Question

Suppose that you want to run a 23 factorial design. The variance of an individual observation is expected to be about 4. Suppose that you want the length of a 95 percent confidence interval on any effect to be less than or equal to 1.5. How many replicates of the design do you need to run?

Answer 1

in the given problem

that if you want to run a 23 factorial design and variance of an individual observation is expected to be about 4.

if the equations of Se (effect) and 100(-) percent confidence interval on the effects shown below. we can intertively estimates the no .of relpicates

from the table of iterations 14 replictes are required

se(Effect)=

n2k

  

Effect $\pm$ t_(1/2,N-P) se(Effect)

n se(Effect) t(0.025,N-p) 95%CI length

12 0.408 1.987 1.623

13 0.392 1.985 1.577

14 0.378 1.983 1.499

15 0.365 1.981 1.447

from the above table,we need 14 replicates are required