2. Objectives
At the completion of this unit learners will be able to
• Define the term population sample and sampling.
• Calculate sample size according to particular type of research,
and purpose.
• Identify and select various software to calculate sample size
according to particular type of research, and purpose.
3. POPULATION & SAMPLE
• A Research Population is a
well-defined collection/set of
individuals or objects that
possess some common
observable characteristics or
attributes
• Sample is defined as a
representative subset of the
population selected to obtain
information on the
population.
4. Population
• All the inhabitants of a given country or area
considered together; the number of
inhabitants of a given country or area
• The population is all elements (individuals,
objective, or substance) that meet certain
criteria for inclusions in a study (Kerlinger,
1986).
5. Population
– Target Population
• The group from which the study population is selected
– Study Population
• The group selected for investigation
– Elements of a population
• The subject on which the measurement is collected
6. Sampling
• Sample
– A sample is a subset of the population that is
selected for a particular study, and the members of
a sample are the subjects.
• Randomization
– When study subjects are randomly allocated in
study groups from population
• Each person is getting equal chance to be selected in
either group
7. Sampling
• The process of selecting a number from all the
subjects
• It is a process of selecting subjects who are
representative of the population being studied
8. Sampling
• Sampling frame
List of Participants
• Sampling Error
The part of the total estimation error of a parameter
caused by the random nature of the sample
• Sampling Bias
Systematic error study of a non-random sample of a
study
12. Sampling Type
• Probability
• Simple Random sampling
• Stratified Random Sampling
• Cluster sampling
• Systematic Sampling
• Non Probability
• Convenience sampling
• Quota Sampling
• Purposive sampling
• Network Sampling
13. Probability Sampling
• Is a 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.
14. Simple Random Sampling
• Objective
– To select n units out of N such that each NCn
has an equal chance of being selected.
• Procedure
– Use a table of random numbers, a computer
random number generator, or a mechanical
device to select the sample.
16. Simple Random Sample
The simplest type of sample survey
design, namely, simple random
sampling. This design does not attempt
to reduce the effect of data variation on
the error of estimation. A simple
random sample of size n occurs if each
Random number tables are quite useful
in determining the elements that are to
be included in a simple random sample
18. Stratified Random Sample
A stratified random sample is one obtained
by separating the population elements
into non-overlapping groups, called
strata, and then selecting a simple
random sample from each stratum.
20. Stratified Random Sample
• Objective
– Divide the population into non-overlapping groups
(i.e., strata) N1, N2, N3, ... Ni, such that N1 + N2 + N3
+ ... + Ni = N. Then do a simple random sample of f
= n/N in each strata.
22. Systematic Random Sampling
Number the units in the population from 1 to
N decide on the n (sample size) that you
want or need k = N/n = the interval size
randomly select an integer between 1 to k
then take every kth unit
23. Systematic Random Sampling
All of this will be much clearer with an example.
Let's assume that we have a population that
only has N=100 people in it and that you want
to take a sample of n=20. To use systematic
sampling, the population must be listed in a
random order. The sampling fraction would
be f = 20/100 = 20%. in this case, the interval
size, k, is equal to N/n = 100/20 = 5.
24. Systematic Random Sampling
Now, select a random integer from 1 to 5. In our
example, imagine that you chose 4. Now, to
select the sample, start with the 4th unit in the
list and take every k-th unit (every 5th, because
k=5). You would be sampling units 4, 9, 14, 19,
and so on to 100 and you would wind up with 20
units in your sample.
26. Cluster Sampling
• In, we follow these steps:
– Divide population into clusters (usually along
geographic boundaries)
– Randomly sample clusters
– Measure all units within sampled clusters
27. Cluster Sampling
• is a probability sample in which each
sample unit is a collection, or cluster, of
elements.
• The first task in cluster sampling is to
specify appropriate clusters.
– Elements within a cluster are often
physically close together and hence tent to
have similar characteristics.
33. A Two-stage cluster sample
• A two-stage cluster sample is obtained by
first selecting a probability sample of
clusters and then selecting a probability
sample of elements from each sampled
cluster.
34. Multi-Stage Sampling
• The four methods we've covered so far -- simple,
stratified, systematic and cluster -- are the simplest
random sampling strategies.
– The most important principle here is that we can
combine the simple methods described earlier in a
variety of useful ways that help us address our sampling
needs in the most efficient and effective manner
possible. When we combine sampling methods, we call
this multi-stage sampling.
35. Non Probability sampling
• Convenience sampling
• Quota Sampling
• Purposive sampling
• Network Sampling
36. Convenience sampling
• is used in exploratory research where the
researcher is interested in getting an inexpensive
approximation of the truth. As the name implies,
the sample is selected because they are
convenient. This non-probability method is often
used during preliminary research efforts to get a
gross estimate of the results, without incurring
the cost or time required to select a random
sample.
