Is the sample large enough to accomplish the goals of the study? This is an age-old question, but it is relatively easy to answer. However, there may not be only one correct answer. The size required is dependent on several variables. Some of those variables relate to your knowledge of the population under study. More often than not prior knowledge is hard to come by unless you are conducting some form of longitudinal study.
The answer to sample size questions isn’t necessarily one number. Obviously, there will be a total sample size for the study, but it is likely to be the sum of the parts. Assuming your study divides into a priori segments that you want to compare, each segment or strata must be of sufficient size. Moreover, the size is dependent on your need to detect changes of a specified order of magnitude. For example, let us assume you are happy with determining that changes of 5% or more are real differences. You further specify that a 90% confidence interval suites you (i.e., you’re willing to take the risk of being wrong about the 5% or more difference 1 in 10 tens), than your sample size requirements are likely to be relatively small (about N=270).
However, if you want to detect differences of 3% or more and your risk tolerance is such that you don’t want to be wrong more than 1 in 20 times (or 95% confidence) the sample becomes much larger, about N=1015.
A 5% margin of error works fine in situations where the difference in proportions is large (e.g., one group of respondents engages in a behavior 20% of the time and another 70% of the time). However, if your respondent group behaviors or perceptions are closer, let’s say one group disagrees with a political candidate’s positions 45% of the time and another group 55% of the time you may need more precise measurements.
Summarizing: To achieve either a lower margin of error and/or a higher probability of being correct (or stated another way – a lower likelihood of being wrong) requires larger sample sizes.
For the best answer to the sample size question use power statistics calculations. The formulas are in several text books, but you won’t have to learn the math simply use one of the many easy to access calculators available online. To find one you like simply type the following request into any good search engine: Sample Size calculator, or calculations, or determination, or formula, or power, or estimation, etc.
In addition, here are a few you can check out:
To learn more about “Sampling Dilemmas and Solutions” find this eBook at: www.atheath.com/booksandseminars