TABLE OF CONTENTS When we have to select a subset from a larger lot, we are always told to take a random sample. We have all seen this, for example, when we draw names out of a hat to determine teams for parlor games, flip a coin to make either/or choices, or draw straws to select one person out of a group.
Why do we do this? Does it make sense? In the cases above with which we are familiar, we have a sense of fairness, of unbiasedness. And unbiased is the word used by statisticians to describe the fact that the average of estimates obtained from many random samples will equal the value of the entire lot. When we sample randomly, the laws of probability apply, meaning that the odds are in our favor of getting a representative sample, though there is no guarantee. This also means that when we get an estimate of a value of the entire lot based on examining a random sample, we can calculate an estimate of the statistical sampling error. Thus, by taking a random sample, we not only have a statistically unbiased estimate, but we also have an idea of how good or bad that estimate is. For example, in polls taken to determine voter preferences of political candidates and issues, the results are stated as a percent with typically a 2% or 3% error. Clearly, the smaller the estimation error, the more faith we have in the...
