I am working on a prevalence study regarding physical activity on the total population of about 7 million people and want to know how much maximum sample size is required. Also, suggest best sampling technique and any sample size calculation method.
In quality measurements the sample size is the square root of the population size, and evenly distributed through the population, based on thermodynamic probabilities of errors in replications. Schrodinger touches on this in his book "What Is Life."
Smaller samples are used, one tenth the square root of population size, for example in television ratings, but with burden of proof reversed.
You need to say what confidence level is needed and who bears the burden of proof for claims that result.
First you have to determine what kind of sampling you will use (probability or intentional). There are many equations for calculating the sample size as well as special tables.
The sample size depends on the type of your population, is it finite population or infinite population.
In the case of finite population, you can use the attached table to estimate the suitable sample size. Or use Slovin formula:
n= N / ( 1+ N * e^2 )
But in the case of an infinite population:
The sample size for any study depends on the standard deviation of the variable ( from previous studies ) and the margin of error you decided. The formula:
n= ( Z^2 * S^2) / E^2
where : Z ( 1.96 for 0.05 and 2.58 for 0.01 )
S = standard deviation from previous studies or pilot study
E = significant level
Also, you can use software to calculate sample size ( SPSS , Minitab , G*power )
My advice to use G*Power .
G*Power software is effective tool to calculate sample size for many ranges of experiments. Also, you can determine effect size and power of the test, G*Power is free to download and easy to use after reading the manual, the download link: