Based on the question and the data attched, answer the following questions 1. Wh

Question

Based on the question and the data attched, answer the following questions

1. What type of design is it?

2. Write the appropriate statistical model for the design?

3. Identify every single term in the model?

15.16 An agricultural experiment station is investigating the appropriate planting density for three commercial varieties of tomatoes: celebrity, sunbeam, and trust. The researcher decides to examine the effects of four planting densities: 5,20, 35, and 50 thousand plants per hectare.The ex- periment station had three large fields which would be appropriate for the study. At each of the fields, 12 plots are prepared and the 12 treatments were randomly assigned to the plots. A separate randomization was done at each of the three fields. The yield data from the 36 plots are given here. Variety Celebrity Sunbeam Trust Density Density Density 20k Field 5k 20k 35k 50k 5k 35k 50k 5k 20k 35k 50k 2 3 33.4 41.1 32.5 39.9 47.2 48.7 42.5 38.2 44.5 43.5 7 53.5 48.4 32.2 33.4 41.8 43.2 51.3 51.2 47.643.5 52.2 55.9 44.1 55.9 49.9 60.8 60.8 59.0 66.1 66.3 70.7 58.3 60.6 67.8 67.6 73.2

Explanation / Answer

There are three comercial varieties of tomatoes celebrity, sunbeam and trust.

Each has four densities 5, 20, 35 and 50 thousand plants per hectare.

Each density has three observations for three various fields.

At each field 12 plots are prepared and 12 treatments were randomly assigned to the plots.

A separate randomization was done at each of the three fields.

This is an randomised block design.

Principles :

1) Replication

2) Randomisation

3) Local control

number of plots = 12

number of treatments (t) = 12

number of blocks = 12

Total number of observations = 36

The model for a randomized block design with one nuisance variable is,

Yij = µ + Ti + Bj + random error

where,

Yij is any observation for which X1 = i and X2 = j

X1 is the primary factor

X2 is the blocking factor

is the general location parameter (i.e., the mean)

Ti is the effect for being in treatment i (of factor X1)

Bj is the effect for being in block j (of factor X2)

Assumption :

Error --> iid N(0, 2)

All observations are independent.

All effects are additive in nature.

Ti = 0 and Bj = 0

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