I only said that power analyses approaches to estimating sample sizes are "more" modern, since they have indeed be around for quite a few years now. What makes them more modern is that they take both Type 2 and Type 1 errors into account, compared to the older approaches that only considered type 1 errors.

And yes, power analyses do require estimates of variance -- which is pretty much unavoidable in any meaningful estimate of sample size.  Beginners too often focus entirely on the population size without considering the variability of the underlying scores. I get past this by using the example of a population where everyone has actually the same value on some measure, so that a sample of size 1 will correctly estimate the value in population, no matter how large the population is.

From there, it is usually easy to see that strongly peaked population distributions require small samples than flatter distributions.

I heard you could use that formula, but I haven't and I am not aware of anyone who does. With that said, determining sample size of a given population for which a survey research is target is easy now. In fact, there are web-based computation mechanisms out there like this one http://www.surveysystem.com/sscalc.htm, which makes your life easier. Also, advanced statistical software such as R, SAS, JMP Pro12.2 had easier statistical ways to compute sample size.

Statistical software can be helpful, but it can also be very dangerous and is rife with misuse.  There is no substitute for an understanding of the methodologies and what the software is actually doing.  There are reasons for the various options that you have.  There are assumptions made that have to be reasonable for your various applications.

There are two ways to do statistical inference: (1) randomized probability of selection designs, and (2) regression model-based methods.  A combination, model-assisted design-based methods, can be very useful. 

Sample sizes are based on standard deviations and the sample required to obtain standard errors.  But designs can become very complex.  You need to know what is appropriate for your application. 

Having looked at it quickly, having seen it before, the sample size calculator in the link above appears to only be for yes/no data, for simple random sampling, and without a finite population correction factor. 

PS - Slovin's formula appears to be an approximation for continuous data and perhaps yes/no.  -  See my answer to Romer's other question on Slovin. 

PSS -  I had not heard the name Slovin until recently, as far as I can recall. I may have seen the 'formula' on ResearchGate before.  It looks only possibly useful for simple random sampling  (SRS).   I never saw it used on the job, and I am retired now.  

"...how do they determine the sample size for a survey research if only the population size is known"  - 

You cannot.  You need estimates of standard deviations.

Consider these sources:

Cochran, W.G(1977), Sampling Techniques, 3rd ed., John Wiley & Sons. 

Blair, E. and Blair, J(2015), Applied Survey Sampling, Sage Publications.

Lohr, S.L(2010), Sampling: Design and Analysis, 2nd ed., Brooks/Cole.

Similarly for model-based sampling and estimation, where you need estimated standard deviations for the random factors of the estimated residuals:

 https://www.researchgate.net/publication/261947825_Projected_Variance_for_the_Model-based_Classical_Ratio_Estimator_Estimating_Sample_Size_Requirements

Also, you should consider when a finite population correction factor might be useful (but don't forget nonsampling error):

 https://www.researchgate.net/publication/262970761_FINITE_POPULATION_CORRECTION_fpc_FACTOR

Conference Paper Projected Variance for the Model-based Classical Ratio Estim...

Article FINITE POPULATION CORRECTION (fpc) FACTOR

James is correct that any sample estimation formula will need to include a value for the variance (or std. deviation) in the population, as well as the N for population size. One way around this, when you do not know the population variance, is to work with a 1-0 variable, where you would be estimating the percentage of the population where the characteristic is present. For that that kind of measure, the maximum variation is at .50, so that is often used as the value to estimate the variance. Since the observed population split will probably be less than 50/50, using that value will produced a "conservative" estimate on the necessary sample size.

In particular, this is the approach that is often used in political surveys, where the question is do you favor Candidate A or Candidate B. Then the results are accompanied by an statement about the "confidence interval" for the estimate.

Having said all that, a more modern approach would be to work with assumptions about the "power" of your test (i.e., your ability to find an effect of a given size). Wikipedia has a useful article on "statistical power" and there are a great many websites that discuss how to use assumptions about statistical power to produce desired sample sizes. This can be a complicated topic, but here is one website that I thought was relatively accessible:

http://documents.software.dell.com/Statistics/Textbook/Power-Analysis

I worked on power so many years ago, and it can be so awkward, that I personally would not consider it as a modern approach, but Blair, E. and Blair, J(2015) - noted above - does show power as another approach to sample size determination, as David says.  However, once again, that actually also still relies on variance. 

To support this, I just came across the following, regarding power, in  https://www.andrews.edu/~calkins/math/edrm611/edrm11.htm: 

"These procedures must consider the size of the type I and type II errors as well as the population variance and the size of the effect." 

