P VALUE — SUPER CLEAR EXPLANATION
1. What is a P value?
A P value tells you:
when:
- Comparing two treatments
- Comparing two groups
- Comparing observed results vs expected results
➡️ “What is the probability that the difference we observed happened by chance, assuming there is actually no real difference?”
This “no difference” idea is called the null hypothesis.
2. What the P value really measures
P value answers ONE question:
👉 If the treatment actually does NOT work, what are the chances we would still see a result like this (or more extreme) just by luck?
- High P value → likely due to chance
- Low P value → unlikely due to chance → real effect
3. Thresholds you MUST memorize
P value | Meaning | |
P < 0.05 | Statistically significant (unlikely due to chance) | <5% due to chance |
P < 0.01 | Highly significant | <1% due to chance |
P < 0.001 | Very highly significant | <0.1% due to chnace |
P > 0.05 | Not significant | >5 due to chance |
6️⃣ Key principle: P value scale
- Lower P value → less likely due to chance
- Lower P value → stronger statistical evidence
- P value never proves causation
- It only measures strength of evidence against the null hypothesis
4. Simple examples (from the book)
Example 1 — P = 0.5
Means:
➡️ 50% chance the difference happened by luck
➡️ Completely non-significant
Like tossing a coin.
Example 2 — P = 0.05
Means:
➡️ 5% chance the difference occurred by luck
➡️ This is the usual cut-off for significance
If you repeat the study 100 times, 5 times you might get this result purely by chance.
Example 3 — P = 0.007
(Example from baby sex ratio study in the book)
Meaning:
➡️ If the treatment truly had no effect, you would see this result only 1 in 140 times
➡️ Very unlikely to be due to chance
➡️ Significant
Example 4 — Comparing two doctors
From the book’s table :
- P = 0.4 → likely due to chance
- P < 0.001 → very highly significant
- P = 0.05 → borderline but significant
5. How to interpret P values in plain English
✔️ P < 0.05 (significant)
“The result is unlikely due to chance, so there is likely a real difference.”
✔️ P > 0.05 (not significant)
“We cannot rule out that this difference is just luck. No real evidence of effect.”
6. P value DOES NOT tell you
This is extremely important for exams:
❌ It does NOT tell you the size of the effect
❌ It does NOT prove the treatment works
❌ It does NOT tell you the probability the hypothesis is true
❌ It does NOT measure clinical importance
❌ It does NOT tell you the chance the result is correct
It only tells you about chance under the assumption of no effect.
7. P value & sample size relationship
- Large sample → easily gives small P values
- Small sample → may fail to reach significance even if effect is real
Example from the book:
Two GPs had mean consultation lengths:
- Dr Jones: 16 min
- Dr Smith: 6 min
→ P < 0.001 (very significant)
But other comparisons with small numbers gave P = 0.4, P = 0.3 → not significant.
Same data pattern from the book .
8. Null Hypothesis (the engine behind P values)
The P value always tests:
➡️ H₀: there is no difference
(e.g., drug = placebo)
A small P value → reject H₀
A large P value → fail to reject H₀
This is why it’s called a significance test.
9. Summary for Exams (best memory tool)
- P = probability result happened by chance
- P < 0.05 → significant
- P < 0.01 → highly significant
- P < 0.001 → very highly significant
- P > 0.05 → not significant
- Does NOT measure effect size.
- Does NOT prove clinical importance.