Statistical Inference Concepts Flashcards
7 cards from real MS-DS Master of Data science practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 7 Statistical Inference Concepts flashcards as text
A study finds a statistically significant result with p = 0.03, but the effect size is d = 0.05. What is the most appropriate conclusion?
Answer: The effect is statistically significant but likely of negligible practical importance
With large enough samples, even trivially small effects become statistically significant; effect size (d = 0.05) indicates negligible practical importance.
The Fisher information I(θ) quantifies:
Answer: The expected curvature of the log-likelihood, reflecting how much data informs about θ
Fisher information measures how sensitive the log-likelihood is to changes in θ, capturing how much the data can tell us about the parameter.
When performing multiple hypothesis tests simultaneously, the Bonferroni correction adjusts α by:
Answer: Dividing α by the number of tests
Bonferroni sets the per-test significance level to α/m (where m is the number of tests) to control the familywise error rate.
Which of the following best describes a sufficient statistic for parameter θ?
Answer: A statistic T(X) such that the conditional distribution of X given T does not depend on θ
A sufficient statistic captures all information in the sample about θ; knowing T(X) renders the rest of the data irrelevant for estimating θ.
The power of a test is defined as:
Answer: The probability of rejecting H₀ when H₀ is false
Power = 1 − β = P(reject H₀ | H₀ is false), measuring a test's ability to detect a true effect.
If X̄ is the sample mean of n i.i.d. observations from a population with mean μ and variance σ², what is Var(X̄)?
Answer: σ² / n
The variance of the sample mean is σ²/n because averaging n independent observations reduces variance by a factor of n.
Which assumption is NOT required for the classical ordinary least squares (OLS) estimator to be BLUE (Best Linear Unbiased Estimator)?
Answer: Normality of errors
The Gauss-Markov theorem guarantees OLS is BLUE under linearity, exogeneity, homoscedasticity, and no perfect multicollinearity — normality is not required.