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Part CCSIR NET June 2024contrasts-live-inside-a-factor-not-across-two

Contrasts live inside a factor not across two

Consider the two-way ANOVA model Yij=μ+αi+βj+εij,i=1,2;j=1,2Y_{ij} = \mu + \alpha_{i} + \beta_{j} + \varepsilon_{ij}, i = 1, 2; j = 1, 2, where μ\mu is the overall mean effect, αi\alpha_{i} is the effect of the i-th level of factor A,βjA, \beta_{j} is the effect of j-th level of factor B,YijB, Y_{ij} is the response of the (i, j)-th experimental unit and εij\varepsilon_{ij} is the corresponding error with E(εij)=0E(\varepsilon_{ij}) = 0 for i = 1, 2; j = 1, 2. Which of the following are estimable linear parametric functions?

  1. A.μ+α2+β2\mu + \alpha_{2} + \beta_{2}✓ Correct
  2. B.α1−β1\alpha_{1} - \beta_{1}
  3. C.α2−β2\alpha_{2} - \beta_{2}
  4. D.μ−α1−β1\mu - \alpha_{1} - \beta_{1}

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 what the inference means.

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50 are analysed free — try those first.

The trap it tests

What the inference means

p-values, size, power and error types say specific things. This was not one of them.

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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