Define p-value.

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A p-value (probability value) is a key concept in hypothesis testing used to determine the strength of evidence against a null hypothesis.

✅ Definition:

The p-value is the probability of observing your data, or something more extreme, assuming that the null hypothesis is true.

• It does not tell you the probability that the null hypothesis is true.

• It tells you how surprising your results are under the assumption that there’s no real effect (i.e., the null is true).

📘 How to Interpret a P-Value:

• Low p-value (≤ 0.05): Strong evidence against the null hypothesis → Reject H₀

• High p-value (> 0.05): Weak evidence against the null → Fail to reject H₀

Example: A p-value of 0.03 means there's a 3% chance of seeing results as extreme as yours if the null hypothesis were true.

🎯 Why It Matters:

• Helps researchers decide whether results are statistically significant.

• Common in A/B testing, clinical trials, and social science research.

🧠 Example:

You're testing a new drug.

• Null hypothesis (H₀): The drug has no effect.

• You run a study and get a p-value = 0.01.

• This means there's a 1% chance of observing your data (or more extreme) if the drug really had no effect — strong evidence against the null.

⚠️ Important Notes:

• A small p-value ≠ proof your hypothesis is true.

• A large p-value ≠ proof the null is true.

• Always consider effect size, sample size, and context.

✅ Summary:

The p-value tells you how likely your results are under the assumption of no real effect. It helps you determine whether to reject the null hypothesis, but it’s not a measure of truth—just evidence.

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