The document provides an overview of sampling methods, emphasizing their purpose, advantages, and disadvantages in research, particularly within the quality control of food and pharmaceutical industries. It details various sampling techniques such as random, systemic, multistage, and cluster sampling, along with sampling plans for starting and finished products. Additionally, it highlights the significance of proper planning to minimize sampling errors and biases, ultimately concluding that effective sampling saves time and resources while yielding reliable results.

1. SAMPLING METHODS
QUALITY SQUARE INDUSTRY
Hardik Mistry
QUALITY SQUARE INDUSTRY

2. Introduction
Sampling is the act, process, or technique of selecting a suitable
sample, or a representative part of a population for the purpose
of determining parameters or characteristics of the whole
populations.

3. Purpose
• Economy : taking a sample requires a fewer resources than a
census.
• Timeliness : A sample may provide you with needed information
quickly
• The large size of many populations : many populations about
which inferences must be made are quite large
• Inaccessibility of some of the population : There are some
populations that are so difficult to get access to that only a
sample can be used

4. Cont….
• Destructiveness of the observation : Sometime the very act of
observing the desired characteristic of a unit of the population
destroys it for the intended
• Accuracy : A sample may be more accurate than a census. A
sloppily conducted census can a provide less reliable
information than a carefully obtained sample.

5. NATIONAL SURVEY On
Milk Adulteration 2011
• The FSSAI (Food safety and Standard Authority of India)
regional offices of Chennai, Mumbai, Delhi, Guwahati and
Kolkata, has conducted a nationwide survey and collected 1791
samples of which 1226 had tested positive for milk adulteration.
• The reports suggest that most Indians are consuming detergents
and other contaminants through milk.
• The first-of-its-kind snapshot survey had found that about 68.4
percent of the samples carried detergents.
• Other contaminants were Urea, Starch, Glucose and Formalin.
http://www.ahmedabadmirror.com/article/3/2012011420120114032756874a111b88d/%E2%80%98Milk-in-city-
capital-unadulterated%E2%80%99.html?pageno=1

6. Cont….
• In Gujarat out of 100, 89 samples were found adulterated by
FSSAI.
• 450 samples taken by the Gujarat government in Ahmedabad
and Gandhinagar using an instant kit have tested negative for
milk adulteration.
• The tests were conducted by Gujarat Food and Drugs Controller
Authority (GFDCA). More tests will be carried out on 2,500
samples sent from across the state at six laboratories
http://news.outlookindia.com/items.aspx?artid=747300

7. Merits
• It saves time.
• It reduces cost of enquiry.
• It gives more reliable results.
• More detailed information can be obtained.
• It is convenient for administration.
• The method is scientific.
• It is only method when investigation is causing the destruction
of the units examined.

8. Demerits
• It requires the services of expert investigators.
• If the survey is not properly planned, we may get misleading
results.
• It requires better supervision, more sophisticated techniques for
planning and execution.
• If the sample is not adequate, it may not indicate true
characteristics of the population.

9. Bias and Errors in Sampling
A sample is expected to mirror the population from which it
comes, however, there is no guarantee that any sample will be
precisely representative of the population from which it comes.

10. Cont….
There are two basic causes for sampling errors.
A. CHANCE
That is the error that occurs just because of bad luck. This may
result in untypical choices.
B. SAMPLING BIAS
• Sampling bias is a tendency to favor the selection of units
that have particular characteristics.
• It is the error that results from solely from the manner in
which the observations are made.

11. Cont….
UNINTENDED ERRORS
• The manner in which the response is elicited
• The social desirability of the persons surveyed
• The purpose of the study
• The personnel biases of the interviewers or survey writer.

12. Sampling Method
• A Sampling method means how a sample is selected from given
population.
• The larger the number of units observed for data collection, the
more representative is the sample of its population.
• The sampling method employed for selecting a sample is
important in determining how closely the sample represents the
population.

13. Sampling Methods
(A) Random sampling
 Simple random sampling
 Stratified random sampling
(B) Systemic sampling
(C) Multistage sampling
(D) Cluster sampling

14. (A) Random sampling
Random
sampling
Simple Stratified
Random
Lottery
number
method
table

15. Simple random sampling
• In this method, the sample is being selected in such a way that
each unit of the population has an equal chance of being
included in sample.
• A simple random sample can be selected by two methods.
(i) Lottery method
(ii) Random number tables

16. (i) Lottery method
Simplest method of selecting a random sample
 Suppose, we have 500 units in population and we wish to
select 50 units out of them.
 So assign the numbers 1 to 500 units of population.
 Prepare slips bearing numbers 1 to 500.
 The slips should be homogeneous in shape, size, colour etc.
 These slips are shuffled and put in box.
 50 slips are selected.
 The units with the numbers on the slips selected will constitute
a random sample.

