# Simple Random Sampling

A sampling procedure that assures that each element in the population has an equal chance of being selected is referred to as simple random sampling. Let us assume you had a school with a 1000 students, divided equally into boys and girls, and you wanted to select 100 of them for further study. You might put all their names in a drum and then pull 100 names out. Not only does each person have an equal chance of being selected, we can also easily calculate the probability of a given person being chosen, since we know the sample size (n) and the population (N) and it becomes a simple matter of division:

n/N x 100 or 100/1000 x 100 = 10%

This means that every student in the school as a 10% or 1 in 10 chance of being selected using this method.

Many statistics books include a table of random numbers, which are predetermined sets of random numbers. It is possible to start at any point on the table and move in any direction to choose the numbers required for the sample size. However, technology has given us a number of other alternatives: many computer statistical packages, including SPSS, are capable of generating random numbers and some phone systems are capable of random digit dialling.

If a systematic pattern is introduced into random sampling, it is referred to as "systematic (random) sampling". For instance, if the students in our school had numbers attached to their names ranging from 0001 to 1000, and we chose a random starting point, e.g. 533, and then pick every 10th name thereafter to give us our sample of 100 (starting over with 0003 after reaching 0993). In this sense, this technique is similar to cluster sampling, since the choice of the first unit will determine the remainder.

There are a number of potential problems with simple and systematic random sampling. If the population is widely dispersed, it may be extremely costly to reach them. On the other hand, a current list of the whole population we are interested in (sampling frame) may not be readily available. Or perhaps, the population itself is not homogeneous and the sub-groups are very different in size. In such a case, precision can be increased through stratified sampling.

Some problems that arise from random sampling can be overcome by weighting the sample to reflect the population or universe. For instance, if in our sample of 100 students we ended up with 60% boys and 40% girls, we could decrease the importance of the characteristics for boys and increase those of the girls to reflect our universe, which is 50/50.