What is a p-value and what does it signify in hypothesis testing?

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A p-value is a key concept in hypothesis testing used to determine the strength of evidence against the null hypothesis (H₀).

Definition:

The p-value is the probability of obtaining results as extreme as, or more extreme than, the observed results assuming the null hypothesis is true.

What It Signifies:

• A low p-value (typically ≤ 0.05) indicates that the observed data is unlikely under the null hypothesis.
  👉 This suggests strong evidence against H₀, so we may reject it.

• A high p-value (> 0.05) indicates that the observed data is likely under H₀.
  👉 This suggests weak evidence against H₀, so we fail to reject it.

Example:

Suppose you're testing a new drug's effectiveness compared to a placebo.

• H₀: The drug has no effect.

• H₁: The drug has an effect.

After conducting the test, you get a p-value = 0.02.
This means there's a 2% chance of observing the results (or more extreme) if the drug really had no effect.

Since 0.02 < 0.05, you reject the null hypothesis, suggesting the drug likely has an effect.

Important Notes:

• A p-value does not tell you the probability that H₀ is true.

• It does not measure the size or importance of an effect — only the evidence against H₀.

• Always interpret p-values in context, alongside effect sizes, confidence intervals, and study design.

In short, the p-value helps decide whether your test results are statistically significant or likely due to chance.

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