For sampling without replacement, Standard error of mean = (sigma/ sqrt n ) sqrt (1- n/N) where sigma = population standard deviation; n = sample size; N = finite population size.

from this you can calculate sample size required to get desired SE.

You should be careful when using an answer like that given by James. Maybe a better way to say this is to point out that there are a large number of conditions or experimental designs where James' answer will not work so well.

What is the distribution of your data? Normal, Poisson, Multimodal, F, something else?

What is your experimental design? James' answer may work quite well for a single question survey. What about two or fifty questions? Are they all continuous, or Likert scale, or categorical?

Will there be missing values? Are you planning a multivariate analysis, or just the most basic t-test? ANCOVA, or regression, mixed models? Even though this is not an experimental research project, there may be categorical variables like gender/sex. At least we can eliminate repeated measures designs, as sampling is done without replacement.

Are you sampling for rare events? So I want to know what kind of bar/tavern is frequented by people who affiliate with different political parties in the USA. It is easy to get a good sample of Democrats, Republicans, and Independents. How about Socialist Party, or Libertarian party. My sample size will have to be very large to get a sufficient number of respondents in these uncommon parties to draw meaningful conclusions.

Will you segregate the data? So I am studying alcohol consumption. I can have the average alcohol consumption. I can have the average alcohol consumption for males versus females. I can have the average alcohol consumption for females in households with two children making 45,000/year, who are members of the Socialist Democrats, age 30 to 35 years old living in the southwest quarter of Nairobi. If all you want is the first number then you sample size can be fairly small (less than 200), if the latter, you might need to sample the whole population just to get sufficient sample size in these very specific categories.

There is a somewhat better tool GPower, that might help (or maybe not). http://gpower.hhu.de/

Whether you use James' suggestion or use GPower (or similar tool), the strategy will be the same. Use the tool for the variable in each category with the largest standard deviation. Add all the outcomes together to get you final sample size. Increase this further to correct for non-responses and incomplete responses.

As the formula from James shows you, there is only a meaningful difference when dealing with small Ns. If you are drawing from a large population, it really doesn't matter much.

Dear Ayo, use the free calculator OpenEpi : "Sample Size for a Proportion or Descriptive Study"

This module calculates sample size for determining the frequency of a factor in a population. Sample sizes are provided for confidence levels from 90% to 99.99%.A finite population correction will be applied if the population size is not large (n/N > 10%). For samples that are not random or systematic, a design effect other than 1.0 may be entered. The calculated sample sizes are multiplied by the design effect.

Exemple : Sample Size for Frequency in a Population

Population size(for finite population correction factor or fpc)(N): 1000

Hypothesized % frequency of outcome factor in the population (p): 30%+/-5

Confidence limits as % of 100(absolute +/- %)(d): 5%

Design effect (for cluster surveys-DEFF): 1

Sample Size(n) for Various Confidence Levels

Confidence Level(%) Sample Size

95% 245

80% 122

90% 186

97% 284

99% 359

99.9% 477

99.99% 561

Equation

Sample size n = [DEFF*Np(1-p)]/ [(d2/Z21-α/2*(N-1)+p*(1-p)]

Results from OpenEpi, Version 3, open source calculator--SSPropor

A big thanks to you all. Your answers were very helpful.