Provide the formula for determining sample size, given a study population. sampling table by different scholars can be of value to me.
The Kish Leslie formula for survey sampling is:
\[ f = \frac{N}{n} \]
Where \( f \) is the sampling interval, \( N \) is the population size, and \( n \) is the desired sample size.
The survey sampling formula by Leslie Kish is a method used to estimate the effective sample size in survey research. It is designed to quantify the effect of weighting a survey to achieve the same level of precision as a simple random sample. The formula is
=(∑ni=1wi) 2 / ∑ni=1w2i
where \( w_i \) is the weight of the \( i^{th} \) respondent. This formula helps in adjusting for different probabilities of selection and varying response rates among different strata in a population. The Kish method is particularly useful because it accounts for the design effect, which is the factor by which the variance of an estimate from a complex survey design exceeds the variance of an estimate based on simple random sampling. It's important to note that while the Kish formula provides a simplified estimate, it may not always be accurate in all survey scenarios, as it does not take into account the correlation between the weight and the data being weighted.
Damasco Okettayot -
There seems to be a little confusion here. Leslie Kish is known for the "deff," or "design effect" as Dr-Zaffar Ahmad Nadaf very well describes it: the efficiency obtained by using a more complex probabilistic survey design as opposed to simple random sampling with the same sample size. This is not a sample size formula, though you can see how much the variance is lowered by the more complex design, with the same sample size.
If you have good stratification, where the variance within each stratum is small and the variance between strata is large, then efficiency will be good. However, a cluster sample is generally less efficient than simple random sampling. A cluster sample might be used, however, if it is easier to accomplish and/or costs less overall.
I did not follow the formula by Dr-Zaffar Ahmad Nadaf, but I did see that he explained the deff.
Cheers - Jim Knaub
Here is another use of this technique for finding comparative efficiency. On page 11 in https://www.researchgate.net/publication/262066356_Quasi-Cutoff_Sampling_and_Simple_Small_Area_Estimation_with_Nonresponse,
I used such an efficiency ratio for model-based small area estimation.
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