TL;DR — Quick Answer
Statistical significance indicates whether a result is likely to reflect a real effect rather than random chance. It is assessed using the p-value — the probability of obtaining the observed result (or a more extreme one) if there were truly no effect. A common threshold is p < 0.05, meaning less than a 5% probability the result occurred by chance. If the p-value is below the threshold, the result is “statistically significant.” Importantly, statistical significance does not mean a result is large, important, or practically meaningful — it only addresses whether the effect is likely real.
Few concepts in research are as widely used — and as widely misunderstood — as statistical significance and the p-value. They appear in countless research papers, often determining whether findings are considered meaningful and publishable. Yet their meaning is frequently misinterpreted, even by researchers, leading to flawed conclusions and overstated claims. Understanding what statistical significance and the p-value actually mean, and what they do not, is essential for anyone conducting or evaluating quantitative research.
This guide explains what statistical significance is, what the p-value really means, the common misconceptions surrounding it, and the crucial distinction between statistical and practical significance — clarifying one of the most important and misunderstood areas of research.
What Is Statistical Significance?
Statistical significance indicates whether an observed result in a study is likely to reflect a genuine effect or relationship, rather than having occurred merely by random chance. When a result is “statistically significant,” it means that the result is unlikely to have arisen by chance alone, suggesting that a real effect is probably present.
The logic behind statistical significance addresses a fundamental problem in research: any observed result could, in principle, be due to random variation rather than a real effect. Statistical significance testing assesses how likely it is that the observed result would have occurred if there were actually no effect. If that likelihood is very low, the result is considered statistically significant, supporting the conclusion that a real effect exists.
What Is the P-Value?
The p-value is the measure used to assess statistical significance. Specifically, the p-value is the probability of obtaining the observed result — or one more extreme — if there were truly no effect (that is, if the null hypothesis were true).
A small p-value means that the observed result would be very unlikely if there were no real effect, which provides evidence against the idea that there is no effect, and therefore in favour of a real effect. A large p-value means the observed result would be reasonably likely even if there were no effect, providing little evidence of a real effect.
Put simply: the p-value tells you how surprising your result would be if there were actually nothing going on. A very small p-value means your result would be very surprising under “no effect,” suggesting something real is happening.
The Significance Threshold
To decide whether a result is statistically significant, researchers compare the p-value to a predetermined threshold, called the significance level or alpha. The most commonly used threshold is 0.05.
If the p-value is less than 0.05, the result is conventionally considered statistically significant — meaning there is less than a 5% probability that the result occurred by chance if there were no real effect. If the p-value is 0.05 or greater, the result is not considered statistically significant by this conventional standard.
| P-Value | Interpretation (at α = 0.05) |
|---|---|
| p < 0.05 | Statistically significant — unlikely due to chance |
| p ≥ 0.05 | Not statistically significant by this standard |
| p < 0.01 | Highly significant — very unlikely due to chance |
It is worth noting that the 0.05 threshold is a convention, not a law of nature. Different fields and studies may use different thresholds (such as 0.01 for more stringent standards), and there is ongoing discussion in the research community about the use and limitations of fixed significance thresholds.
Common Misconceptions About the P-Value
The p-value is one of the most misinterpreted concepts in research. Several common misconceptions are important to correct.
The p-value is not the probability that the null hypothesis is true. It is the probability of the observed data (or more extreme) given that the null hypothesis is true — not the probability that the null hypothesis is true given the data. This is a subtle but crucial distinction.
A statistically significant result is not necessarily a large or important one. Statistical significance only indicates that an effect is likely real, not that it is large or meaningful. A tiny, unimportant effect can be statistically significant, especially with a large sample.
A non-significant result does not prove there is no effect. Failing to find statistical significance does not prove the absence of an effect; it may mean the study lacked the power to detect it, or that the effect is small. Absence of evidence is not evidence of absence.
The p-value does not measure the size of an effect. It addresses whether an effect is likely real, not how big it is. Effect size is a separate matter requiring separate measures.
Statistical versus Practical Significance
One of the most important distinctions in interpreting research is between statistical significance and practical significance.
Statistical significance indicates whether an effect is likely real (unlikely due to chance). Practical significance indicates whether an effect is large enough to matter in the real world.
These are different questions. A result can be statistically significant but practically trivial — a real but tiny effect that makes no meaningful difference. Conversely, a potentially important effect might not reach statistical significance in a small study. Sound interpretation considers both: whether an effect is likely real (statistical significance) and whether it is large enough to matter (practical significance, often assessed through effect size measures).