37. Quota Sampling
• It uses a convenience sampling technique with
added feature - a strategy to ensure the
inclusion of subjects types who are likely to be
underrepresented in the convenience sample
e.g. ethnicity , Hindu religion in Pakistan
38. Quota sampling
• is the non-probability equivalent of stratified
sampling. Like stratified sampling, the
researcher first identifies the stratums and their
proportions as they are represented in the
population. Then convenience or judgment
sampling is used to select the required number
of subjects from each stratum. This differs from
stratified sampling, where the stratums are filled
by random sampling.
40. Purposive /Judgment Sampling
• is a common non-probability method. The
researcher selects the sample based on judgment.
This is usually and extension of convenience
sampling. For example, a researcher may decide to
draw the entire sample from one "representative"
city, even though the population includes all cities.
When using this method, the researcher must be
confident that the chosen sample is truly
representative of the entire population.
41. Network / Snowball Sampling
• is a special non-probability method used when the
desired sample characteristic is rare. It may be
extremely difficult or cost prohibitive to locate
respondents in these situations. Snowball sampling
relies on referrals from initial subjects to generate
additional subjects. While this technique can
dramatically lower search costs, it comes at the
expense of introducing bias because the technique
itself reduces the likelihood that the sample will
represent a good cross section from the population.
43. IMPORTANCE OF SAMPLE SIZE
• If researchers want to draw conclusions that are valid for
the whole study population, they should take care to draw
a sample in such a way that it is representative of that
population.
• We don’t know about the population so how do we know
that our sample is representative of the population.
44. IMPORTANCE OF SAMPLE SIZE
• We don’t have any fool proof method but to be reasonably
sure that our samples are representatives of the population
they are drawn from, we must ensure that:
i. they are drawn randomly
ii. they are of adequate size
45. SAMPLE SIZE CALCULATION
• Student researchers often ask “How big should my sample
be?”.
• The first answer is “use as large a sample as possible”.
• The reason is obvious: the larger the sample, the better it
represents the population.
• But if the sample size is too large, then the value of
sampling — reducing time and cost of the study — is
negligible.
46. SAMPLE SIZE CALCULATION
• The more common problem, however, is having too few
subjects, not too many.
• So the more important question is, “What’s the minimum
number of subjects I need?”
• The question is still difficult to answer.
47. SAMPLE SIZE CALCULATION
• Here are some of the factors which relate to proper sample
size;
1. Accuracy
2. Cost
3. Homogeneity of the population
48. ACCURACY
• In every measurement, there are two components:
• the true measure of the variable and
• error
• In all statistical analysis, the objective is to minimize error and
maximize the true measure.
• As the sample size increases, the random extraneous errors tend to
cancel each other out, leaving a better picture of the true measure of
the population.
49. COST
• An increasing sample size translates directly into increasing costs:
not only of money, but time as well.
• Just think of the difference in printing, mailing, receiving, processing,
tabulating, and analyzing questionnaires for 100 subjects, and then
for 1000 subjects.
• The dilemma of realistically balancing “accuracy” (increase sample
size) with “cost” (decrease sample size) confronts every researcher.
• Inaccurate data is useless, but a study which cannot be completed
due to lack of funds is not any better.
50. HOMOGENEITY OF THE POPULATION
• “Homogeneous” means “of the same kind or nature;
consisting of similar parts, or of elements of the like nature”.
• Homogeneity in a population means that the members of the
population are similar on the characteristic under study.
• We can take a sample of two drops of water from a 10 gallon
drum, and have a good representative sample of the ten
gallons.
51. HOMOGENEITY OF THE POPULATION
• This is because the water in a 10 gallon drum is an
homogeneous solution (if we mix it up well before
sampling).
• But if we take two people out of a group of 500, we will
not have a good representative sample of the 500.
• “People” are much less homogeneous than a water
solution!
52. SAMPLE SIZE CALCULATION
• The eventual sample size is usually a compromise between
what is DESIRABLE and what is FEASIBLE.
• The feasible sample size is determined by the availability
of resources:
i. time,
ii. manpower,
iii. transport, and
iv. money.
54. SAMPLE SIZE: RULE OF THUMB
• Dr. John Curry, Professor
of Educational Research,
North Texas State
University, provided his
research students (fall,
1984) with the "rule of
thumb" on sample size
(see right).
55. SAMPLE SIZE: RULE OF THUMB
• L. R. Gay suggests 10% of large populations and 20% of
small populations as minimums.
• It is left to the student to weigh the factors of accuracy,
cost, homogeneity of the accessible population, type of
sampling and kind of study, and determine the best sample
size for his study.
56. APPROACHES FOR SAMPLE SIZE
• The main determinant of the sample size is, how accurate the
results need to be.
• This depends on the purpose of the study;
i. Descriptive study to determine a summary measure of a
characteristic, or
ii. Analytical study where specific sets of hypotheses are being
tested.
57. References
• Burns, N. & Grove, S.K (2007). Research problems, purposes,
and hypotheses in Understanding Nursing Research, building
an Evidence-Based Practice (4th ed). St. Louis: Saunders.
• Polit, D. F. & Hungler, B. P. (1997). Essentials of nursing
research (4th ed.). Philadelphia: Lippincott.
