Page 152 - DMGT209_QUANTITATIVE_TECHNIQUES_II

Unit 8: Sampling and Sampling Distribution

Notes
Example: Put 100 chits in a box numbered 1 to 100. Pick one number at random. Now the
population has 99 chits. Now, when a second number is being picked, there are 99 chits. In order
to provide equal probability, the sample selected is being replaced in the population.

Varying Probability

This is also called random sampling without replacement. Once a number is picked, it is not
included again. Therefore, the probability of selecting a unit varies from the other.
In our example, it is 1/100, 1/99, 1/98, 1/97 if we select four samples out of 100.

Systematic Random Sampling

There are three steps:
(1) Sampling interval K is determined by the following formula:



(2) One unit between the first and Kth unit in the population list is randomly chosen.
(3) Add Kth unit to the randomly chosen number.

Example: Consider 1,000 households from which we want to select 50 units.

Calculate  

To select the first unit, we randomly pick one number between 1 to 20, say 17. So our sample
begins with 17,37,57………….. Please note that only the first item was randomly selected. The
rest are systematically selected. This is a very popular method because we need only one random
number.

Stratified Random Sampling

A probability sampling procedure in which simple random sub-samples are drawn from within
different strata, which are, more or less equal on some characteristics. Stratified sampling are of
two types:
1. Proportionate stratified sampling: The number of sampling units drawn from each stratum
is in proportion to the population size of that stratum.
2. Disproportionate stratified sampling: The number of sampling units drawn from each
stratum is based on the analytical consideration, but not in proportion to the size of the
population of that stratum.

Sampling process is as follows:
1. The population to be sampled is divided into groups (stratified).
2. A simple random sample is chosen.

LOVELY PROFESSIONAL UNIVERSITY 147