This distinction matters greatly. Focusing only on statistical significance, without considering effect size and practical importance, can lead to overstating the importance of trivial effects or to misjudging the real-world relevance of findings.
As Dr. Madhuri Kanojiya, Founder of Empire Research Press, whose research employs statistical analysis, cautions: “Statistical significance and the p-value are essential tools, but they are widely misunderstood. A small p-value tells you an effect is probably real — not that it is large, important, or practically meaningful. Always ask two questions: is the effect likely real, and is it big enough to matter? A statistically significant but trivial effect is a common trap. Report effect sizes alongside p-values, interpret carefully, and never let statistical significance alone stand in for genuine importance.”
Effect Size — The Important Companion
Because the p-value does not indicate the size of an effect, researchers increasingly report effect size alongside statistical significance. Effect size measures the magnitude of an effect — how large the difference or relationship actually is. Common effect size measures include Cohen’s d (for differences between groups) and correlation coefficients (for relationships).
Reporting effect size addresses the limitation of the p-value by conveying how large an effect is, not just whether it is likely real. Together, statistical significance (is the effect real?) and effect size (how large is it?) provide a fuller, more meaningful picture of research findings than significance testing alone. Good research practice increasingly emphasises reporting both.
Conclusion
Statistical significance indicates whether a research result is likely to reflect a real effect rather than random chance, assessed through the p-value — the probability of obtaining the observed result if there were truly no effect. A result is conventionally considered statistically significant when the p-value falls below a threshold, commonly 0.05.
However, statistical significance is widely misunderstood. It does not indicate that an effect is large, important, or practically meaningful — only that it is likely real. Sound interpretation distinguishes statistical significance from practical significance, considers effect size alongside the p-value, and avoids the common misconceptions. Understanding these concepts properly — what they mean and what they do not — is essential to conducting and evaluating quantitative research honestly and accurately.
Frequently Asked Questions
Q: What is statistical significance?
Statistical significance indicates whether an observed result in a study is likely to reflect a genuine effect or relationship, rather than having occurred merely by random chance. When a result is statistically significant, it means the result is unlikely to have arisen by chance alone, suggesting a real effect is probably present. It is assessed using the p-value compared to a threshold, commonly 0.05. Importantly, statistical significance only addresses whether an effect is likely real — it does not indicate that the effect is large, important, or practically meaningful, which are separate questions requiring separate consideration.
Q: What is a p-value?
The p-value is the probability of obtaining the observed result — or one more extreme — if there were truly no effect (that is, if the null hypothesis were true). A small p-value means the observed result would be very unlikely if there were no real effect, providing evidence in favour of a real effect. A large p-value means the result would be reasonably likely even with no effect, providing little evidence. Put simply, the p-value tells you how surprising your result would be if there were actually nothing going on. It is compared to a threshold, commonly 0.05, to determine statistical significance.
Q: What does p < 0.05 mean?
A p-value less than 0.05 means that, if there were truly no effect, there would be less than a 5% probability of obtaining the observed result (or a more extreme one) by chance. By the common convention, this makes the result “statistically significant,” suggesting a real effect is probably present. The 0.05 threshold is a widely used convention rather than a law of nature — some fields use stricter thresholds like 0.01. Importantly, p < 0.05 indicates only that an effect is likely real, not that it is large or important, which must be assessed separately through effect size and practical significance.
Q: What is the difference between statistical and practical significance?
Statistical significance indicates whether an effect is likely real (unlikely due to chance), while practical significance indicates whether an effect is large enough to matter in the real world. These are different questions. A result can be statistically significant but practically trivial — a real but tiny effect that makes no meaningful difference, which can happen especially with large samples. Conversely, a potentially important effect might not reach statistical significance in a small study. Sound interpretation considers both: whether an effect is likely real (statistical significance) and whether it is large enough to matter (practical significance, assessed through effect size).
Q: What is a common misconception about p-values?
A common misconception is that the p-value is the probability that the null hypothesis is true, or that a statistically significant result is necessarily large or important. In fact, the p-value is the probability of the observed data (or more extreme) given that the null hypothesis is true — not the probability the null hypothesis is true. Also, statistical significance only indicates an effect is likely real, not that it is large or meaningful — a tiny effect can be significant with a large sample. Additionally, a non-significant result does not prove there is no effect; the study may simply have lacked power to detect it.
Article reviewed, edited, fact-checked and approved before publication. — Empire Research Press Editorial Standard