish the estimate from the null, and then give the range.
Consider a hypothetical example, with invented numbers: a risk ratio of 0.85 (95% CI 0.70 to 1.04; p = 0.12). The interval includes 1, so the data do not rule out no effect at the 95% level. But the estimate points to a 15% lower risk, and the interval is compatible with anything from a 30% reduction to a 4% increase. A sentence such as “the study found no difference” hides that spread. A sentence such as “the estimate suggested a lower risk, but the data are compatible with a substantial benefit, no effect, or a small increase” describes what the study actually supports.
Statistical significance is not practical importance
AHA/ASA guidance cautions against letting a p-value threshold carry the conclusion. Whether a result passes a threshold is a different question from whether the effect matters. Compare the whole interval with the effects that would be meaningful in the field: a clinically important difference, a biologically relevant change, or a policy threshold. An interval that is statistically significant but sits entirely below the smallest meaningful effect calls for a different conclusion than one that is significant and large.
What intervals cannot fix
Intervals are only as informative as the analysis that produced them. They do not correct for the following problems, and a results section should say so where they apply:
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- Multiple comparisons. When many outcomes or subgroups are tested, some intervals will exclude the null by chance. Intervals alone do not adjust for this.
- Selective reporting. Reporting intervals for only the favourable outcomes produces a misleading picture, however carefully each one is calculated.
- Confounding and bias. An interval around a biased estimate is a precise measure of the wrong quantity.
- Model misspecification. Intervals depend on the model’s assumptions. If those fail, the stated coverage may not hold.
- Design and measurement. Measurement error, missing data, and analysis choices all shape what the interval means. The American Physiological Society guidance itself warns that reporting rules cannot substitute for understanding the statistical concepts and procedures involved.
The practical consequence is that the methods section must describe the analysis plan, the software or method used to obtain the interval, and how missing data were handled. Without that, the interval cannot be evaluated.
When a different uncertainty framework is used
Bayesian analyses report credible intervals, which are built and interpreted differently from frequentist confidence intervals. A credible interval gives a range that, under the stated prior and model, contains the parameter with the stated probability. It should be labelled as a credible interval and its construction described, rather than presented as interchangeable with a confidence interval. The same principle applies to other summaries: report the appropriate interval or uncertainty measure for the framework actually used.
Some reporting standards extend the same expectation to specific fields. The ARRIVE guidelines for animal research ask for effect sizes with their precision measures in the Results section (item 10b), and that expectation also supports later evidence synthesis.
Where the Census Bureau standard applies, its confidence levels are agency conventions for its own products: 90% for Census Bureau publications and news releases and 90% or more for other listed information products. These are not universal rules, and journals usually expect 95%.
For readers who want more depth, Statistics with Confidence: Confidence Intervals and Statistical Guidelines (second edition, edited by Douglas Altman, David Machin, Trevor Bryant, and Martin Gardner, published by Wiley/BMJ Books) covers worked examples and reporting checklists.
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