THE THEORY AND LOGIC OF PROBABILITY SAMPLING
    Conscious and Unconscious Sampling Bias
    Representativeness and Probability of Selection
    Random Selection
    Probability Theory, Sampling Distributions, and Estimates of Sample Error

    Suppose you were assigned the task of identifying and interviewing a "representative sample" of people in your community.  How would you go about that?  You might wander around the community, stopping people at different locations and interviewing them.  Unfortunately, you would inevitably miss some locations (and the kinds of people who frequent them) while getting too many people from other locations.  Moreover, as you decide who to interview from among those people passiing by, your own likes and dislikes, and even fears, would consciously or unconsciously bias who you chose.

    The central principle of probability sampling is that if every member of a population has an equal chance of selection into a sample, those who are selected will be representative of the whole population.  The most straightforward way to achieve this would be to give everyone in the population a number, select a series of random numbers, and choose into the sample all those people whose numbers had been pick at random.  This is called an EPSEM (Equal Probability of Selection Method) sample.

    The probability theory upon which this principle is based goes a step further.  Not only will the method just described provide a relatively representative sample, it is possible to calculate just how accurately the sample represents the whole population from which it was drawn.  Thus, we can estimate characteristics of the population (e.g., percent voting for Schmertz), and we can also estimate the sampling error of our estimate.  Thus can estimate that 60 percent will vote for Schmertz, and say futher that we are 95% confident that Schmertz will receive between 55 percent and 65 percent, for example.