Basics concepts of Sampling, Sampling error

1. Sample Design
Dr. Shriram S. Dawkhar.
Associate Professor,
Sinhgad Institute of Business Administration &
Research, Kondhwa, Pune.

2. ➢ The following order concerning various steps
provides a useful procedural guideline regarding
the research process.
1. Formulating the research problem
2. Literature survey (use of Library)
3. Formulation of hypothesis
4. Preparing the research design
5.Determining sample design
© Shriram Dawkhar, May- 2010
(Updated - Nov-2019)

3. 6. Collecting the data.(The evidence collected by
research process)
7. Analysis of data
8. Hypothesis Testing
9. Generalization and interpretation &
10. Preparation of the report or presentation of the result.
(i.e. formal write up or conclusions.)
© Shriram Dawkhar, May- 2010
(Updated - Nov-2019)

4. SAMPLE DESIGN
STEP-5

5. Sampling Procedure
Universe
Sample
Probability
Samples
Non-Probability
Samples

6. Determine Sample Design
• Universe or Population
– All the items under consideration in any field of
inquiry constitute a ‘Universe’ or ‘Population’.
• Census
• A complete enumeration / counting of all the items in
to population is known as a census inquiry.
• Census inquiry is not possible in practice because of
quite often researcher select only a few items from
the universe for the study purposes. This items so
selected constitute what is technically called a
‘sample’.

7. Determine Sample Design
• Population:
• refers to entire group of people, events or
things of interest that the researchers
wishes to investigate.
• Sampling:
Sampling is the process of selecting a sufficient number
of elements from the population, so that the study of the
sample & understanding of its properties or characteristics
would make it possible for us to generalize such
properties or characteristics to the population

8. Determine Sample Design
• Sample :
• A sample is a group of units / element selected from
a larger group – the population.
• Sampling frame:
The listing of all accessible population from
which you will draw your sample is called
sampling frame.

9. Determine Sample Design
• Sample Design
– A sample design is a definite plan determined
before any data are actually collected for
obtaining a sample from a given population.

10. Need of Sampling
• Lower Cost
• Greater accuracy of results.
• Greater speed of data collection
• Availability of Population elements
• Sample Versus Census.

11. Characteristics of good sample
design / Sampling
• 1) Sample design must result in a truly
representative sample.
• 2) Sample design must be such which
result in a small sampling error.
• 3) Sample design must be viable in the
context of funds available for the
research study.

12. Characteristics of good sample
design
• 4) Sampling design must be such so that
systematic bias can be controlled in a
better way.
• 5) Sample should be such that the result
of the sample study can be applied, in
general, with a universe with a reasonable
level of confidence.

14. The Sampling Design Process
Define the Population
Determine the Sampling Frame
Select Sampling Technique(s)
Determine the Sample Size
Execute the Sampling Process

15. SAMPLING BREAKDOWN

16. DETERMINATION OF SIZE OF SAMPLE
• Common Misconceptions
– The sample should be a proportion (often 5
or 10 per cent) of the population;
– The sample should total about 500;
– Any increase in the sample size will
increase the precision of the sample
results.
◙ No such rule-of-thumb method is
adequate.

17. Sample Sizes Used in Marketing
Research Studies
Type of Study Minimum Size Typical Range
Problem identification research
(e.g. market potential)
500 1,000-2,500
Problem-solving research (e.g.
pricing)
200 300-500
Product tests 200 300-500
Test marketing studies 200 300-500
TV, radio, or print advertising (per
commercial or ad tested)
150 200-300
Test-market audits 10 stores 10-20 stores
Focus groups 2 groups 4-12 groups

18. SIZE OF SAMPLE
• Most researchers find it difficult to
determine the size of the sample.
• Krejcie and Morgan (1970) have
prepared a table.

