Suppose that we want to count the individuals in a population, but but we can count only a sub-population ( only those individuals that respond to a survey, or are for example subscribers to a mobile phone company etc). How can we infer the total number of individuals staring from the sub-population that we can count?
Using the inferential statistics tests. Statistical inference allows the researcher to assess evidence in favour or some claim about the population from which the sample has been drawn. The tests of significance show the probability of observing a value by chance. But counting the total number of individuals in a population, I don't think it is possible. If it was, then the statistical inference would not be necessary...
There are also statistical softwares which allow the researcher to determine the sample size needed for a given power… such as GPower:
http://www.gpower.hhu.de/
I'm not sure if I understood right your question.
If you were interested in a population level variable (that is you were NOT really interested in subsets) then the best approach would be to take a simple random sample of the Target population. The Target population will vary slightly from the total population. For example if I wanted to count the total persons on one day. On the day of the count- there will be people overseas, in hospital, and not at home.
If you have considered the sample size - your estimate will be useful, and you may note that the estimate is made excluding the persons overseas etc.
The mode of data collection (CATI, face to face, mobile etc will affect the response rate.) The non response can be affected by the Intent of the survey, whether it is government or marketing, and the length (Time ) of the survey . Understanding all these aspects will allow you to get robust data. the inference from a statistically sound survey with randomization of the sample will outweigh the "so called' convenience and purposeful samples. These are only relevant for case studies and their biases make any inferences inappropriate and results flawed.
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