2.7 Hypothesis Testing - 2.7 Hypothesis Testing
Key Concepts
- Null Hypothesis (H0)
- Alternative Hypothesis (H1 or Ha)
- Test Statistic
- P-Value
- Significance Level (α)
- Type I and Type II Errors
Null Hypothesis (H0)
The Null Hypothesis (H0) is a statement that there is no effect or no difference. It represents the status quo or the default assumption. For example, if you are testing whether a new drug is effective, the Null Hypothesis would be that the drug has no effect.
Example: H0: The average return of a mutual fund is equal to 10% per year.
Alternative Hypothesis (H1 or Ha)
The Alternative Hypothesis (H1 or Ha) is a statement that contradicts the Null Hypothesis. It suggests that there is an effect or a difference. Continuing with the drug example, the Alternative Hypothesis would be that the drug is effective.
Example: H1: The average return of a mutual fund is not equal to 10% per year.
Test Statistic
A Test Statistic is a value calculated from the sample data that is used to decide whether to reject the Null Hypothesis. The choice of test statistic depends on the type of data and the hypothesis being tested.
Example: For a mean test, the test statistic might be the t-statistic, calculated as (sample mean - hypothesized mean) / (sample standard deviation / √sample size).
P-Value
The P-Value is the probability of obtaining a test statistic at least as extreme as the one observed, assuming the Null Hypothesis is true. A small P-Value (typically ≤ 0.05) indicates strong evidence against the Null Hypothesis, so you reject it.
Example: If the P-Value is 0.03, it means there is a 3% chance of observing the data if the Null Hypothesis is true. Since 0.03 is less than 0.05, you would reject the Null Hypothesis.
Significance Level (α)
The Significance Level (α) is the threshold used to decide whether to reject the Null Hypothesis. Commonly set at 0.05, it represents the risk of rejecting the Null Hypothesis when it is actually true.
Example: If α = 0.05, you are willing to accept a 5% risk of making a Type I error (rejecting a true Null Hypothesis).
Type I and Type II Errors
A Type I Error occurs when you reject the Null Hypothesis when it is actually true. A Type II Error occurs when you fail to reject the Null Hypothesis when it is actually false.
Example: In a criminal trial, a Type I Error would be convicting an innocent person, and a Type II Error would be acquitting a guilty person.