Hypothesis Testing Steps in Statistics

Hypothesis Testing Steps

• 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 vs. Two-Tailed Tests

• 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.

Test Statistic and Critical Values

• 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 and Type II Errors

• 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 vs. Economic Significance

• 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.