What is hypothesis testing?

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Hypothesis testing is a statistical method used to make decisions or inferences about a population based on sample data. It helps determine whether a claim (hypothesis) about a population is likely to be true.

Key Concepts:

1. Null Hypothesis (H₀)

   • The default assumption (e.g., no effect, no difference).

   • Example: "There is no difference in recovery rates between two treatments."

2. Alternative Hypothesis (H₁ or Ha)

   • The claim you want to test (e.g., there is an effect or a difference exists).

3. Significance Level (α)

   • The probability of rejecting H₀ when it's actually true (Type I error).

   • Commonly set at 0.05 (5%).

4. Test Statistic

   • Calculated from sample data (e.g., t-score, z-score) to assess how extreme the data is under H₀.

5. P-value

   • The probability of obtaining results as extreme as the observed ones, assuming H₀ is true.

   • If p-value ≤ α, reject H₀.

6. Conclusion

   • Reject H₀: evidence supports the alternative hypothesis.

   • Fail to reject H₀: not enough evidence to support a difference or effect.

Example:

You test if a new drug lowers blood pressure more than the current one.

• H₀: The new drug is no better.

• H₁: The new drug is better.

After testing and analysis, you get a p-value of 0.02.

• If α = 0.05 → 0.02 < 0.05, so you reject H₀ and conclude the new drug likely works better.

Summary:

Hypothesis testing helps determine if sample data supports a specific claim about a population, using probability to guide decision-making.

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