Statistical Significance: What It Is, How It Works, and Examples

Statistical significance is a conclusion from hypothesis testing that an observed relationship or difference in data is unlikely to have occurred by random chance alone. Analysts use it to decide whether data support a systematic effect (e.g., a drug reduces symptoms, market returns changed after an event) rather than mere random variation.

How it works

Formulate hypotheses:
Null hypothesis (H0): the observed effect is due to chance (no real effect).
Alternative hypothesis (H1): there is a real effect.
Perform a statistical test appropriate to the data (t-test, chi-square, regression, etc.).
Compute a p-value: the probability of observing results as extreme as (or more extreme than) those seen, assuming the null hypothesis is true.
Compare the p-value to a preselected significance level (α), commonly 0.05 (5%):
If p ≤ α → reject the null hypothesis and conclude the result is statistically significant.
If p > α → fail to reject the null hypothesis; the data are consistent with chance.

What a p-value means (and what it doesn’t)

It quantifies how surprising the observed data would be if H0 were true.
A small p-value suggests the data are unlikely under H0 and supports H1.
It is not the probability that H0 is true, nor a measure of effect size or practical importance.

Examples

Finance: An analyst compares average daily returns before and after a company’s sudden failure to test for evidence of advance knowledge. A p-value of 0.28 (>0.05) indicates the observed difference is compatible with chance; a p-value of 0.0001 (<0.05) would be strong evidence against the chance explanation and warrant further investigation.
Medicine: A randomized 26‑week trial of a new insulin reports a p-value of 0.04. Since 0.04 < 0.05, the reduction in diabetes-related measures is deemed statistically significant, informing regulators, clinicians, and investors.

Common uses

Clinical trials and regulatory evaluation of drugs, vaccines, and medical devices.
Scientific research across disciplines to test hypotheses.
Business and finance for event studies, product effectiveness, and decision-making based on data.

Limitations and cautions

Statistical significance ≠ practical or clinical significance. Small effects can be statistically significant with large samples; large effects can fail to reach significance with small samples.
It does not prove causation; study design (randomization, controls) and context determine causal interpretation.
Results depend on sample size, measurement quality, and chosen test; p-values can be sensitive to these factors.
Best practice: report p-values alongside effect sizes, confidence intervals, and clear description of methods and assumptions.

Key takeaways

Statistical significance assesses whether observed data are unlikely under a chance-only explanation.
Hypothesis testing produces a p-value; a common threshold for significance is 0.05.
Use significance tests as one part of interpretation—consider effect size, confidence intervals, study design, and practical relevance.

References

StatPearls Publishing. “Statistical Significance” (2023).
American Diabetes Association. Onset 7 Trial: Efficacy and Safety of Fast‑Acting Aspart Compared With Insulin Aspart.
Hwang, T. J., et al. “Stock Market Returns and Clinical Trial Results…” PLoS One (2013).
Rothenstein, J., et al. “Company Stock Prices Before and After Public Announcements Related to Oncology Drugs.” Journal of the National Cancer Institute (2011).