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What p-value is significant?

Published in Statistical Significance 4 mins read

A p-value is generally considered significant if it is less than or equal to the predetermined significance level (alpha or α), which is most commonly 0.05. However, this threshold is not fixed and can be adjusted by the researcher based on the specific context and requirements of the study.

Understanding P-Values and Significance

In statistical hypothesis testing, a p-value helps researchers determine the strength of evidence against a null hypothesis. The null hypothesis usually states that there is no effect or no difference.

Statistical significance refers to the unlikelihood that the observed result occurred by random chance. When a result is statistically significant, it suggests that there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis.

The Standard Significance Level (Alpha)

Traditionally, the alpha level (α), or significance level, is set at 0.05. This means that researchers are willing to accept a 5% chance of incorrectly rejecting the null hypothesis (a Type I error).

  • If the p-value is less than 0.05 (p < 0.05), the result is typically judged as statistically significant. This suggests that the observed data is unlikely to have occurred if the null hypothesis were true, providing evidence to reject it.
  • If the p-value is greater than 0.05 (p > 0.05), the result is generally judged as not statistically significant. This indicates that the observed data could reasonably occur under the null hypothesis, and there isn't sufficient evidence to reject it.

Why the Significance Level Can Vary

While 0.05 is the most common alpha level, it is important to understand that the significance probability is a value set by the researcher according to the circumstances of each study. It does not necessarily have to be 0.05. Researchers establish this threshold before conducting their analysis.

The choice of alpha level depends on several factors:

  • Field of Study: Different disciplines may adopt different conventions. For example, in some exploratory social science research, an alpha of 0.10 might be considered acceptable, while in critical medical trials or particle physics, a much stricter alpha like 0.01 or even 0.001 might be used to minimize the risk of false positives.
  • Consequences of Error:
    • If a Type I error (false positive) has severe consequences (e.g., approving an ineffective drug), a lower alpha (e.g., 0.01) is preferred.
    • If missing a true effect (Type II error, false negative) is more costly, a higher alpha (e.g., 0.10) might be tolerated, especially in initial exploratory studies.
  • Sample Size and Effect Size: These factors also influence the power of a study to detect an effect, which can be considered when setting alpha.

Interpreting P-Values

Understanding the numerical value of a p-value is crucial, beyond just comparing it to alpha.

P-Value Range Interpretation (for α = 0.05) Practical Implication
p < 0.001 Very strong evidence against the null hypothesis Highly statistically significant; very unlikely due to chance.
0.001 ≤ p < 0.01 Strong evidence against the null hypothesis Highly statistically significant; unlikely due to chance.
0.01 ≤ p < 0.05 Moderate evidence against the null hypothesis Statistically significant; unlikely due to chance.
0.05 ≤ p < 0.10 Weak evidence against the null hypothesis; borderline significance May warrant further investigation, but not conventionally significant.
p ≥ 0.10 Little or no evidence against the null hypothesis Not statistically significant; results likely due to chance.

Importance of Context

While a significant p-value indicates statistical unlikelihood by chance, it does not automatically imply practical significance or importance. A very large study, for example, might find a statistically significant but very small and practically meaningless effect. Conversely, a non-significant p-value doesn't necessarily mean there's no effect, but rather that the study lacked sufficient power to detect one, or the effect is too small to be deemed statistically significant at the chosen alpha level.

Setting Your Alpha Level

When designing a study, researchers should thoughtfully consider:

  • The specific research question: What kind of effect are you looking for?
  • The potential risks of Type I and Type II errors: Which error is more costly in your context?
  • Conventions in your field: What significance levels are typically used by peers?

By carefully considering these aspects, researchers can choose an appropriate significance level that aligns with the goals and ethical considerations of their study.