When we are doing sampling by means of simple systematic random sampling,how do we calculate the design effect for use during calculation of sample size for our work?
https://psyarxiv.com/9d3yf/download?format=pdf
Lakens, D. (2021, January 4). Sample Size Justification. https://doi.org/10.31234/osf.io/9d3yf
Or you could get a copy of Schaeffer et al, Elementary survey sampling read it and proceed as they direct. D. Booth
Abhishek De -
The deff compares the efficiency of your sample with that of random sampling, which it seems that you probably already know. In W.G. Cochran's book, Sampling Techniques, 3rd ed, Wiley, at the bottom of page 208, referring to equations he developed just before that, Cochran says "This important result, which applies to cluster sampling in general, states that systematic sampling is more precise than simple random sampling if the variance within the systematic samples is larger than the population variance as a whole." He goes on to say that you therefore do better with systematic sampling if the "... units within the same sample are heterogeneous..." to which I will add that in cluster sampling that does not generally happen, and thus cluster sampling generally has higher variance than simple random sampling (but it is generally easier to carry out more sampling with cluster sampling, so that is why it can be desirable). For systematic sampling, I guess this can vary. Also, you may not know the population variance that exactly. I think that for those reasons, I think that in many cases one might just assume that the variance for systematic random sampling is about the same as that for simple random sampling.
I suggest that you borrow or find a used copy of Cochran. I also have a copy of the first edition from 1953, and I see this material on page 163 there, where you can compare the two variances. You can probably find it elsewhere, in other textbooks, or perhaps the internet. (I have found that in many cases the material that the Pennsylvania State University puts online is helpful. I haven't looked in this case.)
Best wishes - Jim
PS - Please note that on page 205 in the 3rd ed of Cochran, and on page 160 in the 1st edition, he notes how "Intuitively, systematic sampling seems likely to be more precise than simple random sampling," and goes on to compare it to stratified random sampling.
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