Simple Random Sample - Distinction Between A Systematic Random Sample and A Simple Random Sample

Distinction Between A Systematic Random Sample and A Simple Random Sample

In a simple random sample, one person must take a random sample from a population, and not have any order in which one chooses the specific individual.

Let us assume you had a school with 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 bucket 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):

1. In the case that any given person can only be selected once ie. after selection person is removed from the selection pool (basic probability):

2. In the case that any selected person is returned to the selection pool ie. can be picked more than once (Geometric distribution):

This means that every student in the school has in any case approximately 1 in 10 chance of being selected using this method. Further, all combinations of 100 students have the same probability of selection.

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. 0533, 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. This is no longer simple random sampling, because some combinations of 100 students have a larger selection probability than others - for instance, {3, 13, 23, ..., 993} has a 1/10 chance of selection, while {1, 2, 3, ..., 100} cannot be selected under this method.