Statistical Inference and Hypothesis Testing Flashcards

What does the power of a hypothesis test measure?

Answer: Probability of rejecting H₀ when H₀ is false

Power = 1 − β, where β is the Type II error rate; it is the probability of correctly detecting a true effect.

A one-sample chi-squared test is used to test whether observed category frequencies match:

Answer: Expected frequencies from a theoretical distribution

The chi-squared goodness-of-fit test compares observed counts to expected counts derived from a hypothesized distribution.

Increasing sample size while keeping α fixed will generally:

Answer: Narrow the confidence interval and increase power

Larger samples reduce standard error, producing narrower confidence intervals and greater ability to detect true effects (higher power).

The Kolmogorov-Smirnov test is primarily used to:

Answer: Test whether a sample comes from a specified distribution

The KS test measures the maximum distance between an empirical CDF and a theoretical CDF to assess distributional fit.

Which scenario correctly illustrates a Type II error?

Answer: Failing to detect a real difference between two drug dosages

A Type II error (false negative) occurs when we fail to reject H₀ even though H₁ is actually true.

A likelihood ratio test compares two nested models by:

Answer: Computing twice the difference in log-likelihoods, which follows a chi-squared distribution

Under regularity conditions, −2(ℓ_restricted − ℓ_unrestricted) ~ χ²(df) where df equals the number of constraints imposed.

Bayesian credible intervals differ from frequentist confidence intervals in that they:

Answer: Express a direct probability statement about where the parameter lies

A Bayesian 95% credible interval means there is a 95% posterior probability that the parameter falls in that range, incorporating prior information.