The document discusses various sampling methods used in research. It describes probability sampling methods like simple random sampling, systematic sampling, stratified sampling, cluster sampling, and multistage sampling. It also discusses non-probability sampling methods such as purposive sampling, volunteer sampling, snowball sampling, quota sampling. The document provides examples and formulas for calculating sample sizes for both categorical and continuous variables to achieve the desired level of precision and confidence level. It emphasizes the importance of random selection and adequate sample sizes to obtain results representative of the population.

1. Types of Sampling
• 1. Probability Sampling
• 2. Non Probability Sampling
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Dr. D. P. Singh, School of Research Methodology, TISS

2. Probability Sampling Methods
1. Simple Random Sampling
2. Systematic Sampling
3. Stratified Sampling
4. Cluster Sampling
5. Multistage Sampling
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Dr. D. P. Singh, School of Research Methodology, TISS

3. 1. Simple Random Sampling : A Simple Random Sample of n
subjects from a population is one in which each possible
sample of that size has the same probability of being selected.
How to Select a Simple Random Sample?
• Before selecting a Random Sample, we need a list of all
subjects in the population. The list is called Sampling Frame.
The most common method for selecting a simple random
sample from the sampling frame is the use of a random
number table.
• A random number table is a table containing a sequence of
numbers that is computer generated according to a scheme
whereby each digit is equally likely to be any of the integers
0,1,2, ... ,9
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Dr. D. P. Singh, School of Research Methodology, TISS

4. Appendix B: Random Number Table (5 Digits)
Col 1 2 3 4 5 6 7 8 9 10
1 13962 70992 65172 28053 02190 83634 66012 70305 66761 88344
2 43905 46941 72300 11641 43548 30455 07686 31840 03261 89139
3 00504 48658 38051 59408 16508 82979 92002 63606 41078 86326
4 61274 57238 47267 35303 29066 02140 60867 39847 50968 96719
5 43753 21159 16239 50595 62509 61207 86816 29902 23395 72640
6 83503 51662 21636 68192 84294 38754 84755 34053 94582 29215
7 36807 71420 35804 44862 23577 79551 42003 58684 09271 68396
8 19110 55680 18792 41487 16614 83053 00812 16749 45347 88199
9 82615 86984 93290 87971 60022 35415 20852 02909 99476 45568
10 05621 26584 36493 63013 68181 57702 49510 75304 38724 15712
11 06936 37293 55875 71213 83025 46063 74665 12178 10741 58362
12 84981 60458 16194 92403 80951 80068 47076 23310 74899 87929
13 66354 88441 96191 04794 14714 64749 43097 83976 83281 72038
14 49602 94109 36460 62353 00721 66980 82554 90270 12312 56299
15 78430 72391 96973 70437 97803 78683 04670 70667 58912 21883
16 33331 51803 15934 75807 46561 80188 78984 29317 27971 16440
17 62843 84445 56652 91797 45284 25842 96246 73504 21631 81223
18 19528 15445 77764 33446 41204 70067 33354 70680 66664 75486
19 16737 01887 50934 43306 75190 86997 56561 79018 34273 25196
20 99389 06685 45945 62000 76228 60645 87750 46329 46544 95665
21 36160 38196 77705 28891 12106 56281 86222 66116 39626 06080
22 05505 45420 44016 79662 92069 27628 50002 32540 19848 27319
23 85962 19758 92795 00458 71289 05884 37963 23322 73243 98185
24 28763 04900 54460 22083 89279 43492 00066 40857 86568 49336
25 42222 40446 82240 79159 44168 38213 46839 26598 29983 67645
Source: The Rand Corporation, A Million Random Digits with 100,000 Normal Deviates (New York: The Free Press, 1955)
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Dr. D. P. Singh, School of Research Methodology, TISS

5. 2. Systematic Sampling: If a sample of size n is
to be selected from a population size by N and let
k = N/n. A systematic random sample
1. Selects a subject at random from the first k names in the
sampling frame, and
1. Selects every kth subject listed after that one. The
number k is called the skip number.
k = 3
Random Start
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Dr. D. P. Singh, School of Research Methodology, TISS

6. 3. Stratified Sampling : A stratified random
sample divides the population into separate
groups, called strata and then selects a simple
random sample from each stratum.
The population is divided into k homogeneous
strata with stratum size N1, N2, …, Nk such
that N1 + N2 + …+ Nk=N
N1 N2
Nk
+ +……+ = N
n1 n2
nk
+ +……+ = n
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Dr. D. P. Singh, School of Research Methodology, TISS

7. Comparison of SRS, STRS and SYRS
Sample 1 2 3 4 5 6 7 8 9 mean
Population 2 2 2 5 5 5 8 8 8 5
Simple Random Sampling
2 2 2 2 Underestimate
5 5 5 5
8 8 8 8 Overestimate
1 2 5 8 5
2 2 5 8 5
Dr. D. P. Singh, School of Research Methodology, TISS
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8. 4. Cluster Sampling: Simple, systematic and stratified
random sampling are very expensive or ever impossible to
implement in many situations particularly when a
complete and up to date sampling frame is not available.
In cluster sampling, the population is divided in to
large number of groups, called clusters. A cluster
sample is one for which the sampling units are the
subjects in a random sample of the clusters.
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Dr. D. P. Singh, School of Research Methodology, TISS

9. 5. Multistage Sampling: Multi-stage sampling methods
use combinations of various sampling techniques. For
example, to study various characteristics of adult residents
in Maharashtra state, one could treat districts as clusters
and select a random sample of a certain number of them.
Now within each district selected one could take cluster
sample of villages. Within each village selected, one could
systematically sample every 10th household. Within each
household selected, one could select one adult at random
from the sample.
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Dr. D. P. Singh, School of Research Methodology, TISS

