Type II Error Rate:- (Failing to reject H₀ when it's false)
Statistical Power:- (Correctly rejecting H₀ when it's false)
Understanding Hypothesis Testing
Hypothesis testing is a statistical method for making decisions using data. We start with a null hypothesis (H₀) and test whether the evidence is strong enough to reject it in favor of an alternative hypothesis (H₁).
Key Concepts:
P-value: The probability of observing data at least as extreme as what we got, assuming H₀ is true
Significance level (α): The threshold for rejecting H₀ (commonly 0.05)
Type I Error: Rejecting H₀ when it's actually true (false positive)
Type II Error: Failing to reject H₀ when it's actually false (false negative)
Power: The probability of correctly rejecting a false H₀ (1 - Type II error rate)
Decision Rule: If p-value < α, reject H₀; otherwise, fail to reject H₀