What Is a Simple Random Sample?

Statistical sampling  begins with a group to be studied, called a population. Rather than study every individual of the population, it is more practical to form a subgroup and then study this subgroup. This smaller collection of individuals is called a statistical sample. Samples can be formed in a number of different ways, and not all of these ways are equally good. The gold standard for most statistical studies is a type of sample that is called a simple random sample. This is used so often that some textbooks simply refer to a simple random sample as SRS.

Definition of a Simple Random Sample

We begin by defining exactly what makes a sample a simple random sample. To begin with, and quite unsurprisingly, the selection of the sample must be done randomly. This means that a random sample is one in which any member of the population is equally likely to be a member of the sample. To be asimple random sample of size n the sample must be a random sample for which every group of size n is equally likely to be formed.

Forming Simple Random Samples

Simple random samples can be very difficult to obtain in practice. When dealing with a large population it is hard to ensure that every member is equally likely of being chosen. Sometimes the mechanism for guaranteeing a truly random selection requires some ingenuity. Human subjects make matters even more difficult as they can simply refuse to participate in a statistical sample.

If it is possible to label every member of a population with an identification number, then forming a simple random sample becomes a straightforward exercise in the use of a table of random number digits. Assuming that our table of random digits was generated by a random process, these numbers correspond to the individuals to be selected for a simple random sample.

Typically simple random samples are formed without replacement. This means that an individual cannot be chosen more than once to be in the same sample. The result is that the selection of individuals is not truly independent. However, as long as the sample size is not greater than five percent of the population, there is no need for concern.

Importance of Simple Random Samples

Simple random samples are important in statistics for a number of reasons. The role of randomness eliminates bias in our studies. Furthermore, many results in statistics are derived from probability theory. Probability assumes that random processes are at work. In order for our statistical results to be valid, we need to use samples that can be treated as random variables. Simple random samples allow us to do this.