Hypothesis Testing Steps in Statistics

Study Notes

State the hypothesis: Define the null hypothesis (H₀) – what's being tested (e.g., =, ≥, or ≤) – and the alternative hypothesis (H₁) – what the researcher wants to conclude (e.g., suggests a difference compared to H₀). Example: Does a reward/incentive program increase corporate profits?
Select a test statistic: Choose a metric (e.g., mean, standard deviation) appropriate for the data and hypothesis.
Specify the significance level (α): Set the acceptable probability of rejecting H₀ when it's actually true (Type I error). A common value is 5% (0.05).
State the decision rule: Define the criteria (critical values) for rejecting H₀ based on the test statistic.
Collect data and calculate statistics: Gather a sample and compute the test statistic.
Make a decision about the hypothesis: Compare the test statistic to the critical value(s). If the test statistic exceeds the critical value (or falls outside a range of critical values), reject H₀. Otherwise, fail to reject H₀.
Make a decision based on test results: Conclude whether sufficient evidence supports H₁.

One-tailed test: Used for testing a specific direction (greater than or less than). Example: Does the return on stock options exceed zero?
Two-tailed test: Used for testing any difference (greater than or less than). Example: Is the return on stock options simply different from zero?
Most hypothesis tests commonly used are two-tailed due to increased flexibility in detecting differences in either direction.

The test statistic, calculated from sample data, is compared to critical values.
Critical values define boundaries for rejecting the null hypothesis (H₀).
Critical values are similar to confidence intervals.

Type I error: Rejecting H₀ when it's actually true (false positive). The probability of a Type I error equals α (the significance level).
Type II error: Failing to reject H₀ when it's false (false negative).

Statistical significance (p-value < α): Indicates the result is unlikely to have occurred by chance.
Economic significance: Considers practical implications and factors like transaction costs, taxes, and risk. A result can be statistically significant but not economically meaningful if the effect is too slight when factoring in costs.