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CSS Statistics QUESTION #2009
Question 1
In the ANOVA table for an RCB design with \(SS_{error} = 2.6249\) and error \(df = 24\), the standard error for the difference between two treatment means \((\bar{y}_{i.} - \bar{y}_{j.})\) is:
  • \(\sqrt{\dfrac{MS_E}{b}}\)
  • \(\sqrt{\dfrac{2 \cdot MS_E}{b}}\)✔️
  • \(\sqrt{MS_E}\)
  • \(\dfrac{MS_E}{b}\)
Correct Answer Explanation
The standard error for comparing two treatment means in RCBD is \(SE_{diff} = \sqrt{\dfrac{2 MS_E}{b}}\), where \(b\) is the number of blocks (replications per treatment). Here \(MS_E = 2.6249/24 = 0.1094\), so \(SE_{diff} = \sqrt{2(0.1094)/9} \approx 0.1559\).