Ismaheel -

Sample size 'formulas' are old and perhaps hard to trace.  In Cochran's first edition of Sampling Techniques, on page 55, he states that "A good discussion of sample size for proportions, with a specific application, is given by Cornfield(1951)."  On page 59, Cochran mentions "For continuous data, Stein(1945) developed a method which guarantees that the confidence interval will be no larger than some stated amount."  He goes on to give formulas, but I did not notice any reference to their origins. 

Cochran has a chapter on sample size, and in his third edition, 1977, I know he uses that to carefully develop what you need to know for simple random sampling for both continuous data and for proportions (yes/no) data.  He then has chapters on more complicated designs, and offers information needed there.  After a while you can consider tradeoffs between, say number of clusters and cluster size, for example.  As Johannes noted, designs can become complicated.  Cochran also gave a hint of the use of models, and in work others have done in model-assisted design-based approachs, and/or prediction/model-based approachs, there are more concerns, so that sample size considerations often do not reduce to a simple formula. 

Many on ResearchGate have referred to online sample size calculators, but you have to be certain that what they are calculating, or any formula you find is calculating, actually is suitable for your application.  Consider type of data, sampling and estimation or prediction methodology, to include how do you get preliminary standard deviation(s), and what about a finite population correction (fpc) factor?

As for tracing the origins of a lot of this work, it's hard to say.  I've seen the ratio estimator traced back hundreds of years, and I don't think the origins of that are completely known. 

So, to decide who first wrote a specific fornula is hard to say.  This is especially true since once you think you have decided on that, you may find a much older formula in different notation which is fundamentally the same. 

It might be impossible to say. 

Cheers - Jim

Dear Ismaheel,

for populations that are large, Cochran developed the equation

no= Z2pq / d2

to yield a representative sample for proportions. See: Cochran, W. G. 1963. Sampling Techniques, 2nd Ed., New York: John Wiley and Sons, Inc.

In many situations, however, the correct design effect is not computed, either because it is too complicated, too computationally expensive or there is insufficient information for it to be computed. For such instances, Kish developed an approximate formula for computing effective sample size:

Effective size = https://wikimedia.org/api/rest_v1/media/math/render/svg/94a41e41a0fe5a39144227a8c790d8fafd57d23c

where wi is the weight of the ith respondent. See: Kish, Leslie. 1965. Survey Sampling. New York: John Wiley and Sons, Inc.

Please use above URL to display formula in your browser.

Wishing you best of success,

Johannes

Ismaheel -

Sample size 'formulas' are old and perhaps hard to trace.  In Cochran's first edition of Sampling Techniques, on page 55, he states that "A good discussion of sample size for proportions, with a specific application, is given by Cornfield(1951)."  On page 59, Cochran mentions "For continuous data, Stein(1945) developed a method which guarantees that the confidence interval will be no larger than some stated amount."  He goes on to give formulas, but I did not notice any reference to their origins. 

Cochran has a chapter on sample size, and in his third edition, 1977, I know he uses that to carefully develop what you need to know for simple random sampling for both continuous data and for proportions (yes/no) data.  He then has chapters on more complicated designs, and offers information needed there.  After a while you can consider tradeoffs between, say number of clusters and cluster size, for example.  As Johannes noted, designs can become complicated.  Cochran also gave a hint of the use of models, and in work others have done in model-assisted design-based approachs, and/or prediction/model-based approachs, there are more concerns, so that sample size considerations often do not reduce to a simple formula. 

Many on ResearchGate have referred to online sample size calculators, but you have to be certain that what they are calculating, or any formula you find is calculating, actually is suitable for your application.  Consider type of data, sampling and estimation or prediction methodology, to include how do you get preliminary standard deviation(s), and what about a finite population correction (fpc) factor?

As for tracing the origins of a lot of this work, it's hard to say.  I've seen the ratio estimator traced back hundreds of years, and I don't think the origins of that are completely known. 

So, to decide who first wrote a specific fornula is hard to say.  This is especially true since once you think you have decided on that, you may find a much older formula in different notation which is fundamentally the same. 

It might be impossible to say. 

Cheers - Jim

Dear Ismaheel

As other colleagues mentioned sample size formulas are old and hard to trace. Sometimes before 2010, I had worked on the subject of sample size and reviewed literature on the subject and I found some old papers in which researcher had worked on much more advance materials on sample size formulas, for examples Stein(1945) and Cox (1952). I have just uploaded a full paper in my publications list, entitled “TWO-PHASE SAMPLE SIZE ESTIMATION WITH PRE-ASSIGNED VARIANCE UNDER NORMALITY ASSUMPTION”. My coauthor are my late dearest friend and mentor Professor Paul Levy and Professor JKN Rao.

Here is a previous thread of interest to this one:

https://www.researchgate.net/post/Who_is_Slovin_and_where_and_how_did_the_Slovins_Formula_for_determining_the_sample_size_for_a_survey_research_originated

Note especially Romer Castillo's comment of January 30, 2016.

Who developed this formula for sample size estimation? I think the more important is to know "How To Determine Sample Size" . man start by an idea then the others add more and more ideas about his idea. So let history says his words.

There are different formulae for estimating sample used at different situations,were developed by different authors.