17. (ii) Random number tables
• Used as device to choose samples which included in survey, a
quality control inspection sample, or to assign experimental
units to treatments such as assigning patients to drug
treatments.
• It is most practical and inexpensive method of selecting a
random sample.

18. Cont….
• This method has been constructed in such a way that each of the
digits 0,1,2,…,9 appear with approximately the same frequency
and independent of each other.
• Suppose, we want to select random sample of size 50 out of
500,then give numbers 1 to 500 to the units of the population.
• Then, open any page of the random number table, select any row
or any column and consider a three digit random number.
• If the random number is less than 500, say 237, then select the
unit number 237 from population.
• If the random number is greater than 500, then ignore the
number.
• The units selected constitute the random sample.

19. (B) Systemic sampling
• This technique is used when complete and up-to-date list of
all units in the population is available.
• First unit is selected by method of random sampling and the
remaining units are selected according to some predetermined
pattern involving regular spacing of units.

20. Cont….
• Suppose there are 500 units in the population and we wish to
select a sample size 10.
• Then we say that out of every 50(=500/10) units, we have to
select one unit.
• Then select a random number from 1 to 50.
• Suppose the random number selected is 27, then the systemic
sample will consist of the units bearing numbers 27, 77,
127,… 477.
• It is useful only when complete and up to date frame is
available and units are arranged in some specific order.

21. (C) Multistage sampling
• This method is useful in many large scale surveys where the
preparation of the list of all units in the population is difficult.
• In this method, random selection is primary, intermediate and
final (or the ultimate) units from a given population.
• Thus, the area of investigation is restricted to a small number
of final units.
• This will reduce the cost compared with simple random
sampling from the whole population.

22. Cont….
• Suppose a socio-economy survey is to be conducted in a state
where complete list of all households is not available.
• In this case, select a random sample of some districts from the
total districts of the state.
• Within the selected districts, select random samples of some
talukas.
• Then from selected talukas, select random sample of some
villages and finally random samples of households from the
selected villages.
• This is a four stage sampling.

23. (D) Cluster sampling
• In this method, population from which sample is to be drawn
is divided into number of groups or clusters each of which
contain “sub-units.”
• The clusters may or may not have equal number of units.
• We select a random sample of some clusters from these
clusters and then observe and measure, each and every unit in
selected clusters.

24. Cont….
• Suppose, we are interested in obtaining the information about
the income of the residents in a city, the whole city may be
divided into N different blocks or localities (which form the
clusters) and a simple random sample of n blocks (clusters) is
drawn.
• The residents in the selected blocks constitute the cluster
sample.

25. Sampling with and without
Replacement
• If we draw a ball from an urn containing balls numbered 1 to
N, we have the choice of replacing or not replacing the ball
into the urn before a second ball is drawn.
• In the first case the particular ball can be drawn again and
again, whereas in the second case it can only be selected once.
• Sampling where each unit of the population may be chosen
more than once is called as sampling with replacement, while
if each unit cannot be chosen more than once it is called as
sampling without replacement.

26. Sampling Plans

27. Single Sampling Plan
• Inspect a sample “n” place from the lot “N”.
• If the number of defects found in sample does not exceed “c”
(accep. No.) the lot is accepted.
• If the number of defects found in sample exceed the value “c”
all the pieces in the reminder of lot inspected.

28. Double Sampling Plan
• In this sampling : after test three conditions arises
• Accept lot
• Reject lot
• No decision : in this case second sample is taken and the to
combine result of both the sample and made final decision

29. Content Uniformity
I.P.2010 Capsule Content uniformity
• Determine the content of active ingredient in each of 10 capsules taken at
random using the method given in the monograph or by any other suitable
analytical method of equivalent accuracy and precision.
• The capsules comply with the test if not more than one of the individual
values thus obtained is outside the limits 85 to 115 percent of the average
value and none is outside the limits 75 to 125 percent.
• If two or three individual values are outside the limits 85 to 115 percent of
the average value repeat the determination using another 20 capsules.
• The capsules comply with the test if in the total sample of 30 capsules not
more than three individual values are outside the limit 85 to 115 percent and
none is outside the limits 75 to 125 percent of the average value.