10. Non-Probability Sampling Methods
Social research is often conducted in situations
that do not allow the kinds of probability
sampling discussed so far, for large-scale social
surveys. Suppose we want to study
homelessness. Neither a list of all homeless
individuals is available nor it can be created.
Moreover, there are times when probability
sampling wouldn’t be appropriate. Such
situations call for non-probability sampling.
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Dr. D. P. Singh, School of Research Methodology, TISS

11. Methods of Non-Probability Sampling
1. Purposive or Judgement Sampling;
2. Volunteer Sampling;
3. Snowball Sampling;
4. Quota Sampling; and
Selecting Informants
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Dr. D. P. Singh, School of Research Methodology, TISS

12. 1. Purposive or Judgement Sampling
Sometimes it is appropriate to select a sample on the basis of knowledge of
a population and the purpose the study. This type of sampling is called
purposive or judgement sampling.
2. Volunteer Sampling
One of the most common non-probability sampling methods is volunteer
sampling. In this method subjects volunteer themselves for the sample. A
good example of volunteer sampling is visible almost any day on television.
Some T.V. programmes ask viewers to offer their opinions on any issue or
vote for any celebrity for his/her performance through SMS or calling a phone
number. The danger in this method is that the sample will poorly represent the
population and may yield misleading conclusions.
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Dr. D. P. Singh, School of Research Methodology, TISS

13. 1. Snowball Sampling
Snowball sampling method is appropriate when the
members of a special population or individuals with a
rare characteristic are difficult to locate such as
persons in a village who were bitten by snake. In this
method, the researcher collects data from the few
members of the target population; then asks those
individuals to provide information needed to locate
other members of the target population whom they
happen to know.
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Dr. D. P. Singh, School of Research Methodology, TISS

14. 1. Quota Sampling
Quota sampling begins with a matrix, or table,
describing the relevant characteristics of the target
population. Depending on your research purposes, you
may need to know what proportion of the population is
male and what proportion female as well as what
proportion of each gender fall into various age
categories, educational levels, ethnic groups, and so
forth.
Once you have created such matrix and assigned a
relative proportion to each cell in the matrix, you
proceed to collect data from people having all the
characteristics of a given cell. You then assign a weight
to all the people in a given cell that is appropriate to
their total population. When all the sample elements are
so weighted , the overall data should provide a
reasonable representation of the total population.
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Dr. D. P. Singh, School of Research Methodology, TISS

15. Sampling Error
The sampling error of a statistic is the error
that occurs when a statistic based on a sample
estimates or predicts the value of a
population parameter.
1. Other Sources of Variability/Error
2. Under-coverage
3. Response Bias
4. Non-response
5. Missing Data
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Dr. D. P. Singh, School of Research Methodology, TISS

16. Sample Size
• Feasible and Desirable
• Time, Money, Manpower and transport
• More variation more samples
• Estimates, confidence, margin of error
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17. Sample size calculation
• Proportion
• N = (1.96)2 * p * (1-p) / E2
• Where 1.96 is t test value at 95% confidence level
• P is proportion of prevalence taking .5 gives optimal sample size
• Changing p from .5 will lead to reduction in sample size
• E is margin error reducing it from .05 to .02 will increase sample
size
• An illustration with 95% confidence level, margin of error 5 %, p
value .5
Dr. D. P. Singh, School of Research Methodology, TISS 17

18. One Sample, Dichotomous Outcome (p)
• Confidence Level (e.g., 95%) 95%
• Estimate of true proportion (p),
• if unknown, enter 0.5 0.5
• Margin of Error (E) 0.05
• Sample Size Required 385
• Attrition? Enter Percentage Expected to be Lost/Missing Data
0%
• Sample Size Required, Accounting for Attrition
• n = 385
Dr. D. P. Singh, School of Research Methodology, TISS 18

19. Example : p=0.1, E=.05, CI-95%
• Confidence Level (e.g., 95%) 95%
• Estimate of true proportion (p),
• if unknown, enter 0.5 0.1
• Margin of Error (E) 0.05
• Sample Size Required 139
• Attrition? Enter Percentage Expected to be
Lost/Missing Data 0%
• Sample Size Required, Accounting for Attrition
• n = 139
Dr. D. P. Singh, School of Research Methodology, TISS 19

20. Population Size Sample size for permissible Error (proportion)
0.05 0.03 0.02 0.01
100 79 91 96 99
200 132 168 185 196
500 217 340 414 475
1000 278 516 706 906
10000 370 964 1936 4899
100000 382 1056 2345 8762
1000000 384 1066 2395 9513
Dr. D. P. Singh, School of
Research Methodology,
TISS 20

21. Estimate for continuous variable
Dr. D. P. Singh, School of Research Methodology, TISS 21
Where z is the value of standard normal distribution based on pre
selected confidence level (level (for example 1.645 for 90%
confidence level, 1.96 for 95% confidence level and 2.64 for 99%
Confidence level). σ is Standard deviation of outcome variable,
and E is margin of error – 5% or 1%
Remember smaller margin of error would require more sample
and similarly higher confidence level require larger sample

22. Example 1
• Suppose a sample of persons suffering from blood pressure in a industrial town is to
be selected by simple random sampling to estimate the level of diastolic blood
pressure. The precision is to be ± 5 with 95% confidence. An earlier survey found
the standard deviation as 20. Find the sample size for a population size of 1000 and
10,000.
• Substituting the information in relation no = t² S²/ d²
•
• no = (1.96)² * (20)² / (5)² = 61.46 or 62 approx.
•
• Since no/N=.062 Using equation (iv) we get 62/{1+(62/1000)}= 59
•
• For a population of 10,000, the ratio no/N is negligible and one can take sample of
62 as optimum sample.
•
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