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Common statistical errors usually come from treating a single number—especially a p-value—as a complete answer. Reliable interpretation requires the study design, sample, measurements, effect estimate, uncertainty, analysis choices, and real-world importance to be considered together.
1. Misreading what a p-value means
A p-value is calculated from data relative to a specified statistical model. It describes how compatible the observed data are with that model and its assumptions. It is not the probability that a hypothesis is true, and it is not the probability that chance alone produced the data.
For example, a p-value of 0.03 does not mean there is a 3% chance that the null hypothesis is true. To interpret it, you need to know the model, the hypothesis being tested, the data collection process, and whether the assumptions are reasonable.
2. Treating p < 0.05 as a truth switch
Crossing a conventional threshold does not turn a claim into fact. Failing to cross it does not prove that no effect exists. The American Statistical Association advises that scientific, business, and policy conclusions should not rest only on whether a p-value crosses a chosen threshold.
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A result just below 0.05 and one just above 0.05 can provide very similar evidence, especially when estimates are uncertain. Report and interpret the full result rather than assigning all meaning to a cutoff.
3. Confusing statistical significance with practical importance
Statistical significance does not measure the size, usefulness, cost, or human importance of an effect. A very small effect can produce a small p-value when the sample is large or measurements are precise. Conversely, a potentially meaningful effect can remain statistically uncertain in a small or noisy study.
What to examine instead
- Effect estimate: How large is the difference, association, or change?
- Uncertainty: What confidence interval or other interval estimate surrounds it?
- Context: Would that range matter scientifically, clinically, economically, or operationally?
- Measurement: Could imprecise or biased measurements change the conclusion?
4. Reporting a p-value without the estimate or uncertainty
A p-value alone prevents readers from judging magnitude and precision. Quantitative results should ordinarily include the effect estimate, its confidence interval, the associated p-value, and the exact sample size used for each test or subgroup. American Heart Association author guidance also asks authors to state whether p-values were adjusted for multiple comparisons and, if so, how.
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A useful report might state the estimated difference, its 95% confidence interval, the sample size contributing to that analysis, and the p-value in the same passage. The interval is not a guarantee that the true value lies inside it; it communicates the range of values supported by the method and data under the stated assumptions.
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5. Hiding the analysis path
Analysts may examine several outcomes, subgroups, models, transformations, time points, or statistical tests. If only favorable results are reported, the displayed p-values no longer have the straightforward interpretation readers may assume. This practice is often described as selective reporting or outcome switching; the central problem is lack of transparency, not an accusation about intent.
Questions to ask
- How many hypotheses, outcomes, subgroups, and model specifications were considered?
- Which analysis was planned in advance, and which decisions were made after seeing the data?
- Were all measured outcomes reported, or only those meeting a threshold?
- Were p-values adjusted for multiple comparisons, and what method was used?
Transparent reports identify the analysis plan, deviations from it, exclusions, and the reason the presented analysis was selected. Readers should treat an isolated favorable result cautiously when the analysis search was broad or undisclosed.
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6. Calling an association causal
A correlation, regression coefficient, statistically significant group difference, or other association does not by itself show that one variable caused another. A third variable may influence both, the direction may be reversed, or selection and measurement processes may create the pattern.
How design changes the causal question
- Randomized experiments can support stronger causal conclusions when randomization is implemented well and outcomes are measured appropriately.
- Observational studies can estimate associations and sometimes support causal analysis with strong design and justified assumptions, but statistical significance alone is not a substitute for those requirements.
- Cross-sectional data often make temporal order difficult to establish, limiting causal interpretation.
Before accepting a causal claim, ask what creates comparability between groups, whether confounders were measured and handled, whether exposure preceded outcome, and whether alternative explanations remain plausible.
7. Assuming a larger sample fixes a biased sample
A large sample can reduce random sampling error, but it does not automatically correct biased selection. If the people included differ systematically from the target population, adding more people with the same selection problem can make the estimate more precise without making it more accurate.
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Check representativeness
- Who was eligible and who was excluded?
- Who declined, dropped out, or was unreachable?
- Which groups are missing or underrepresented?
- What population, setting, and time period can the result reasonably describe?
Generalization should follow the sampling process and study context, not the sample-size headline alone.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.8. Ignoring study design, measurement, and model assumptions
A numerical result inherits weaknesses from how data were collected and analyzed. Poor measurement, non-independence, missing data, inappropriate functional forms, and violated distributional assumptions can make a precise-looking result misleading. A small p-value cannot repair these problems.
Evaluate whether the outcome and exposure were defined consistently, whether the statistical model matches the design, how missing observations were handled, and whether the reported uncertainty reflects the actual sampling and analysis process.
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How to compare two studies or competing claims
When two studies appear to disagree, compare the features that determine what each result can support rather than comparing p-values alone.
| Comparison axis | What to examine |
|---|---|
| Study design | Does the design support the stated descriptive or causal claim? |
| Sample selection | Who was included, who was left out, and what target population is relevant? |
| Effect and uncertainty | Compare estimates and intervals, not just whether each p-value crossed 0.05. |
| Measurement and assumptions | Were variables measured well, and are the model assumptions defensible? |
| Analysis transparency | How many analyses were attempted, and were selection decisions disclosed? |
| Practical meaning | Would the estimated effect matter in the real setting? |
Different populations, outcomes, time frames, or estimands can make apparently conflicting findings answer different questions.
A practical checklist for reading statistical results
- Identify the claim. Is it descriptive, predictive, or causal?
- Read the design first. Check randomization, timing, comparison groups, and follow-up.
- Inspect the sample. Assess selection, exclusions, attrition, and applicability to the target population.
- Find the effect estimate. Look for a difference, ratio, slope, or other quantity—not only a p-value.
- Read the uncertainty. Examine the confidence interval and its width and location.
- Check the analysis path. Look for multiple outcomes, subgroups, models, and any adjustment for multiple comparisons.
- Test the causal wording. Ask whether confounding or reverse causation could explain an association.
- Judge practical importance. Decide whether the plausible effect sizes matter in context.
- Review assumptions and measurement. Consider missing data, variable definitions, and model fit.
- State limits explicitly. Keep the conclusion within the population, design, and evidence actually studied.
The guiding principle
Statistical evidence is one part of scientific reasoning, not a replacement for it. As Ronald L. Wasserstein wrote on behalf of the American Statistical Association Board of Directors, “No single index should substitute for scientific reasoning.” A sound interpretation combines the data, design, assumptions, uncertainty, transparency, and consequences of being wrong.
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