CHAPTER FOUR
SAMPLING PROCEDURES
March 11, 2015
SAMPLING PROCEDURES
– Population and Sampling
– The Need for sampling
– Characteristics of Good Sampling
– Probability Sampling
– Non Probability Sampling
4.1. What is population ?
• The term population refers to the group or units of interest
(married couples, English teachers, students of English,
clients of FNB) during the time of interest (since 2011, during
August 2011, till October 2015.
• A population is a group of individuals persons, objects, or
items from which samples are taken for measurement.
• Defining the population is the essential first step in selecting a
sample. This process includes three parts:
– Identifying the group of interest
– Naming the geographic area where the group is found
– Indicating the time period of interest
4.2. What is a sample?
• A sample is a finite part of a statistical population
whose properties are studied to gain information
about the whole (Webster, 1985).
• A set of respondents (people) selected from a larger
population for the purpose of a survey.
4.3. What is sampling?
• 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 population.
4.3. What is sampling?
4.3.1. What is sampling?
4.3.2.Sampling Process
• The sampling process comprises several stages:
– Defining the population of concern
– Specifying a sampling frame, a set of items or
events possible to measure
– Specifying a sampling method for selecting items
or events from the frame
– Determining the sample size
– Implementing the sampling plan
– Sampling and data collecting
– Reviewing the sampling process
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4.3.3. SAMPLING FRAME
• In the most straightforward case, such as the
sentencing of a batch of material from production
(acceptance sampling by lots), it is possible to
identify and measure every single item in the
population and to include any one of them in our
sample. However, in the more general case this is not
possible. There is no way to identify all rats in the
set of all rats. Where voting is not compulsory,
there is no way to identify which people will actually
vote at a forthcoming election (in advance of the
election)
• As a remedy, we seek a sampling frame which has
the property that we can identify every single
element and include any in our sample .
• The sampling frame must be representative of the
population
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4.4. What is the purpose of sampling?
• To draw conclusions about populations
from samples, we must use inferential
statistics which enables us to determine a
population's characteristics by directly
observing only a portion (or sample) of the
population.
4.4. What is the purpose of sampling?
• There would be no need for statistical theory if a
census rather than a sample was always used to
obtain information about populations. But a
census may not be practical and is almost never
economical.
• There are six main reasons for sampling instead
of doing a census. These are; 1.
2.
3.
4.
5.
6.
Economy
Timeliness
The large size of many populations
Inaccessibility of some of the population
Destructiveness of the observation
Accuracy
4.5. TYPES OF SAMPLES
4.5.1. Probability (Random) Samples
1.
2.
3.
4.
5.
6.
Simple random sample
Systematic random sample
Stratified random sample
Multistage sample
Multiphase sample
Cluster sample
4.5.2. Non-Probability Samples
1. Convenience sample
2. Purposive sample
3. Quota
4.5. TYPES OF SAMPLES
4.5.1. Probability Sampling
What is probability sampling?
– A probability sampling method is any method of sampling
that utilizes some form of random selection.
– In order to have a random selection method, you must set
up some process or procedure that assures that the
different units in your population have equal probabilities of
being chosen.
– Humans have long practiced various forms of random
selection, such as picking a name out of a hat, or choosing
the short straw.
– These days, we tend to use computers as the mechanism
for generating random numbers as the basis for random
selection.
4.5.1. Probability Sampling
1.
A simple random sample
•
A simple random sample is obtained by choosing elementary units in such a way
that each unit in the population has an equal chance of being selected.
•
A simple random sample is free from sampling bias. However, using a random
number table to choose the elementary units can be cumbersome.
•
Applicable when population is small, homogeneous & readily available
•
All subsets of the frame are given an equal probability. Each element of the frame
thus has an equal probability of selection.
•
It provides for greatest number of possible samples. This is done by assigning a
number to each unit in the sampling frame.
•
A table of random number or lottery system is used to determine which units are to
be selected.
• Disadvantages
– If sampling frame large, this method impracticable.
– Minority subgroups of interest in population may not be present
in sample in sufficient numbers for study.
4.5.1. Probability Sampling
2. A systematic random sample
• A systematic random sample is obtained by selecting one unit on a
random basis and choosing additional elementary units at evenly
spaced intervals until the desired number of units is obtained.
•
For example, there are 100 students in your class. You want a sample
of 20 from these 100 and you have their names listed on a piece of
paper may be in an alphabetical order. If you choose to use systematic
random sampling, divide 100 by 20, you will get 5.
• Randomly select any number between 1 and five. Suppose the number
you have picked is 4, that will be your starting number. So student
number 4 has been selected. From there you will select every 5th
name until you reach the last one, number one hundred. You will end
up with 20 selected students.
SYSTEMATIC SAMPLING……
•
As described above, systematic sampling is an EPS method, because all
elements have the same probability of selection (in the example given, one in
ten). It is not 'simple random sampling' because different subsets of the
same size have different selection probabilities - e.g. the set
{4,14,24,...,994} has a one-in-ten probability of selection, but the set
{4,13,24,34,...} has zero probability of selection.
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SYSTEMATIC SAMPLING……
ADVANTAGES:
• Sample easy to select
• Suitable sampling frame can be identified easily
• Sample evenly spread over entire reference population
DISADVANTAGES:
• Sample may be biased if hidden periodicity in population coincides with
that of selection.
• Difficult to assess precision of estimate from one survey.
