There are many approaches to computing sample size. In public policy evaluation, for example, one is usually tented to check if there is statistical evidence on the impact of a intervention over a population of interest. This vignette is devoted to explain the issues that you commonly find when computing sample sizes.
You may have been fooled for some people telling you do not need a large sample size. The sample size is an issue that you have to pay a lot of attention. The conclusions of your study could have been misleaded because you draw a sample with no enough size. For example, from last figure, one may conclude that with a sample size close to 600, the power of the test is as low as 30%. That is simple unacceptable in social research.