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Part CCSIR NET December 2023estimability-in-anova

Estimability in anova

Consider the one-way fixed effects ANOVA model Yij=μ+αi+εij,j=1,…,ni;i=1,…,kY_{ij} = \mu + \alpha_{i} + \varepsilon_{ij}, j = 1, \dots, n_{i}; i = 1, \dots, k, with uncorrelated errors of mean 0 and variance σ2\sigma^{2}. Let Ȳi_{i} be the i-th group mean. Which of the following statements are true?

  1. A.(1/∑ni)∑i∑jYij(1/\sum{}n_{i}) \sum_{i}\sum_{j} Y_{ij} is an unbiased estimator of μ\mu
  2. B.2μ+α1+α22\mu + \alpha_{1} + \alpha_{2} is an estimable linear parametric function✓ Correct
  3. C.μ+α1+α2\mu + \alpha_{1} + \alpha_{2} is an estimable linear parametric function
  4. D.(1/n2)∑j(Y2j−(1/n_{2}) \sum_{j} (Y_{2j} - Ȳ2)_{2}) is an unbiased estimator of α2\alpha_{2}

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests hypothesis dropped.

See pricing

50 are analysed free — try those first.

The trap it tests

Hypothesis dropped

A theorem applied without checking one of its preconditions.

Drill statements like this

Related counterexample: OLS is the BLUE in every linear model

More on this topic

The chapter behind this: Linear models, Gauss–Markov and ANOVA — free to read

From Linear Models and Multivariate › Gauss–Markov, regression, ANOVA basics

Last revised . Found a mistake? Tell us — corrections are the fastest thing we act on.

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