"Is the sample large enough to accomplish the goals of my study?" This is an age-old question, but it is relatively easy to answer if you know how to approach the question and you have the right tools.
However, there may not be only one correct answer.
The sample size required for a study 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.
Estimation is required.
As stated, the answer to the sample size question is not necessarily one number.
Obviously, there will be a total sample size for the study, but it is likely to be the sum of two or more 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 sample 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 in a specific measure of 5% or more are real differences (i.
, the probability is the difference is not due to measurement error).
You further specify that a 90% confidence interval suites you (i.
, you re willing to take the risk of being wrong 10% of the time or 1 out of 10 times), 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 between groups is large (e.
, 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 answers to your sample size questions use power statistics calculations.
The formulas for power statistics are in several textbooks.
However, you won't have to learn the math, you can simply use one of the many easy to access calculators available online.
That being said it probably would be to your advantage to read up a little on the various ways to perform power statistics.
There are calculations for proportions and others for means tests.
To help you find one you like simply type one of the following requests into any good search engine: Sample Size calculator, Sample Size calculations, Sample Size determination, Sample Size formula, Sample Size power or estimation.
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