19. TABLE FOR DETERMINING SAMPLE SIZE FROM A GIVEN POPULATION
N S N S N S
10 10 460 210 2600 335
20 19 500 217 2800 338
30 28 550 226 3000 341
40 36 600 234 3500 341
50 44 700 248 4000 351
60 52 800 260 4500 354
70 59 900 269 5000 357
80 66 1000 278 6000 361
90 73 1200 291 7000 361
100 80 1300 297 8000 367
120 92 1400 302 9000 368
140 103 1500 306 10000 370
160 113 1600 310 15000 375
180 123 1700 313 20000 377
200 123 1800 317 30000 379
250 152 1900 320 40000 380
300 169 2000 322 50000 381
360 186 2200 327 75000 382
400 196 2400 331 100000 384
N=Population S=Sample Size

20. There is only one method of determining
sample size that allows the researcher to
PREDETERMINE the accuracy of the sample
results…
The Confidence Interval
Method of Determining
Sample Size

21. Sample Size Formula - Proportion
• The sample size formula for estimating a
proportion (also called a percentage or share):

22. The Central Limit Theorem allows us to
use the logic of the Normal Curve
Distribution
• Since 95% of samples drawn from a
population will fall within + 1.96 x
Sample error (this logic is based
upon our understanding of the
normal curve) we can make the
following statement: ….

23. Practical Considerations in Sample Size
Determination
• How to estimate variability (p and q
shares) in the population
• Expect the worst case (p=50%; q=50%)
• Estimate variability: results of previous
studies or conduct a pilot study

24. Practical Considerations in Sample Size
Determination
• How to determine the amount of desired
sample error
• Researchers should work with managers
to make this decision. How much error is
the manager willing to tolerate (less error
= more accuracy)?
• Convention is + 5%
• The more important the decision, the less
should be the acceptable level of the
sample error

25. Practical Considerations in Sample Size
Determination
• How to decide on the level of confidence
desired
• Researchers should work with managers
to make this decision. The higher the
desired confidence level, the larger the
sample size needed
• Convention is 95% confidence level
(z=1.96 which is + 1.96 s.d.’s )
• The more important the decision, the more
likely the manager will want more
confidence. For example, a 99%
confidence level has a z=2.58.

26. Sample Size…
• Many numerical techniques for
determining sample sizes are available ,
but suffice it to say that the larger the
sample size is, the more accurate we can
expect the sample estimates to be.

27. Types of Error
Sampling Nonsampling
10-27
Errors in sampling

28. Sources of Error in Sampling
• Sampling Errors – error caused by the act of
taking a sample.
– They cause sample results to be different from the
results of census.
• Nonsampling errors – errors not related to
selecting the sample.
– They can be present even in a census.

29. Sampling and Non-Sampling Errors…
• Two major types of error can arise when a sample of
observations is taken from a population:
• sampling error and non sampling error.
• Sampling error refers to differences between the sample
and the population that exist only because of the
observations that happened to be selected for the sample.
Random and we have no control over.
• Non sampling errors are more serious and are due to
mistakes made in the acquisition of data or due to the
sample observations being selected improperly.
Most likely caused by poor planning, sloppy work, act of the
Goddess of Statistics, etc.

30. Sampling Error…
• Sampling error refers to differences
between the sample and the population
that exist only because of the observations
that happened to be selected for the
sample.
• Increasing the sample size will reduce this
type of error.

31. Sampling errors
• Random sampling error – the deviation between the
sample statistic and the population parameter caused by
chance in selecting a random sample.
– this is only component of the margin of error
• Bad Sampling Methods
– Convenience Sampling
– Voluntary Response
• Undercoverage – when some members of the
population are left out of the process of choosing the
sample.

32. Undercoverage
• sampling frame is the list of individuals
from where the samples are actually
chosen.
– If the sampling frame leaves out certain classes
of people, random sample from that frame will be
biased.

33. Example- Undercoverage
• We used a telephone book to randomly
choose numbers to dial and ask “What
brand of soap do you use most often?”
– Population: All Indian adults
– Sampling Frame: All adults with listed phone numbers
– Error: Undercoverage
• By using the telephone book, we have left out all those
people who do not have phones and all the people who
have unlisted phone numbers.

34. Reducing sampling error
• If sampling principles are applied carefully within the
constraints of available resources, sampling error can be
kept to a minimum.

35. Nonsampling errors
• Processing errors- mistakes in mechanical
tasks, such as doing arithmetic or entering
responses into a computer.
• Response errors – occurs when a subject
gives an incorrect response.
– i.e. not understanding a question, lying about a
question.
• Nonresponse – the failure to obtain data from
a selected individual in the survey.

36. Nonresponse
• One of the most serious types of nonsampling
errors.
• Can happen for a variety of reasons.
– Most nonresponse happens because some subjects can’t be
contacted or because some subjects who are contacted
refuse to participate.
• Can cause bias, which easily overwhelm the random
sampling error.
– Different groups have different rates of nonresponse.

