5. The following data set comes from Sokal & Rohlf (1995). The oven-dry weights (in grams)...

 

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5. The following data set comes from Sokal & Rohlf (1995). "The oven-dry weights (in grams) of new growth in hybrid poplars grown in concrete soil frames and treated with lime (L), nitrogen (N), phosphorus (P), and potassium (K) are given below. The frames were laid out in three blocks." Note that O represents a control (no supplement). Blocks 1 2 3 Blocks 1 2 3 O P L 13.9 14.3 15.8 22.1 14.2 14.7 22.8 12.8 13.3 PK LP LPK Treatments K 13.6 31.7 12.7 15.5 Treatments NK LK 57.9 49.5 25.6 21.7 35.5 25.7 31.0 30.7 LNK N 15.3 11.8 17.8 16.6 41.2 19.4 23.2 21.4 20.1 59.3 15.9 22.7 20.6 15.1 32.0 NP LN NPK 43.0 63.8 62.5 59.7 37.1 41.3 49.7 38.1 36.3 LNP LNPK 53.4 53.5 58.5 (a) How would you describe the design of this experiment? Write out an appropriate model equation for this experiment, if we assume blocks do not interact with treatment factors but all treatment factor interactions are possible. (b) How would you set up the data frame for analysis in R? (c) Write out the Source and df columns for the ANOVA table. (d) How many df would be associated with the error if all interactions involving three or more interactions were pooled with the error? (e) For your model, what are the values of Y2... and Y.21..? (f) How would the randomization have been conducted in this experiment? 5. The following data set comes from Sokal & Rohlf (1995). "The oven-dry weights (in grams) of new growth in hybrid poplars grown in concrete soil frames and treated with lime (L), nitrogen (N), phosphorus (P), and potassium (K) are given below. The frames were laid out in three blocks." Note that O represents a control (no supplement). Blocks 1 2 3 Blocks 1 2 3 O P L 13.9 14.3 15.8 22.1 14.2 14.7 22.8 12.8 13.3 PK LP LPK Treatments K 13.6 31.7 12.7 15.5 Treatments NK LK 57.9 49.5 25.6 21.7 35.5 25.7 31.0 30.7 LNK N 15.3 11.8 17.8 16.6 41.2 19.4 23.2 21.4 20.1 59.3 15.9 22.7 20.6 15.1 32.0 NP LN NPK 43.0 63.8 62.5 59.7 37.1 41.3 49.7 38.1 36.3 LNP LNPK 53.4 53.5 58.5 (a) How would you describe the design of this experiment? Write out an appropriate model equation for this experiment, if we assume blocks do not interact with treatment factors but all treatment factor interactions are possible. (b) How would you set up the data frame for analysis in R? (c) Write out the Source and df columns for the ANOVA table. (d) How many df would be associated with the error if all interactions involving three or more interactions were pooled with the error? (e) For your model, what are the values of Y2... and Y.21..? (f) How would the randomization have been conducted in this experiment?

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ANSWER a This experiment is a randomized complete block design with three blocks and eight treatments The model equation is Yijklmno i j k l m n o ijklmno where Yijklmno is the response variable is the overall mean i is the effect of block i j is the effect of treatment ... View the full answer