A p-value Less Than 0.05 — What Does it Mean?

If you've ever read a science article, you've probably come across the expression p < 0.05, and maybe you've asked yourself what does a p-value less than 0.05 mean?. If so, you're not alone in this. This little number has become one of the most famous cut-offs in research, being the gold standard in determining statistical significance. In this article, you can learn more about:

• What a p-value is;
• Where the p-value comes from;
• What a p-value greater than 0.05 means; and
• The meaning of a p-value less than 0.05.

A p-value, or probability value, helps scientists understand whether the observed data is more likely to have occurred by chance or whether it has a real effect. It is based on the null hypothesis, which states that there is no effect or difference. The p-value measures how likely it is to observe results at least as extreme as those obtained, assuming the null hypothesis is true:

• Small p-value (<0.05) — means the observed results would be unlikely if the null hypothesis were true, so the data give evidence against the null hypothesis.

• Larger p-value (>0.05) — means the results are more compatible with the null hypothesis.

The origin of the p-value traces back to the early 20th century, when Karl Pearson introduced the chi-square test in his 1900 publication in Biometrika, and William S. Gosset (under the pseudonym "Student") developed the t-test for small samples, which allowed probabilities of extreme results to be calculated in small datasets. The modern concept and use of p-values were later formalized by Ronald Fisher in Statistical Methods for Research in the 1920s, who also expanded their application to a wide range of research fields.

The main idea of a set threshold of 0.05 was to create a practical guide for researchers. However, the value 0.05 is not random. It roughly matches the chance of a value landing more than two standard deviations away from the mean in a normal distribution. In other words, if there's really no effect, you'd only see a result this extreme about 5% of the time.

The p-value threshold is a handy rule of thumb that simplifies statistical calculations, which is exactly why it remains the standard in statistical testing.

What does a p-value less than 0.05 mean?

A p-value less than 0.05 means that it is unlikely that the observed result has occurred just by random chance — assuming the null hypothesis is true. In other words, if we assume there is no true effect, there is less than a 5% probability of seeing such an extreme result. Although this does not prove that there certainly is an effect, it rather indicates that the observed outcome is unusual enough to consider an alternative hypothesis. This is why p < 0.05 is considered statistically significant in science.

What does a p-value greater than 0.05 mean?

A p-value greater than 0.05 means the observed result isn’t rare enough to confidently rule out chance. So, if the null hypothesis were true, your result wouldn't be that uncommon. This also doesn’t prove that there is no effect, only that the evidence isn’t strong enough to claim a statistically significant finding. What p > 0.05 suggests is that your data is consistent with random variation, which means that your "effect" could be just noise.

Though widely used and accepted, the p-value threshold also has its shortcomings:

• Rigidness — 0.05 is a convenient threshold, yet results with slightly higher or lower values don't automatically lose their meaning;

• Misinterpretation — It only shows how likely the observed effect is under the null hypothesis, but it cannot confirm or deny if there is an effect; and

• Data manipulation — p < 0.05 has been overemphasized and encourages selective reporting, achieving statistical significance rather than understanding the phenomenon.

p-values tell only part of the story. To really understand your results, you also need to consider effect sizes, confidence intervals, study design, and the scientific context.