Statistical Inference and Hypothesis Testing Flashcards

Which nonparametric test is the rank-based alternative to the independent samples t-test?

Answer: Mann-Whitney U test

The Mann-Whitney U test compares rank sums from two independent groups without assuming normality, serving as an alternative to the two-sample t-test.

In a two-sided hypothesis test with α = 0.05, the critical region is placed:

Answer: Split equally between both tails

A two-sided test splits α/2 = 0.025 into each tail, rejecting H₀ when the test statistic is extreme in either direction.

What is a sufficient statistic?

Answer: A statistic that captures all the information in the data about the parameter of interest

A sufficient statistic T(X) for parameter θ means the conditional distribution of the data given T does not depend on θ, so T contains all parameter information.

The Neyman-Pearson lemma states that the most powerful test for simple H₀ vs. simple H₁ uses:

Answer: A likelihood ratio threshold as the rejection region

Neyman-Pearson shows that rejecting H₀ when the likelihood ratio L(θ₁)/L(θ₀) exceeds a constant k produces the most powerful level-α test.

A researcher tests 20 independent null hypotheses, each at α = 0.05. The expected number of false rejections under all null hypotheses being true is:

Answer: 1

Expected false positives = 20 × 0.05 = 1, illustrating the multiple testing problem even when every null is actually true.

The false discovery rate (FDR), controlled by the Benjamini-Hochberg procedure, is defined as:

Answer: The expected proportion of rejected nulls that are false rejections

FDR = E[V/R] where V is false rejections and R is total rejections; BH controls this expected proportion, offering more power than Bonferroni.

An estimator is consistent if, as sample size increases:

Answer: It converges in probability to the true parameter value

Consistency requires that the estimator converges in probability to the true θ as n → ∞, meaning it gets arbitrarily close with high probability.