30. Sampling Plan is used for
• In Starting materials
• Finished products
• Packaging materials
Sampling Plan for Starting Materials
• “n- plan”
• “p- plan”
• “r- plan”
WHO Technical Report Series, No. 929, 2005, Annex 4
WHO guidelines for sampling of pharmaceutical products and related materials

31. 1- The ‘n-plan’
• Only used when material is consider uniform and from a
recognized source.
n=1+
• N = sampling units in the consignment (e.g individual
package, drum or container)
• Calculate “n” (n = units to be sampled)
• Select at random “n” units from N.
• Take a sample from these units.
• QC lab checks appearance + identify of each sample.
• If results concordant => combine samples into a single final sample .
• Take “analytical sample” for full testing
• Keep the test as “retention sample.”

32. Cont..
Value of n, p or r Value of N
n plan p plan r plan
2 Up to 3 Upto 25 Upto 2
3 4-6 26 - 56 3-4
4 7-13 57 - 100 5-7
5 14-20 101 - 156 6 -11
6 21-30 157 - 225 12 - 16
7 31-42 17 -22
8 43-56 23 - 28
9 57-72 29 - 36
10 73-90 37 - 44
e.g. N = 40 = > n =7 (units to be sampled)

33. II- The ‘p-plan’
• May be used when material is consider uniform, from a
recognized source and the main purpose is to test for identity.
• p = 0.4
• N = sampling units in the consignment (e.g individual
package, drum or container)
• Sample each of the N sampling units
• QC lab checks appearance + identify of each sample.
• If results concordant => p final samples are formed by appropriate pooling
• Keep the p samples for retention (or full testing if required)

34. Cont..
Value of n, p or r Value of N
n plan p plan r plan
2 Up to 3 Upto 25 Upto 2
3 4-6 26 - 56 3-4
4 7-13 57 - 100 5-7
5 14-20 101 - 156 6 -11
6 21-30 157 - 225 12 - 16
7 31-42 17 -22
8 43-56 23 - 28
9 57-72 29 - 36
10 73-90 37 - 44
e.g. N = 40 = > p =3 ( final samples after testing + pooling)

35. III- The ‘r-plan’
• May be used when material is consider non-uniform and/or
obtained from a not well know source.
• Can be used herbal medicinal products used as starting
materials r = 1.5
• N = sampling units in the consignment (e.g individual
package, drum or container)
• Sample each of the N sampling units
• QC lab checks appearance + identify of each sample.
• If results concordant => r final samples are randomly selected.
• R Samples individually fully tested.
• If results concordant = > combine the r samples for the retention sample.

36. Cont..
Value of n, p or r Value of N
n plan p plan r plan
2 Up to 3 Upto 25 Upto 2
3 4-6 26 - 56 3-4
4 7-13 57 - 100 5-7
5 14-20 101 - 156 6 -11
6 21-30 157 - 225 12 - 16
7 31-42 17 -22
8 43-56 23 - 28
9 57-72 29 - 36
10 73-90 37 - 44
e.g. N = 40 = > p =3 ( final samples after testing + pooling)

37. Sampling Plan for Finished Products
• The minimum size of the samples to be taken is determined
by the requirements of the analytical procedure used to test
the product (tests of unit dosage forms for uniformity of
weight, volume or content, or sterility tests can require a large
number of samples).
• Sampling and testing may be adjusted according to the
experience with the source of the product, e.g. manufacturer
or supplier.

38. Sampling Plan for Finished Products
&
Packaging Material
5.2 Sampling plans for packaging materials should be based on
defined sampling standards, for example, British Standard BS
6001-1, ISO 2859.
5.3 As for packaging materials, sampling plans for finished
products should be based on defined sampling standards such
as BS 6001-1, ISO 2859 or ANSI/ASQCZ 1.4-1993. or
ANSI/ASQCZ1.4-1993.

39. ISO 2859 or ANSI/ASQC Z 1.4-1993. BS 6001-1,

40. Conclusion
• In conclusion, it can be said that using a sample in research
saves mainly on money and time, if a suitable sampling
strategy is used, appropriate sample size selected and
necessary precautions taken to reduce on sampling and
measurement errors, then a sample should yield valid and
reliable information.

41. The only way to do great work is
To love what you do