RANDOM SAMPLES

What is a good sample? A sample is supposed to let you draw conclusions about the population from which it is taken. Therefore, a good sample is one that is similar to the population you are studying . But you should not go out and just look for animals, vegetables, or minerals that you think are "typical" of your population. With that kind of a sample (a judgment sample), the reliability of the conclusions you draw depends on how good your judgment was in selecting the sample ” and you cannot assess the selection scientifically. If you want to back up your research judgments with statistics (one of the reasons, I hope, why you are reading this book), you need a random sample . Statisticians have studied the behavior of random samples thoroughly. As you will learn in later chapters, the very fact that a sample is random means that you can determine what conclusions about the population you can reasonably draw from the sample.

So what is a random sample, if it is so important? It is a sample that gives every member of the population (animal, vegetable, mineral , or whatever) a fair chance of selection. Everyone or everything in the population has the same chance. No particular type of creature or thing is systematically excluded from the study, and no particular type is more likely than any other to be included . Also, each unit is selected independently: including one particular unit does not affect the chance of including another.

If you are interested in the opinions of all the adults in Los Angeles, do not rely on a door-to-door poll in mid-afternoon or ask questions of people as they leave church services on a rainy Sunday. Such samples exclude many of the types of people you want to draw conclusions about. People who have jobs are usually not home on weekday afternoons, so their opinions would not be included in your results. Similarly, people standing in the rain may express different opinions ( especially about umbrellas, for example) than they would if they were warm and dry. Polling in the rain would lead you to a bad guess about the proportion of the city's residents interested in your new product (disposable umbrellas). To make things worse , you cannot tell what the effects of excluding dry people will be. You cannot tell whether your observed results are biased one way or another, and you cannot tell by how much. You might even be on target, but you do not know that, either.

From any particular random sample, of course, the results are not exactly the same as the results you would get if you included the entire population. Later chapters will show you how statistical methods take into account the fact that different samples lead to somewhat different results. You will then understand how much you can say about a population from the results you observe in a sample.