Hypothesis testing is a statistical procedure used to make decisions about population parameters based on sample data. It involves making an assumption (hypothesis) about the population and then testing it using sample evidence.
Null Hypothesis (H₀): A statement of no effect, no difference, or no relationship. It is the hypothesis we are testing and assume to be true unless evidence suggests otherwise.
Alternative Hypothesis (H₁ or Hₐ): A statement that contradicts the null hypothesis. It represents what we are trying to prove or detect.
Examples of H₀ and H₁
H₀: μ = 50 (Population mean equals 50) vs H₁: μ ≠ 50 (Two-tailed)
H₀: μ ≤ 50 vs H₁: μ > 50 (One-tailed right)
H₀: μ ≥ 50 vs H₁: μ < 50 (One-tailed left)
H₀: There is no significant difference between two groups.
| Basis | Null Hypothesis (H₀) | Alternative Hypothesis (H₁ or Ha) |
|---|---|---|
| Meaning | States that there is no effect or no difference | States that there is an effect or difference |
| Assumption | Assumes the situation is true by default | Contradicts the null hypothesis |
| Purpose | Used for testing and verification | Represents the research claim or expectation |
| Symbol | H₀ | H₁ or Ha |
| Nature | Conservative statement | Experimental or research-based statement |
| Decision Outcome | Either rejected or not rejected | Accepted only when H₀ is rejected |
| Example | H₀: There is no difference in marks between boys and girls | H₁: There is a difference in marks between boys and girls |
| Role in Testing | Acts as the hypothesis to be tested directly | Represents the result supported if H₀ is rejected |
| Equality Sign | Always contains equality (=, ≤, ≥) | Contains inequality (≠, <, >) |
| Decision Focus | We test whether there is enough evidence to reject H₀ | We try to find evidence to support H₁ |
| Type of Error | Description |
|---|---|
| Type I Error (α) | Rejecting H₀ when it is actually true. Also called 'False Positive'. α = P(Type I Error) = Level of Significance. |
| Type II Error (β) | Accepting H₀ when it is actually false. Also called 'False Negative'. β = P(Type II Error). |
| Power of Test (1-β) | Probability of correctly rejecting a false H₀. |
| Level of Significance (α) | Maximum allowable probability of committing a Type I error. Common values: 0.05 (5%) and 0.01 (1%). |
Critical Region (Rejection Region): The set of values of the test statistic for which the null hypothesis is rejected. It is located in the tail(s) of the distribution.