Consider a randomized complete block design in which the blocking variable has 4
ID: 3256426 • Letter: C
Question
Consider a randomized complete block design in which the blocking variable has 4 levels (i.e. there are 4 blocks), and there are 5 treatments to be applied. (a) If there are to be two replicates of the experiment, how many experimental units are needed? (b) What is the limitation of this design if only one replicate is obtained? (c) Suppose that by using the blocking variable, you can reduce the residual standard error from 2.5 to 1.7 units. How much does this save you in terms of the number of samples you will need?Explanation / Answer
Answer to part a)
The total number of units needed = number of blocks * number of treatments * number of replicates
total number of units = 4 * 5* 2 = 40
Thus total 40 experimental units are needed.
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Answer to part b)
If no replicates are done , ti would be difficult to find the true influence of the treatment , as the difference may be generated by the block design rather than the 5 different treatments. thus it is mandatory to do conduct experiment with replicates.
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Answer to part c)
The number of samples saved due to decrease in residual standard error is :
1 - (2.5-1.7)^2
1 - 0.64 = 0.36
Thus it saves 0.36 times