Understanding P-Values Without the Jargon

Understanding P-Values

Plain-Language Definition

A p-value answers a narrow, specific question: if there were actually no real relationship in the population, how likely would it be to see data this extreme just by chance? A small p-value means “pretty unlikely by chance alone” — which is evidence (not proof) that something real is going on.

Why It Matters

P-values are the single most misinterpreted number in business analytics. Getting the interpretation right — and wrong interpretations avoided — is often what separates a “Competent” write-up from an “Approaching Competence” one on quantitative tasks.

The Two Most Common Misreadings

• “A p-value of 0.03 means there’s a 97% chance the relationship is real.” No — the p-value doesn’t tell you the probability that your hypothesis is true. It tells you the probability of seeing data this extreme if the null hypothesis were true.
• “A p-value above 0.05 means there’s definitely no relationship.” No — it means this particular dataset didn’t provide strong enough evidence to reject the null hypothesis. A larger sample might.

Recent peer-reviewed work on statistical significance has pushed back specifically against both overcorrecting away from p-values entirely and misusing them carelessly — the right posture is careful, correct use, not abandonment or blind trust.

Worked Example (Fictitious Company)

Ferngate Retail Group’s regression output shows a p-value of 0.001 for the training-hours coefficient, with a significance level set at α = 0.05.

Correct interpretation: “Because the p-value (0.001) is less than the significance level (0.05), we reject the null hypothesis. This provides statistical evidence of a relationship between training hours and complaint rate — though it doesn’t prove training hours cause lower complaints, only that the pattern is unlikely to be due to chance alone.”

Incorrect interpretation to avoid: “There’s a 99.9% chance training reduces complaints.” — This overstates what the p-value actually tells you.

Key Takeaways

• A p-value measures the strength of evidence against the null hypothesis, not the probability the null hypothesis is true
• Statistical significance is not the same as practical or business importance — a tiny, meaningless effect can still be “significant” with a large enough sample
• Always report the p-value alongside your stated significance level, and show the comparison explicitly rather than asserting a conclusion
• Significance says nothing about causation on its own

Related Content

• C207 Course Roadmap
• C207 QUM3 Task 1 Guide: Linear Regression Analysis
• What Is Hypothesis Testing? (In Plain Language)

References & Further Reading

• Mayo, D. G., & Hand, D. (2022). Statistical Significance and Its Critics: Practicing Damaging Science, or Damaging Scientific Practice? Synthese, 200(3), 220. — A peer-reviewed defense of correctly-used p-values against both misuse and premature abandonment, directly addressing the two misreadings covered above.