Lecture to Master of Business Management Students (MBM) at the Moshi Cooperative University, Moshi Tanzania. The Objective was that at the end of the lecture students should be able to determine sample size scientifically.

1. SAMPLING
Mangasini, A. Katundu PhD
Lecture to Master of Business Management (MBM)
Students
2017/18

2. SAMPLING PROCEDURES

3. SAMPLING PROCEDURES
• What is a Sample?
The sample of a study is simply the
participants in a study. Part of the
population to be studied.
• What is Sampling?
Sampling is the process whereby a
researcher chooses her sample.

4. Sampling Procedures Cont.
• Sampling Process
1. Identify the population of interest.
A population is the group of people that you want
to research on.
For example, Brooke wants to know how much
stress college students experience during finals.
Her population is every college student in the world
because that's who she's interested in. Of course,
there's no way that Brooke can feasibly study every
college student in the world, so she moves on to
the next step.

5. Sampling Procedures Cont.
• 2. Specify a sampling frame.
A sampling frame is the group of people from which
you will draw your sample.
For example, Brooke might decide that her sampling
frame is every student at the university where she
works.
Notice that a sampling frame is not as large as the
population, but it's still a pretty big group of people.
Brooke still won't be able to study every single
student at her university, but that's a good place
from which to draw her sample.

6. Sampling Procedures Cont.
• 3. Specify a sampling method.
There are basically two ways to choose a sample
from a sampling frame: randomly (probability) or
non-randomly (non-probability).
There are benefits to both. Basically, if your
sampling frame is approximately the same
demographic makeup as your population, you
probably want to randomly select your sample,
perhaps by flipping a coin or drawing names out of
a hat.

7. Sampling Procedures Cont.
• 4. Determine the sample size.
• In general, larger samples are better, but they
also require more time and effort to manage.
• If Brooke ends up having to go through 1,000
surveys, it will take her more time than if she
only has to go through 10 surveys.
• But the results of her study will be stronger with
1,000 surveys, so she (like all researchers) has to
make choices and find a balance between what
will give her good data and what is practical.

8. Sampling Procedures Cont.
• 5. Implement the plan.
• Once you know your population, sampling
frame, sampling method, and sample size, you
can use all that information to choose your
sample.

9. Sampling Procedures Cont.
• NOTE: 1. To be able to estimate the
sample size one needs to have the
population to be studies and set:
The degree of confidence. Normally set
at 95%
The margin of error. Normally set at 5%
Skewness Level. Normally set at 50%

10. Sampling Procedures Cont.
• The degree of confidence/confidence interval (CI)/
confidence level : refers to the percentage of all
possible samples that can be expected to include the
true population parameter.
• For example, suppose all possible samples were
selected from the same population, and a
confidence interval were computed for each sample.
• A 95% confidence level implies that 95% of the
confidence intervals would include the true
population parameter.

11. Sampling Procedures Cont.
• The margin of error: a small amount that is allowed
for in case of miscalculation or change of
circumstances.
For example, a researcher might report that 50% of
voters will choose the UKAWA candidate in 2015
elections.
To indicate the quality of the survey result, he might
add that the margin of error is +5%, with a
confidence level of 90%.
This means that if the survey were repeated many
times with different samples, the true percentage of
UKAWA voters would fall within the margin of error
90% of the time.

12. Sampling Procedures Cont.
• Skewness Level: Is the response distribution
• A symmetrical distribution/normal distribution has a
skewness of zero.
• If the distribution is symmetric then the mean is equal
to the median and the distribution will have zero
skewness.If, in addition, the distribution is unimodal,
then the mean = median = mode
• A distribution with a long tail to the right (higher values)
has a positive skew.
• A distribution with a long tail to the left (lower values)
has a negative skew.

13. Skewness Level

14. Sampling Procedures Cont.
• Note 2: All the sample size formula and
software will try to estimate these three
parameters.
• Note 3: Manipulation of any of these
parameters will result to change in the sample
size.
• Example: Visit the
http://www.raosoft.com/samplesize.html
web page and try manipulating the
parameters.

15. Sampling Procedures Cont.
• Sample size Determination
• There are 3 basic techniques for
determining a sample size. These are:
Non-mathematical/non-
scientific/convenient method
Using Statistical Formulae/Scientific
Statistical Tables/Scientific

16. Sampling Procedures Cont.
• Statistical Formulae to determine Sample
Size
• 1. Formula by Cochran (1963) for large
populations (Exceeding or equal to 10,000)
2
2
e
PqZ
n =

17. Sampling Procedures Cont.
• 2. Formula by Fisher et al. (1991) for large
populations (Exceeding or equal to 10,000)
2
2
d
PqZ
n =

18. Sampling Procedures Cont.
• NOTE: The two formula are similar.
• Where:
• n = is the sample size required;
• Z = Standard normal deviation, set at 1.96 (or 2)
corresponding to 95% confidence level;
• P = Is % of population estimated to have a
particular characteristics if not known use 50%;
• q = 1-P;
• d/e = degree of accuracy desired, set at 0.05 or
0.02

19. Sampling Procedures Cont.
• EXAMPLE 1: Suppose we wish to evaluate a
district-wide extension program in which
farmers were encouraged to adopt a new
practice. Assume there is a large population
but that we do not know the variability in the
proportion that will adopt the practice;
therefore, assume p= 0.5 (maximum
variability). Furthermore, suppose we desire a
95% confidence level and ±5% precision. Using
Fisher et al. (1991) formula what is the desired
Sample Size?

20. Solution of Example 1
2
2
d
PqZ
n = 2
2
)05.0(
)5.0)(5.0()96.1(
=n
)0025.0(
)25.0)(8416.3(
=n
)0025.0(
)9604.0(
=n
16.384=n or 385=n
=
=

21. Sampling Procedures Cont.
• 3. Cochran (1963)/ Fisher et al. (1991) sample
size determination formulae for populations
less than 10,000, is given below (where: n=
sample size, N = population):
N
n
n
n
)1(
1
−
+
=

22. Sampling Procedures Cont.
• Example 2: Suppose our evaluation of farmers’
adoption of the new practice only affected
2,000 farmers. The sample size that would now
be necessary is:
2000
)1385(
1
385
−
+
=n =
2000
)384(
1
385
+
=n
192.01
385
+
=n=
9865772.322=n 323=

23. Sampling Procedures Cont.
• Sampling Techniques
• There are two main sampling strategies:
i.e.
• a) Probability- all items/participants have
equal chance of being selected.
• b) Non-probability-items/participants
have unequal chance of being selected.

24. Sampling Procedures Cont.
• Probability Sampling Techniques
• The techniques include:
Simple random sampling (SRS),
Stratifies Sampling,
Area/Cluster Sampling,
Systematic Sampling.

25. Sampling Procedures Cont.
• Non-Probability Sampling techniques
include:
• Convenient or purposive sampling,
• Quota sampling and
• Snowball Sampling.

26. Thank you.