Sample Selection Procedure

Standard procedure for sample selection as illustrated in Cochran, W. G. (2002), has been implemented for developing this software. Details of implementation of different procedures of sample selection have been described below:

Equal probability based selection

The selection of sampling units based on equal probability is Simple Random Sampling With and Without Replacement (SRSWR and SRSWoR) and Systematic sampling.

Simple Random Sampling (SRS):

In this method each element has an equal probability of being selected from population sampling frame (without and with replacement). The algorithm for implementing this method of sample selection is given below:

1. Create an array containing the list of the population units from the selected excel file.

2. Get the desired sample size as input from the user.

3. Assign all individuals on the list a consecutive number from zero to the required number. Each individual must have the same number of digits as each other individual.

4. Select an arbitrary number in the table of random numbers.

5. For the selected number, look only at the number of digits assigned to each population member.

6. If the number corresponds to the number assigned to any of the individuals in the population, then that individual is included in the sample.

7. Go to the next number in the column and repeat step #7 until the desired number of individuals has been selected for the sample.

Systematic sampling:

In this method an ordered sampling frame is used for selection of elements. The most common form of systematic sampling is an equal probability method, in which every kth element in the frame is selected, where k is sampling interval. Only the first unit is selected at random. The process involves the following steps:

1. Create an array containing the list of the population units from the selected excel file.

2. Determine the desired sampling fraction, say 50 out of 1000; and also the number of the K'~unit. [K=N/n= 1000/50 = 20].

3. Starting with a randomly chosen number between 1 and K, both inclusive, select every K'~unit from the list. If in the above example the randomly chosen number is 4, the sample shall include the 4th, 24th, 44th, 64th, 84th units in each of the series going upto the 984th unit.

Unequal probability selection

Probability Proportional to Size (PPS):

Auxiliary information present on the frame is used to calculate the probabilities of each unit in the population. Each member of the survey population has a chance of being included in the sample. In this method, unit with bigger size has higher chance of being included in the sample. The auxiliary variable available on the frame is used for selecting the units by cumulative frequency method. The algorithm, given below, has been followed in this software:

1. Compute cumulative totals for the sizes Xi, i=1,2,........N.

2. Chose a random number r, such that 1≤ r ≤ X

3. Select the ith population unit if Ti-1 < r ≤ Tr where Ti-1 = X1 +X2 + .......Xi-1 and T = Ti-1 + Xi .

4. For selecting a sample of n units with PPS with replacement, repeat the method n times. Where, n = number of units to be selected from the population