Complete the ANOVA for the following situations. Assume that factors A, B, and C are fixed effects.

a) 3x2x2 factorial for an RCBD

b) RCBD with a split plot arrangement, whole plot is a factorial arrangement of factors A and B.

c) RCBD with a split-split plot arrangement.

d) RCBD with a split block arrangement, horizontal whole plot is a factorial arrangement of factors A and B, vertical whole plot is factor C.

e) For the previous four ANOVAs, compute LSDs for the sources of variation where the F-tests were significant.

f) Compute single degree of freedom orthogonal contrasts for all treatment combinations (there are 11).

Question

13-10-2024
Mathematics

High School

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Complete the ANOVA for the following situations. Assume that factors A, B, and C are fixed effects.

a) 3x2x2 factorial for an RCBD

b) RCBD with a split plot arrangement, whole plot is a factorial arrangement of factors A and B.

c) RCBD with a split-split plot arrangement.

d) RCBD with a split block arrangement, horizontal whole plot is a factorial arrangement of factors A and B, vertical whole plot is factor C.

e) For the previous four ANOVAs, compute LSDs for the sources of variation where the F-tests were significant.

f) Compute single degree of freedom orthogonal contrasts for all treatment combinations (there are 11).

Answer :

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TylerWoods1 TylerWoods1 · Answer 1 · 2024-12-20T22:04:18-05:00

Completing ANOVAs for various RCBD designs requires understanding factorial effects, the block effect, and the interactions. Significant effects are further explored using the Least Significant Difference (LSD) and single d.f. orthogonal contrasts for specific treatment comparisons.

Completing the ANOVAs for various factorial and block designs, including an RCB (Randomized Complete Block design) with different plot arrangements is a higher-level statistical analysis often completed in college-level studies.

For a 3x2x2 factorial in an RCBD, the ANOVA would include factors for each level of A, B, and C, their interactions, and the block effect. Similarly, a RCBD with a split plot where the whole plot is a factorial arrangement of A and B would include those factorial effects, the block effect, and the subplot effect within the whole plot. In split-split and split block designs, additional sub-plot levels are accounted for, bringing in more complex interactions.

After conducting ANOVA, the Least Significant Difference (LSD) is computed for sources of variation with significant F-tests to determine which means are significantly different from each other. Furthermore, computing single d.f. orthogonal contrasts allows for comparisons of specific treatment combinations based on a priori hypotheses.