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4.5.1. Probability Sampling
3. A stratified sample
• Where population embraces a number of distinct categories, the frame
can be organized into separate "strata." Each stratum is then sampled
as an independent sub-population, out of which individual elements can
be randomly selected.
• Every unit in a stratum has same chance of being selected.
• Using same sampling fraction for all strata ensures proportionate
representation in the sample.
• Adequate representation of minority subgroups of interest can be
ensured by stratification & varying sampling fraction between strata as
required.
4.5.1. Probability Sampling
3. A stratified sample
• Finally, since each stratum is treated as an independent population,
different sampling approaches can be applied to different strata.
• Drawbacks to using stratified sampling.
•
First, sampling frame of entire population has to be prepared
separately for each stratum.
• Second, when examining multiple criteria, stratifying variables may be
related to some, but not to others, further complicating the design, and
potentially reducing the utility of the strata.
•
Finally, in some cases (such as designs with a large number of strata, or
those with a specified minimum sample size per group), stratified
sampling can potentially require a larger sample than would other
methods
STRATIFIED SAMPLING…….
Draw a sample from each stratum
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4.5.2. Nonprobability Sampling
• Any sampling method where some elements of population have no
chance of selection (these are sometimes referred to as 'out of
coverage'/'undercovered'), or where the probability of selection can't
be accurately determined. It involves the selection of elements based
on assumptions regarding the population of interest, which forms the
criteria for selection. Hence, because the selection of elements is
nonrandom, nonprobability sampling not allows the estimation of
sampling errors..
• Example: We visit every household in a given street, and interview the
first person to answer the door. In any household with more than one
occupant, this is a nonprobability sample, because some people are
more likely to answer the door (e.g. an unemployed person who spends
most of their time at home is more likely to answer than an employed
housemate who might be at work when the interviewer calls) and it's
not practical to calculate these probabilities.
4.5.2. Nonprobability Sampling
• Nonprobability Sampling includes:
1. Purposive Sampling
2. Quota Sampling and
3. Snowball Sampling
In addition, nonresponse effects may turn any probability
design into a nonprobability design if the characteristics
of nonresponse are not well understood, since nonresponse
effectively modifies each element's probability of being
sampled.
4.5.2. Nonprobability Sampling
• At least with a probabilistic sample, we
know the odds or probability that we have
represented the population well. We are
able to estimate confidence intervals for
the statistic.
• With nonprobability samples, we may or
may not represent the population well, and
it will often be hard for us to know how well
we've done so.
4.5.2. Nonprobability Sampling
1. Purposive Sampling
• In purposive sampling, we sample with a purpose in mind.
We usually would have one or more specific predefined
groups we are seeking.
• For instance, have you ever run into people in a mall or on
the street who are carrying a clipboard and who are
stopping various people and asking if they could interview
them?
• Most likely they are conducting a purposive sample (and
most likely they are engaged in market research).
4.5.2. Nonprobability Sampling
2. Quota Sampling
• In quota sampling, you select people non-randomly
according to some fixed quota.
• There are two types of quota sampling: proportional and
non proportional.
4.5.2. Nonprobability Sampling
2. Quota Sampling
• In proportional quota sampling you want to represent the
major characteristics of the population by sampling a
proportional amount of each. For instance, if you know the
population has 40% women and 60% men, and that you
want a total sample size of 100, you will continue sampling
until you get those percentages and then you will stop. So,
if you've already got the 40 women for your sample, but not
the sixty men, you will continue to sample men but even if
legitimate women respondents come along, you will not
sample them because you have already "met your quota."
The problem here (as in much purposive sampling) is that
you have to decide the specific characteristics on which you
will base the quota. Will it be by gender, age, education
race, religion, etc.?
4.5.2. Nonprobability Sampling
3. Snowball Sampling
• In snowball sampling, you begin by identifying someone who
meets the criteria for inclusion in your study. You then ask
them to recommend others who they may know who also
meet the criteria. Although this method would hardly lead to
representative samples, there are times when it may be the
best method available. Snowball sampling is especially
useful when you are trying to reach populations that are
inaccessible or hard to find. For instance, if you are studying
the homeless, you are not likely to be able to find good lists
of homeless people within a specific geographical area.
However, if you go to that area and identify one or two, you
may find that they know very well who the other homeless
people in their vicinity are and how you can find them.
Test Two
Exercises on Sampling Methods
1. Question One: The postgraduate unit of the Department of
communication at Namibia Science and Technology University admitted
the following students in the year 2014:
2. Alan
13. Karen
24. James
3. Rachel
14. Azar
25. Kathryn
4. Sacha
15. Hannah
26. Sushi
5. Salif
16. Joseph
27. Joshua
6. Lucy
17. Jayne
28. Helen
7. Ben
18. Grace
29. Mohammed
8. Halim
19. Anna
30. Lisa
9. Annie
20. Nadima
31. Fatoumata
10. Tom
21. Miles
11. Emma
22. Sophie
12. Daniella
23. Matthew
1.1. Select a systematic sample of size 5
1.2. Create a quota sample of size 10 from the class.
1.3. Select a systematic sample of size 10 from the class
2. Question Two: There are 400 trees in a plantation. All the trees have been
planted in rows. Create a systematic sample of 24 trees.
3. The houses in a street are numbered from 1 to 340. Create a systematic
sample of size 20.
4. A theatre group has 40 members of whom 15 are boys. A quota of size 8 is
to be interviewed. How many girls and how many boys should be included
in the sample?