Hi,

I am not sure that it will work in your situation. There is a classic problem about counting the number M  of fish in a pond called "sample-resample":  you catch some fioshes L, mark them and  put them back in the pond,  and fish another sample. Using the ratio of marked fishes in your secod sample, you can obtain the estimate of  M.

Sorry if your situation does not allow to use this method to estimate population size.

Best, Ilya Gertsbakh

In most of the survey context the sampling size is not known and must be estimated with the sample. The sample size is defined on the basis of the accuracy of the estimate. 

We are not sure what is your real problem. It is better to give us some details. The sample size depends on the relative error of the estimate and the variation coefficient of the target variable for the population. The most simple sample size formula is n=t^2*C^2/E^2 where t is the t-value at some confidence level (0.05), C is the  variation coefficient of the target variable, and E is the expected relative error. For a complicated sample design, the formula might be more complicated. Best wishes!

I second Wei-Sheng's request for more details. What might the criteria be in this case? Are we dealing with insects or people? Is sampling painful, cruel, fatal? Is the process costly? Is there special hardship involved (samples are taken from an active war zone, or the animal is very rare or hard to collect because it lives in deep caves/pelagic/remote locations? The best sample size is not determined by statistics alone.

@wei-sheng Zenfg. 

I am using criteria based sampling method. The Sampling frame is  CEOs or CTOs of IT product companies located in Bangalore. There is no definitive no. on Total no. of firms located in Bangalore(neither govt. nor the trade association has). So given the situation how to compute sample size for the survey.

The population size only matters when you expect the sample size to be a fairly large fraction of the population size.  Usually the sampling fraction (sample size over population size) can be set to 0 as a good approximation and, at any rate, it is conservative to do so.  The formula given by Wei-Sheng Zeng makes this approximation.

It is possible to estimate previously the population size, and after this, to estimate the sample size substituting the population size for its estimation. This would be an approximation to the sample size.

There is a lot of confusion in the question - the sample size (little n) is how many you decide and are able to collect - you will know what you have done!. In the main - the population size is not an issue - Big N does not normally enter the standard error formula. You real question is about statistical power - how big does little n need to be to get reliable results and detect effects.

Power is increased in the following circumstances

•little noise in the system; clear signal

•the effect is substantial

•α is set leniently (0.05 and not 0.01)

•large sample size - little  n is  big

In practice, can usually only do something about size.

EG: 2-Sample t Test: Calculating power for mean 1 = mean 2 + difference;  Alpha = 0.05  Sigma = 1

            Sample  Target  Actual

Difference    Size   Power   Power

      0.10    1571  0.8000  0.8001

      0.25     253  0.8000  0.8014

      0.50      64  0.8000  0.8015

      0.75      29  0.8000  0.8014

      1.00      17  0.8000  0.8070

•To be able to detect a small difference of 0.10 of a SD between two sample means with 80% power and 5% significance require 2* 1571 for total sample

• To be able to detect a large difference of 1.0 SD between two sample means with 80% power and 5% significance require 2* 17 for total sample

There are good free tools to calculate power in many circumstances eg

http://www.gpower.hhu.de/en.html