Post by If you’ve ever run a t-test, ANOVA, regression, or chi-square analysis and then stared at a number like p = 0.043, wondering, “So what does that mean for my hypothesis?”—you’re in very good company. Even experienced scientists and PhD students occasionally misunderstand p-values. It’s one of the most frequently misinterpreted pieces of statistical output.
Why does it matter? Because a shaky understanding of p-values can lead to:
• Wrong conclusions about your data
• Manuscript rejection by journals and peer reviewers
• Poor decision-making in business, public health, and clinical practice
This guide will make p-values clear — without drowning you in intimidating formulas. We’ll explain what a p-value actually is, how to interpret it step by step, and how to report it correctly in APA style. Along the way, we’ll address frequent myths, show examples, and provide ready-to-use resources.
If you get stuck with your own analysis, remember: you don’t have to wrestle with statistics alone. TactResearch’s Data Services can help you clean your dataset, run appropriate tests, and prepare publishable, reviewer-ready results.
What Exactly Is a p Value? (Simple Definition)
A p-value is the probability of obtaining results at least as extreme as the ones you got, assuming that the null hypothesis is true.
If the null hypothesis says there is no effect/no difference, a small p value means your data would be unusual if there really were no effect. A large p-value means your data could easily happen by chance even if the null were true.
Think of the p-value as the surprise factor:
• Low p → “This result would be surprising if nothing’s going on.”
• High p → “These numbers aren’t surprising; random chance could produce them.”
Important: The p-value does NOT tell you the probability that your hypothesis is true or false. It’s about your data given the null, not the other way around.
How to Interpret p Values — Step by Step
| p-Value Range | Meaning | Action |
| p < 0.001 | Extremely strong evidence against the null | Highly significant — effect almost certainly present |
| p < 0.01 | Strong evidence | Significant — likely a real effect |
| p < 0.05 | Moderate evidence | Common cutoff for “statistical significance” |
| p ≥ 0.05 | Weak evidence | Not significant — cannot confidently reject the null |
Common Misinterpretations of p Values (and the Truth)
- ❌ p = 0.03 means a 3% chance that the null is true. ✅ Reality: p is about your data, assuming the null, not the probability of the null itself.
- ❌ p > 0.05 proves there’s no effect. ✅ Reality: A non-significant p means insufficient evidence to reject the null; you can’t prove no effect.
- ❌ 0.05 is magical — below is truth, above is false. ✅ Reality: The 0.05 cutoff is a convention, not a law. Context, study design, and multiple testing matter.
- ❌ Small p-values mean big effects. ✅ Reality: p reflects evidence strength, not effect size. A huge sample can make tiny differences significant.
Reporting p Values in APA Style — Quick Reference
Proper reporting makes your work credible and submission-ready.
• Report exact p values whenever possible: p = .032 (not just “p < .05”).
• Round to three decimals.
• If p < .001, report p < .001 (never write 0.000).
• Italicize the letter p when writing.
• Include test statistic, degrees of freedom, and p-value.
Example sentence:
“The new training significantly improved test scores, t(38) = 2.23, p = .032.”
Key Takeaways
- P-values show how surprising your data would be if the null hypothesis were true.
- Don’t treat 0.05 as a strict pass/fail line — combine with effect size and CI.
- Report exact p-values and follow APA guidelines.
- Avoid myths (p ≠ probability hypothesis is true).
- For complex data or publication prep, professional statistical support is worth it.