Sampling from a Population

We often use samples instead of the entire population because the cost and time of measuring every item in the population would be prohibitive. Also, in some cases measurement requires destruction of individual items. In general, we achieve greater accuracy by carefully obtaining a random sample of the population instead of spending the resources to measure every item. There are two important reasons for this result. First, it is often very difficult to obtain and measures every item in a population, and even if possible, the cost would be very high for a large population.

Simple Random Sample

Suppose that we want to select a sample of size n objects from a population of N objects. A simple random sample is selected such that every object has an equal probability of being selected and the objects are selected independently—the selection of one object does not change the probability of selecting any other objects.

Simple random sampling can be implemented in many ways. We can place the N population items—for example, colored balls—in a large barrel and mix them thoroughly. Then from this well-mixed barrel w can select individual balls from different parts of the barrel. In practice, we often use random numbers to select objects that can be assigned some numerical value. Various statistical computer software and spreadsheets have routines for obtaining random numbers, and these are generally used for most sampling studies.

To see how to use random number table, suppose that we have 100 employees in a company and wish to interview a randomly chosen sample of 10. We could get such a random sample by assigning every employee a number of 00 to 99, consulting a Random Number Table, and picking a systematic method of selecting two-digit numbers. In this case, let’s do the following:

Go from the top to the bottom of the columns beginning with the left-hand column, and read only the first two digits in each row.

Systematic Sampling

In systematic sampling, elements are selected from the population at a uniform interval that is measured in time, order, or space. If we want to interview every twentieth student on a college campus, we would choose a random starting point in the first 20 names in the student directory and then pick every twentieth name thereafter.