I'm trying to compute the minimum sample size for a psychometric test based on 7 point Likert scales. I'd like to run ANOVA on each scale to look for differences between groups.

Most online survey sample size calculators seem to be designed for polls, e.g. Yes/No, Agree/Disagree. They take as input population size, a confidence interval and a proportion (50% Yes/50% no) and then return the required sample size.

Most statistical books suggest using power tests (such as R's power.t.test), which take as input a minimum effect size, alpha, beta and a statistical test and then return the required sample size.

For my purposes power tests seems to make the most sense, but what has me concerned is that none of them take into account the population size, which seems like it ought to have at least some effect on the outcome.

So my question is, what is the correct calculation to use in my specific survey situation and more generally what is the connection between power tests and these online survey sample size calculators, does population size matter in some way, perhaps helping to capture the notion of representative sample?