# Systematic Random Sampling

Sometimes we do not have the details of every member (unit) in a population. If we wanted a probabilistic sample, we would then employ sampling techniques other than simple random sampling.

Systematic Random sampling is one such technique. Put simply, it is random sampling with a “system”. Here, all it means is that the sampling follows a pattern.

Requirements:

The population must be homogeneous (the subjects should be uniformly distributed).

The total population (N) must be known.

The required sample size (n) must be known.

Procedure:

Once we have satisfied ourselves that the basic requirements are satisfied, we proceed to determine the “Sampling Interval“.

The sampling interval is what provides the “system” or pattern to this technique. It is merely the number of sampling units we need to skip between one selection and the next.

Suppose we needed 10 student representatives from a class of 100 students. The sampling interval (k) is given by the equation

k= N/n

where k is the sampling interval;

N is the total population;

n is the size of the sample we require.

In our example, we get

k= 100/10;        Therefore, k=10

What this means is that we will select every 10th individual in the class.

Wait a minute! Didn’t we learn that random means unguessable? If we already know that every 10th student will be selected, how is it “random”?

The randomness is introduced by the selection of the starting point in a random manner.

You see, while we know that every 10th student will be selected, we don’t know (and can’t guess) from which point onwards we will begin the process of selection.

If the starting point is 1, we will select 1, 11, 21, 31, 41, 51, and so on.

If the starting point is 3, we will select 3. 13, 23, 33, 43, 53, and so on.

If the starting point is 35, we will select 35, 45, 55, 65, 75, 85, and so on..

The crucial point is, that we do not know the starting point in  advance.

How do we obtain the starting point, then?

There are many ways, but one preferred by many is the currency note method. Establish rules first:

1. We will consider the last three digits of the note only (since we are dealing with 100 subjects, considering only two digits would mean that 100 can never get selected).

2. If the number is greater than 100, it will be discarded and another note will be drawn.

3. Once a number between 001 and 100 (both inclusive) is obtained, it will be designated the starting point and will not be changed subsequently.

Take a currency note from a stack of notes (you should not have studied or “planted” the notes in advance).  Follow the rules till you obtain the starting point. Let’s assume the starting point was 54. Then you will proceed to select 54, 64, 74, 84, 94..

At this point, you realize that 94 + 10= 104; but we have only 100 students. Now what?

We simply count till we hit 100, then continue from 1 and proceed the same way.

Imagine that the students are seated in a circle, and that 100 is followed by 1. So the count would be 94, 95, 96, 97, 98, 99, 100, 1, 2, 3, 4,,,. We want the 10th student from the 94th one. Therefore, the next student to be selected would be the 4th one. After that, simply keep adding the sampling interval (10 in this example), till the required sample size is obtained (also 10 in this example).

Our final sample would thus be: 54, 64, 74, 84, 94, 4, 14, 24, 34, 44th students.

Another way to do this would be to use a Table of Random Numbers. Establish reading rules and then proceed as mentioned in the previous post.

The details of members of the population are not required.

This procedure can be applied to moderate to large size populations.

After obtaining the starting point, it is possible to send out multiple parties to identify and interview the other subjects (maintaining the sampling interval), saving time.

It is unsuitable for sampling very large populations (an entire state or province; a country, for example).

It is unsuitable in populations where there is a pattern (if every 10th house in every street is occupied by a person of Chinese origin; and the sampling interval is 10; we may either obtain only people of Chinese origin, or none at all- the sample will not be representative of the population).

Summary:

Systematic Random Sampling is a probabilistic sampling technique.

It requires knowledge of the total population and required sample size.

The sampling interval (k) is given by k= N (Total population)/ n (sample size)

After randomly obtaining the starting point, every kth subject is selected.

It is unsuitable for very large populations and those where the population is distributed in a pattern