Populations and Samples
Population - Any set of people or events from which the sample is selected and to which the study results will generalize.
Sample - A group of people or events drawn from a population. A research study is carried out on a sample from a population. The goal is to be able to find out true facts about the sample that will also be true of the population. In order for the sample to truly reflect the population, you need to have a sample that is representative of the population. The best method to use to obtain a representative sample is to randomly select your sample from the population. A study that has a large, randomly selected sample or a carefully matched sample is said to have external validity.
A non-random sample reduces the external validity of the study. Much medical research is done on the patients one sees in the clinic, this is a non-random sample that is not representative of a larger population and will not generalize. Because it will not generalize is not a fatal flaw in the study. A study with a non-random sample still identifies true facts about the sample and perhaps those findings will be true for others as well. It is best to define your population first, and then obtain a random sample.
The sample size required depends on the requirements of the study and size of the population. As a rule the bigger the better. If the sample is too small then the performance of a few individuals can have a big effect on the data, and render the data less representative of the population.
http://www.sahs.utmb.edu/pellinore/intro_to_research/wad/pop&samp.htm
What Is a Variable?
A variable is something that can be changed, such as a characteristic or value. Variables are generally used in psychology experiments to determine if changes to one thing result in changes to another.