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Consider a Randomized Block Design with b blocks and k treatments. Let the observation corresponding to the ith treatment and the jth block be yij, 1 ≤ i ≤ k, 1 ≤ j ≤ b, which satisfies the usual linear model. Which of the following is true?

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CSIR-UGC (NET) Mathematical Science: Held on (26 Nov 2020)
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  1. The estimates of any two treatment contrasts are uncorrelated
  2. The error sum of squares has bk - 1 degrees of freedom
  3. The estimate of any treatment contrast is uncorrelated with the estimate of any block contrast
  4. The correlation between the estimates of two treatment contrasts is always negative

Answer (Detailed Solution Below)

Option 3 : The estimate of any treatment contrast is uncorrelated with the estimate of any block contrast
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The estimate of any treatment contrast is uncorrelated with the estimate of any block contrast

Option (3) is correct

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