When Results are Statistically Significant, What Does it Really Mean?

Statistical significance refers to whether an observed result is unlikely to be explained by random chance alone.  In research, policy, litigation, and other applied fields, understanding statistical significance is essential for interpreting findings and evaluating evidence.

This article explains what statistical significance is — and what it isn’t — while highlighting common misunderstandings.

Key Takeaways

• Statistical significance is not the same as practical or real-world importance, often referred to as practical significance.
• Common misinterpretations include (i) equating sample size with significance, and (ii) assuming a lack of significance means no effect.
• P-values are only part of the picture. Effect sizes, confidence intervals, and study design often provide more context than p-values alone.
• Significance should be interpreted alongside context: data quality, methodology, and decision-making needs.

What Statistical Significance Is — and What It Isn’t

The phrase “statistically significant” is common across medicine, social science, business, and litigation — but it is often misunderstood.

Think of flipping a coin.  If you flip it 10 times and get 8 heads, you might wonder: Is this coin fair, or could the difference from the expected 50/50 result be due to chance?  Statistical testing asks: Is the observed difference (8 heads vs. 5 expected) likely due to chance alone?  What about 80 heads out of 100?  800 heads out of 1,000?

A few basics:

• P-values estimate the probability of observing data as extreme as those found, assuming the null hypothesis is true.  They are not the probability that the null is true.
• A result is usually labeled statistically significant when the p-value falls below a threshold (commonly 0.05).[1] This suggests the finding is unlikely to be explained by chance alone.
• Importantly, statistical significance does not imply a large or practically relevant effect.  It only indicates that random chance is an unlikely explanation.

Common Misinterpretations

Misunderstanding #1: “The sample isn’t statistically significant.”

Samples themselves are never significant — it’s the results from analyzing them that may be.  The better-framed question is whether a sample allows valid probability-based inferences. 

Misunderstanding #2: “If it’s statistically significant, it must be meaningful.”

A trivial difference in test scores can be statistically significant in a huge dataset but irrelevant in practice.  Significance answers, “Could this be due to chance?” — not “Is this worth caring about?” That is where understanding practical significance becomes key.

Misunderstanding #3: “If it’s not statistically significant, there’s no effect.”

Statistically insignificant differences may reflect either a tiny effect or an underpowered study with too few observations.  Remember: absence of evidence is not evidence of absence.  For example, a small clinical trial may not detect significance even if a treatment has meaningful effects.  Evaluating the alternative hypothesis and being mindful of false negatives is critical here. 

Misunderstanding #4: “We found some significance — case closed.”

Running many tests can increase the odds of false positives, a problem stemming from multiple testing.  Without corrections or replication, isolated “significant” results can be misleading, especially without a robust statistical framework.

Looking Beyond the P-Value and Statistical (In)Significance

Statistical significance is one piece of the puzzle.  A thoughtful interpretation also considers:

• Effect size — How large is the difference or relationship?
• Confidence intervals — What range of parameter values is plausible based on the data?
• Study design — How were data collected, and what limitations or biases exist?
• Practical implications — Do the results matter in the real world?

Final Thought: Significance Is Not Substance

Statistical significance is a tool, not a verdict.  It tells us whether chance is a likely explanation.  Whether the result is important or actionable may be related but is a different question.  Sound decisions come from combining significance with context, effect size, and expert judgment.

Preguntas frecuentes

What is statistical significance?

It’s the probability of observing data as extreme as those found, assuming the null hypothesis is true.

Can a sample itself be statistically significant?

No. Samples are never “statistically significant” — only results from analyzing them may be. Random samples are advantageous because they put the practitioner in a strong position to make probability-based inferences.  The size of a random sample can affect the power of a study (i.e., its ability to detect an effect if one exists), but the label of “significant” applies to results, not to the sample or its size.

Does statistical significance imply that the results are important?

Not necessarily.  A result can be statistically significant but inconsequential as a practical matter. Understanding both statistical and practical significance is crucial.

Can a small sample reveal statistically significant results?

Yes — but it typically requires a much larger effect to reach significance. Small samples are also more vulnerable to outliers, and at the same time, outliers themselves are harder to detect when data are limited.

Does significance prove causation?

No.  Statistical significance relates only to probability, not cause and effect.

What matters besides the p-value?

Effect size, confidence intervals, the hypotheses being tested, and study design all provide valuable context.

Why are adjustments potentially needed when performing multiple comparisons?

Testing many hypotheses in parallel raises the chance of false positives.  Without context, “significant” results can be misleading.