1. Simple Random Sampling
Module 3
Session 5

2. Session Objectives Define simple random sampling
To demonstrate how a Simple random sample is selected in practice

3. Simple Random Sampling
Simplest sampling design
In simple random sampling each element has an equal chance of being selected
The procedure for selecting a Simple Random Sample is as follows:
List all the units in the population (construct a sampling frame if one does not exist already), say from 1,..,N

4. How to select the sample
In other words, give each element a unique Identification (ID) starting from 1 to the number of elements in the population N
N is the total number of units in the population
Using random numbers or any other random mechanism (eg Lottery or goldfish bowl), select the sample of n units from the list of N units one at a time without replacement

5. How to select the sample
There many different random number tables. One example is given on the next slide.

6. Random Numbers

7. How to use a random number table?
Decide on the minimum number of digits
Start anywhere in the table and going in any direction choose a number/(s)
The sequence of reading the numbers should be maintained until the desired sample size is attained
If a particular number is not included in your range of population values, choose another number
Keep selecting the numbers till you have the required number of elements in your sample

8. How to use a random number table?
This process of selecting a large sample using random number tables is tedious
Usually we use computer generated random numbers

9. Example
Suppose we want to select 5 elements from a population of 8000.
We number the population from 1 to 8000
We use the random number table given on slide 6
Suppose for convenience we start at the top left hand corner and read across

10. Example
We need to use four digits at a time as there is a minimum of four digits in our sample ID’s.
Let us start. The first set of 4 digits is 8442
8442 not in our population-ignore
5653-use for sample -1
8775-ignore
1891-use for sample -2

11. Example 7666- use for sample -3 6483- use for sample -4 9711-ignore

12. The sample
So our sample consists of the units numbered 5653,1891,6483,7666, and 6941.
Here we have used sampling without replacement.
Sampling with replacement (WR) - units can be selected more than once.
Sampling without replacement (WOR) - units cannot be selected more than once

13. Need to explain the lottery method of sampling
This involves writing the unique numbers on identical items which are then put in an urn. Then one item is drawn at a time and the unit to which the drawn number corresponds is included in the sample.
This can also be done with or without replacement

14. Advantages/Disadvantages of Simple Random Sampling
Sample is easy to select in cases where the population is small
Disadvantages:
Costs of enumeration may be high because by the luck of the draw, the sampled units may be widely spread across the population
By bad luck, the sample may not be representative because it may not be evenly spread across all sections of the population

15. Estimation
Having selected the sample, we now need to produce estimates from the sample to make certain statements about the population
Usually we want to provide estimates of certain parameters in the population
eg mean, medians, totals or proportions

16. Estimation More will be said about estimation in a later module.
However, with simple ransom sampling:
Population mean is estimated by the sample mean
e.g. the mean yield of wheat in a small district
Population total is estimated by taking the sample total and scaling up by the number of elements in the population.
etc.