I'm not sure how good this reference is - I just found it - but it looks like it could be helpful.  (Just be wary of anything on the internet, though this looks like a good source.) 

For proportions - yes/no questions covered by available calculators on the internet, as shown at the beginning of this thread - Cochran(1977), section 4.4, and other sources clearly show how p and q fit into variance, and it is then obvious why p=q=0.5 is a worst case.

So though various sampling designs and methods of inference can become quite complex, the underlying driver in sample size estimation is variance, whatever approach you take. 

FYI - This may be of interest: 

https://www.researchgate.net/publication/262971440_Practical_Interpretation_of_Hypothesis_Tests_-_letter_to_the_editor_-_TAS

Article Practical Interpretation of Hypothesis Tests - letter to the...

I only said that power analyses approaches to estimating sample sizes are "more" modern, since they have indeed be around for quite a few years now. What makes them more modern is that they take both Type 2 and Type 1 errors into account, compared to the older approaches that only considered type 1 errors.

And yes, power analyses do require estimates of variance -- which is pretty much unavoidable in any meaningful estimate of sample size.  Beginners too often focus entirely on the population size without considering the variability of the underlying scores. I get past this by using the example of a population where everyone has actually the same value on some measure, so that a sample of size 1 will correctly estimate the value in population, no matter how large the population is.

From there, it is usually easy to see that strongly peaked population distributions require small samples than flatter distributions.

Agreed David. 

By the way, Romer has two questions now asking about Slovin, and it seems no one knows how he (or she) made that approximation from the usual one that I pointed out in Cochran on the other Slovin/Romer question thread.  I think I saw that 'formula' on a list that someone else on ResearchGate contributed, but as I recall, it was just a list of 'formulas.'  I think it was another one of your countrymen, Romer.  I'll see if I can find him, and send him your question threads.  - I'm curious, as I did not see what Slovin did to make that (apparently an) approximation.  (If it is exactly equivalent, I don't see it, though I suppose doing some examples and comparing results might settle that.)     :-)  

Jim,

It was in the mid 1970s that foreign donations were overflowing in the country and where nation wide feasibility studies were required national samples were to be calculated. Two names became popular- one was a local- Pagoso, and other one was Slovin. Later literature would prove that the spelling was Sloven. The popularity of the so-called formula arose from the fact that during those times all researchers in the country used only one or two easy-to-use books on sampling. And like a snowball, the formula was used from one researcher to another, for there is no more convenient else than the formula that required only as input population size and margin of error, not realizing that it was meant for variables with dichotomous categorical measures (quantitatively measured in terms of proportion)

-the derivative formula for estimating population proportion with population known.

It grew so popular that it is being used for populations that are not really very large, an obvious blunder of a “blind” imitator.

Ed

Jim, am posting here my mathematical derivation for the sample size calculating formula for estimating population proportion with population known. The formula presupposes a proportion P of 0.5, a confidence level of 95.44 percent, and a very large population size.. Cheers, Ed.

https://www.researchgate.net/publication/281322207_The_Sampling_Formula_n_N_Ne2_1

Research The Sampling Formula n = _ N__ Ne2+ 1

Romer -

It looks like Eddie is familiar with the 'formula' you noted. This also makes apparent the importance of studying a book such as Cochran's, so that you understand what the assumptions, uses, misuses, and consequences are when a given 'formula' is used.  Here, you see a formula for a specific purpose.  I can certainly see why you said "However, its use (or misuse) is now also being questioned."  Recall that I noted the sample size 'calculators' you will find on the internet, and their very limited use. I'd say the danger they pose is similar.

In Cochran, on page 77, you will see how e (there, r Y_bar), for continuous data, directly relates to the standard deviation, and for proportions, he shows how p and q relate to standard deviation on page 51, equations 3.4, 3.5, and 3.6, and pages 75 and 76.  Section 4.7, pages 78 to 81 is on "Advance Estimates of Population Variance," and 4.8, pages 81-82 is "Sample Size with More than One Item."  4.9, pp. 82-83, is on "Sample Size When Estimates are Wanted for Subdivisions of the Population."  You will also see how to make the most reasonable, informed estimates for needed information for different designs. There is a chapter in that book on sampling, and page 77, as noted, is very informative, but the sample size selection information, for various designs and data, is spread throughout the book.  (Page 77 is for simple random sampling for continuous data.)  The Blair & Blair book is simplified, but Cochran puts a lot of good information into a not-so-large book, and writes clearly.  Lohr is a good book, and she writes very clearly. Note that I provided those three references above.  Below are a couple of additional books containing some more advanced topics in survey statistics:

Särndal, CE, Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling, Springer-Verlang.     

