Hypothesis Testing Summary

Statistics · Axiom Academy

Let's review the complete framework for making statistical inferences about populations. The Hypothesis Testing Framework Purpose: Make decisions about population parameters based on sample data Structure: Set up competing claims, collect evidence, make a decision using probability Goal: Determine if sample data provides sufficient evidence to reject a claim about the population Foundation: Uses sampling distributions and probability to quantify uncertainty Null vs Alternative Hypotheses Null Hypothesis (H₀): The default claim or status quo (usually "no effect" or "no difference") Alternative Hypothesis (H₁ or Hₐ): The research claim we're testing for (what we suspect is true) Key Principle: We assume H₀ is true and look for evidence against it Decision: Either reject H₀ or fail to reject H₀ (never "accept" H₀) Definition: A standardized measure of how far our sample statistic is from the null hypothesis value Purpose: Convert sample data to a common scale for comparison P-value Connection: The test statistic determines the p-value via the sampling distribution Type I Error (α): Rejecting H₀ when it's actually true (false positive); controlled by significance level Type II Error (β): Failing to reject H₀ when it's actually false (false negative) Power (1 - β): Probability of correctly rejecting a false H₀; higher power is better Trade-off: Decreasing α increases β; increase sample size to improve both

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