I want a project proposal regarding the following: This essentially corresponds

Question

I want a project proposal regarding the following:

This essentially corresponds to steps (a) – (d) in the Checklist for Planning Experiments:

(a) Define the objectives of the experiment.
(b) Identify all sources of variation, including:
(i) treatment factors and their levels,
(ii) experimental units,
(iii) blocking factors, noise factors, and covariates.
(c) Choose a rule for assigning the experimental units to the treatments.
(d) Specify the measurements to be made, the experimental procedure, and the anticipated
difficulties.

This does not need to be overly formal. Some items that you should consider when developing your proposal:

· Identify a research question that may be answered with a designed experiment. Ideally this will be a question of interest to you, but importantly it must be a question that may be addressed through the conduct of a reasonably simple experiment.

· Identify potentially important factors and their levels. This includes treatment factor(s), and nuisance factors (blocking, noise, covariates). You do not need to contemplate every possible factor. It is more relevant that you try to identify those factors that are most likely to be important sources of variation. Consider how you will make use of randomization.

· Consider hypotheses you may wish to test, and comparisons or contrasts that may be of interest.

· Consider what response measurements will be appropriate for addressing your question(s) of interest and how many observations you will complete.

· Suggest a suitable design. Your design must have at least two treatment factors.

· Difficulties that may be encountered.

Explanation / Answer

(a) Suppose you and 2 of your friends each have 4 baby rose plants (or any other plant for that matter). You have heard different views regarding the amount of water and sunlight that leads to the best or fastest growth of the plant. For this, you conduct an experiment with different combinations of water and sunlight supplied to your respective plants. Your objective is to determine the perfect treatment that is to be applied to the plant for the best growth. (Here, treatment is nothing but a combination of water and sunlight at their various levels).

(b) Let A -> amount of water needed; there are 2 possible levels;

Let B -> sunlight necessary (in hours per day)

(i) So the treatment factors are A and B, each at 2 levels (a0, a1) and (b0, b1) respectively .

(ii) The experimental units are your plants; each plant is an experimental unit; so each of you have 4 experimental units, with a total of (4×3) =12 experimental units in all the 3 replications combined.

(iii) Suppose that each of you have 2 of the plants in pots and the remaining 2 directly in your garden soil amd not in pot. So you have 2 blocks, the type of place where you are growing your plants being the block; each block containing 2 experimental units .

Let B1: 1st block with potted plants, B2: 2nd block with plants in garden soil .

Hence, the sources of variation are the treatments (different combinations of the levels of A and B), the blocks (the 2 types of places where you are growing your plants) and noise or error-which is the unexplained source of variation .

(c) Now you have 4 treatments:

Having 4 treatments and 4 experimental units, it is a good idea to assign the treatments randomly to the units and in each block . So what you do is:

For B1, choose a plant, draw a random number between 1 and 4, whatever number you get, assign the treatment corresponding to that serial number (as given before ) to that plant. Then choose another random number from the remaining 3 numbers, except the one that you already used. Take the treatment corresponding to this second serial number and assign it to the second plant in B1.

Now you are left with the 2 plants in B2 and 2 treatments. As before, choose randomly one of the 2 remaining serial numbers and assign it to a plant in B2 and assign the last treatment to rhe last remaining plant in B2.

So your rule of assigning treatments is block-wise random allocation.

One treatment effect would be confounded with the block effect . If you want to decide for yourself which treatment to confound, then after choosing the bery first treatment of B1, assign the treatment to the next plant not by random allocation but by considering the linear contrast that would confound your desired treatment effect.

(d) Each of you can take the measurements of each plant after month, by noting the height and width (at the widest part) with an appropriate scale. So you have 3 replications of the experiment between you and your 2 friends.

The hypothesis to be tested is

H0: There is no significantly different growth observed due to the different treatments applied,

vs, H1: The treatments have significantly different effects on the growth.

The test is conducted at any suitable (say, 5%) level of significance. Reject H0 if p-value of the test is less than 5% or 0.05. If rejected , the treatments maybe supposed to vary among themselves Then you may perform suitable post-hoc tests like Duncan's test or Tukey's test, etc, ro determine which ulis tbe best treatment .

This is a factorial treatment design (as the factors are interacting with each other at different levels) ; the design used is Randomized Block Design or RBD.

Some of the possible difficulties maybe the unavailability of a very sensitive scale that can note even the slightest difference in growth, maintaining the exact same soil conditions throughout the experiment, possibility of a pest attack and hence requiring the application of pesticide that will in turn affect yhe growth, etc.

After collecting data simply perform RBD with 3 replicates in the usual manner and arrive at your conclusion.

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