Systematic Sampling - Statistical Technique

In "Systematic Sampling" one unit is selected randomly and subsequent units are selected according to a pre-determined system. Invariably uniform distance is adopted for pre-assigned system.

Types of Systematic Sampling:- 

1. Linear Systematic Sampling

Linear systematic sampling is a systematic sampling method where samples aren't repeated at the end and 'n' units are selected to be a part of sample having 'N' population units. It follows a linear path and then stops at the end of a particular population.

K = N/n 

K = Sampling or Skip Interval,

n = Sample size, and

N = Total population. 

2. Circular Systematic Sampling

In circular systematic sampling, a sample starts again from the same point once again after ending, thus the name.

K = N/n

K (Skip interval) = N (Population) / n (Sample size)

 

Question:

A sample of size 3 is to be selected from a population of 10 households. List all possible samples by :-
(a) Linear Systematic Sampling
(b) circular systematic Sampling

Answer:

Given,
Sample size (n) = 3
Total Population (N) = 10
So,
Skip Interval (K) = Total Population / Sample size
                               = N/n
                               = 10/3 (Nearest Integer Value)
                               = 3
                       
(a) Linear Systematic Sampling

Now, Arranging Households of population using skip interval, in linear way as given

          1      2      3
          4     5      6
          7     8      9
         10
         
Selecting a random number (r) between 1 to 3.
so, Total Possible samples are (1,4,7) (2,5,8) (3,6,9).

(b) Circular Systematic Sampling

Now, Arranging Households of population using skip interval, but in circular way as given


Selecting a random selection (r) be 1 then Possible sample (1,4,7), if random start will be 4, then Sample will be (4,7,10). Like this we can create remaining 8 samples,
Hence, Total number of sample in Circular Systematic Sampling is N=10.