Brewer, KRW (2002), Combined survey sampling inference: Weighing Basu's elephants, Arnold: London and Oxford University Press.  

You can also find other books somewhat similar to Cochran in the level of statistical development, such, I think, as those by Leslie Kish and by Hansen, Hurwitz, and Madow.  

Thank you for the interesting question.

Cheers - Jim

Thanks everyone for great answers. These help us a lot. We will be looking for the references you had mentioned. For those who have additional information, please continue posting here.

Sir Jim and Sir Ed:

Slovin or Sloven? Or may be Slonim? I looked at the Bibliography of Cochran (1977) and found the entry: Slonim, M. J. (1960). Sampling in a Nutshell. Simon & Schuster, New York. I do not have yet the book of Slonim and not sure if the "formula" or similar to that is in there. But is it also possible that "Slonim" was just misspelled as "Slovin" by some authors? 

Romer, we honor a person for a great reason. Both Pagoso and Slov....n, simply presented and applied the "formula" in their books. They did not explain, they did not show its derivation,they did not "cite" their source. They were just the first to have used the formula in the country. For using a "ready made" formula without citing its source, should the formula be named after them? I have derived the same formula, stated its prerequisites and its limitations, should the formula now be called SEE'S FORMULA?

You had a good point there Sir Ed. But as I can see, it is now the community of researchers and statisticians that can decide on who should be given the credit and maybe after another decade of doing research. Thanks a lot.

Romer - 

As your two questions on "Slovin" have come together now, I will repeat this response under both of them. 

Yes, I had noticed a reference in Cochran(1977) to "Slonim," and wondered about it, but according to the author index, Slonim(1960) is only referenced on page 4 as follows: "The books by Deming (1960) and Slonim (1960) contain many interesting examples showing the range of applications of the sampling method in business."  (W. Edwards Deming became quite famous regarding business and quality, by the way.  He was also one of the well-known authors of a population sample study in Greece in 1947.  See Cochran on page 160: Jessen, etal(1947).  I'm glad you found a copy of the 3rd ed of Cochran.) 

I don't know where you can find Slonim (1960), but I note that Eddie See does not believe that Slonim came up with this formula. It is hard to say when things get lost in time.  I think the worst thing missing is probably the caveats of its limitations whenever someone uses it. But as for giving it a name, I can see Eddie's point that if he (she?) did not first develope it, why name it that way?  But then, I can also see that if he made (hopefully) good use of it, then why not give it his name if the true origin is unknown and you want to refer to it quickly?  But actually, I don't really see it as being too very useful anyway. 

Maybe, as I think that perhaps you indicated, the origins may be discovered.

By the way, I did a similar historical check in the area of weighted least squares regression/heteroscedasticity, regarding the coefficient of heteroscedasticity and its use in a commonly employed format for regression weights. Phil Kott, a US statistician, had told me he'd seen it as far back as Cochran's. 1st edition, as I recall, but Ken Brewer, the author of one of the books I cited in at least one of these two "Slonin" questions, sent me to a much earlier reference: 

Fairfield Smith (1938). An empirical law describing heterogeneity in the yields of agricultural crops. The J. Agri. Sci., 28, 1-23.

(I'm told that "Fairfield Smith" is an unhyphenated, two-word last name.) 

So things do get lost in time.  On page 158 in the 3rd ed of Cochran, 1977, Cochran gives Ken Brewer (1963), and Richard Royall (1970) credit, basically, for starting model-based inference for finite populations (or at least its modern use). However, in one of my papers I have this:

 "From Cochran (1978), page 5, an even earlier application of an “…estimated ratio of population to births …” than that of Laplace was documented by John Graunt in

1662. Cochran (1978), page 7, went on to say, that Laplace made use of

superpopulations, and that 'So far as I know, this use of an infinite superpopulation in studying the properties of sampling methods was not reintroduced into sample survey

theory until 1963, when Brewer (1963), followed by Royall (1970), applied it to the ratio estimator ...'" 

- This is an example of model-based inference for a finite population. 

 Cochran, W.G. (1978), “Laplace's Ratio Estimator,” Contributions to Survey Sampling and Applied Statistics, ed. HA David. New York: Academic Press., 3-10.

So ... it can be interesting to know these things, and perhaps it might be best if names were not given to methodologies where the origin is not clear.   People like to use names, however.  - Consider the way new diseases are named.   :-) 

Interesting.

Cheers - Jim

I utilize G-Power (developed and delivered as academic purpose, Google It!) for determining sample size/power analysis for different situations.