37. Reducing non-sampling errors
• Can be minimised by adopting any of the following
approaches:
– using an up-to-date and accurate sampling
frame.
– careful selection of the time the survey is
conducted.
– planning for follow up of non-respondents.
– careful questionnaire design.
– providing thorough training and periodic
retraining of interviewers and processing staff.

38. Reducing non-sampling errors – cont’d
- designing good systems to capture errors that occur
during the process of collecting data, sometimes called
Data Quality Assurance Systems.

39. Classification of Sampling
Techniques
Sampling Techniques
Nonprobability
Sampling Techniques
Probability
Sampling Techniques
Convenience
Sampling
Judgmental
Sampling
Quota
Sampling
Snowball
Sampling
Systematic
Sampling
Stratified
Sampling
Cluster
Sampling
Other Sampling
Techniques
Simple Random
Sampling

40. Non-Probability Sampling Methods
◼ Convenience Sample :
The sampling procedure used to obtain those
units or people most conveniently available.
✓Subjects selected because it is easy to access them.
• No reason tied to purposes of research.
▪Students in your class, people on State Street, friends
◼ Why: speed and cost
◼ External validity?
◼ Internal validity
◼ Is it ever justified?

41. ◼ Advantages
◼ Very low cost
◼ Extensively used/understood
◼ No need for list of population elements
◼ Disadvantages
◼ Variability and bias cannot be measured
or controlled
◼ Projecting data beyond sample not
justified.

42. Convenience Sampling
Convenience sampling attempts to obtain a sample of
convenient elements. Often, respondents are selected
because they happen to be in the right place at the right
time.
– use of students, and members of social organizations
– mall intercept interviews without qualifying the
respondents
– department stores using charge account lists
– “people on the street” interviews

43. ◼ Judgment or Purposive Sample
◼ The sampling procedure in which an
experienced researcher selects the sample
based on some appropriate characteristic of
sample members… to serve a purpose.
➢Subjects selected for a good reason tied to
purposes of research
➢ Small samples < 30, not large enough for power of
probability sampling.
➢ Nature of research requires small sample
➢ Choose subjects with appropriate variability in what
you are studying
➢ Hard-to-get populations that cannot be found
through screening general population

44. ◼ Advantages
◼ Moderate cost
◼ Commonly used/understood
◼ Sample will meet a specific objective
◼ Disadvantages
◼ Bias!
◼ Projecting data beyond sample not
justified.

45. Judgmental Sampling
Judgmental sampling is a form of convenience
sampling in which the population elements are selected
based on the judgment of the researcher.
– test markets
– purchase engineers selected in industrial marketing
research
– expert witnesses used in court

46. ◼ Quota Sample
◼ The sampling procedure that ensure that
a certain characteristic of a population
sample will be represented to the exact
extent that the investigator desires.
◼ Specific number of sample unit (Quota)

48. ◼ Advantages
◼ moderate cost
◼ Very extensively used/understood
◼ No need for list of population elements
◼ Introduces some elements of
stratification
◼ Disadvantages
◼ Variability and bias cannot be measured
or controlled (classification of subjects)
◼ Projecting data beyond sample not
justified.

49. Quota Sampling
Quota sampling may be viewed as two-stage restricted judgmental
sampling.
– The first stage consists of developing control categories, or quotas, of
population elements.
– In the second stage, sample elements are selected based on
convenience or judgment.
Population Sample
composition composition
Control
Characteristic Percentage Percentage Number
Sex
Male 48 48 480
Female 52 52 520
____ ____ ____
100 100 1000

50. ◼ Snowball sampling
◼ The sampling procedure in which the
initial respondents are chosen by
probability or non-probability methods,
and then additional respondents are
obtained by information provided by the
initial respondents

51. ◼ Advantages
◼ low cost
◼ Useful in specific circumstances
◼ Useful for locating rare populations
◼ Disadvantages
◼ Bias because sampling units not
independent
◼ Projecting data beyond sample not
justified.

52. Panel Sampling
• The same units or elements are measured
on subsequent occasion.
• E.g. : Some households – to know
consumption pattern & after six months
same house holds.

53. Master Samples
• A master sample is one form which
repeated sub-samples can be taken as
and when required from the same area of
population.

54. Probability Sampling
• Please refer class notes provided during
class.