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 • 8442 5653 8775 1891 7666 6483 9711 • 6941 8092 3875 4200 6543 9063 1003 • 8754 2564 8890 4195 8888 6490 3476

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 • 6941-use for sample- 5

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 • Advantages: • 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.