Chapter 9 sampling and statistical tool

Chapter 9 58
Sampling

THE SAMPLING

 Define what a sampling is.
 Identify a good and defective sampling.
 Explain how to determine a sample size
 Discuss and identify the different types of sampling techniques

9.1 Sampling Defined

The following are the terms that a researcher should comprehend.

o Sampling is a process of choosing a representative portion of a population to represent
the entire population.

o Sample. It is a proportion, an element or a part of the population which is scientifically and
randomly drawn that actually possesses the same characteristics as the population. This
implies that every person has an equal opportunity to be selected for your sample

o An element is considered as a member of a population. It is a unit in which data is
collected and analyzed

o Population pertains to total number of elements to be studied. It includes all members of
a defined group that we are studying or collecting information on the data driven
decisions.

o Parameter is the summary description of a given variable in a population. The mean
income, the mean age of all the families are parameters. The age distribution of all people
is a parameter.

o Sample size is the number of subjects in your study.

o Margin of Error is the allowable error in percent due to the use of the sample, instead of
the population

o Sampling Error is the error attributed to chance difference between a random sample
and the chosen population. It does not result from measurement or computation errors but
contributory to inaccuracy of data.

Sample vs Population

As follows are some reasons why researchers use a sample rather than the entire population in
the conduct of their study.

1. Sometimes population is difficult to identify who makes up the entire population.

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2. Sample is cheaper, faster, more accurate and can yield to more comprehensive
information.
3. Getting the population is too costly in terms of human resources and other expenses, and
time consuming.
4. In population, there is a lot of error to control and monitor.
5. Sometimes lists are rarely up to date.

9.2 Good and Defective Sampling

Keys to Good Sampling
 formulate the aims of the study
 decide what analysis is required to satisfy this aims
 decide what data are required to facilitate the analysis
 collect the data required by the study

Defective Sampling

1. Sampling that is too small or not a representative will be biased, invalid and unreliable.
2. The sampling becomes very complicate if the population is too large or has many sections
and subsection.
3. The sample (respondents) should have common characteristics in order to eradicate
faulty conclusions.
4. The sampling becomes biased and unrepresentative if the researcher does not possess
the necessary skills and technical know-how of the sampling procedure.

9.3. The Sample Size

One of the most frequent problems in statistical analysis is the determination of the
appropriate sample size. One may ask why sample size is so important. The answer to this is that
an appropriate sample size is required for validity. If the sample sizes are too small, it will not yield
valid results. An appropriate sample size can produce accuracy of results. Moreover, the results
from the small sample size will be questionable. A sample size that is too large will result in
wasting money and time. It is also unethical to choose too large a sample size. There is no certain
rule of thumb to determine the sample size. Some researchers do, however, support a rule of
thumb when using the sample size. For example, in regression analysis, many researchers say
that there should be at least 10 observations per variable. If we are using three independent
variables, then a clear rule would be to have a minimum sample size of 30. Some researchers
follow a statistical formula to calculate the sample size.

Size of sample depends on some factors:
1. Degree of accuracy required
2. Amount of variability inherent in the population from which the sample was taken
3. Nature and complexity of the characteristics of the population under consideration

Determine sample size

Slovin Formula: Where:
n = sample size
N = population size
e = desired margin of error

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Example1: What should be the representative sample size if the population from which
the sample will be taken is 10,000 and the desired margin of error is 2%?

Solution: To determine the sample size, use the formula;

The sample size is 2,000
This formula in finding the sample size cannot be used when the normal approximation of the
population is poor or small.

Example 2: The population of Barangay Dodong is 10,600. What would be your
representative sample size of Brgy. Sebuas if the population is 10,600 and the desired margin
of error is 5%?

9.4 Types of Sampling Techniques

1. Non-probability Sampling (Non-scientific). This type of sampling does not provide every
member of the population an equal chance of being selected as part of the sample.
Additionally, the data gatherers choose sample cases as they WISH. These have 3 kinds:

a. Purposive sampling is used when the researcher selected samples which are
according to the purposes of the researcher.
b. Quota sampling is used if a stratum is small in the population but important to the
research questions being presented. This is done by merely looking for individuals with
requisite characteristics.
c. Convenience sampling, exactly what the name suggests, are oftentimes what we have
to use because of reality. We cannot draw a sample, but we have a group that is
accessible, is representative of our target population and just available to us. Instead of
becoming purists and throwing out the chance for collecting data for decisions, use what
you have with the honest acknowledgement that there are limitations.

2. Probability Sampling (Scientific sampling). In this type of sampling, the researcher follows a
procedure that assures that all elements in the population are given equal chance of being
selected as a sample unit. There are 6 types:

a. Simple random sampling may be done by drawing of lots or with the use of a table of
random digits. This gives all elements as equal chance of being selected as a sample.

Steps in Simple Random Sampling
1. Determine the population of the study
2. Determine the desired sample size ( You can use Pagoso formula, Gay’s formula or
other formulae in determining sample size)
3. List down the respondents (population) of the study in a sheet of paper.
4. Write in a small sheets of paper, names of the respondents or codes, roll these pieces
of papers and place them in a box big enough to accommodate them. Shake
thoroughly the box

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5. Draw the sample one at a time after shaking the box until the desired sample size is
drawn. The names are drawn include in the sample.

b. Systematic sampling is an often-used sampling strategy and cost effective. Again, you
must have a population sampling frame list that is in random order and non-overlapping.
Determine both the size of the population and the size of the sample you want to work
with. Then, divide the sample size (n) into the population (N) size to get your key number,
symbolized as “k”(sampling interval) a method of selecting a sample by taking the kth
(sampling interval) units from an ordered (alphabetical /chronological) population. The
formula applied is : K=N/n (where: K is desired interval, N population and n is the sample
size)

1. Identify the population of the study
2. Determine the desired sample size, then, apply the formula above. For example. Is
you have a population of 800 and your desired sample size is 10%, then you will have
a sample of 80. Applying the formula above 800/80=10), the sampling interval is 10
3. Hence, every 10th in the list (or arrangement of households as the case may be) is
taken as a member of the sample
4. Close your eyes and run your finger down the list and then stop. The number, which
the finger points to at, is the random start number.
5. From the random start number, pick every 10 th in the list (or arrangement of the
households) until the desired sample size of 80 is obtained.

c. Stratified random sampling is used when the population is heterogeneous and it is
important to represent the different strata or sub-populations. There is a proportional
representation of strata in the sample - proportional to the population strata. We divide the
entire population into strata (groups) to obtain groups of people that are more or less
equal in some respect.

1. Determine the stratum or class to which all elements in the population belong.
2. Group the elements of the population according to the characteristics inherent in the
whole class or stratum
3. Apply either the pure random sampling method or systematic sampling in the actual
selection of the sample. Do this for every class or stratum.
Note: The same sample size should be proportional or the same percent is applied for
each class or stratum.

For example:

Types of Farmers Population Fraction Sample size
Rice farmers 30 30/75 x 30 12
Sugar farmers 20 20/75 x 30 8
Vegetable farmers 10 10/75 x 30 4
Cutflower producers 15 15/75 x 30 6
TOTAL 75 30

d. Cluster Sampling – selecting a clusters of elements or blocks where each consists of
heterogeneous elements (Calderon et al, 1993).

Steps in Cluster Sampling
1. Make a listing of sampling unit, the primary sampling units ( the first clusters
to be sampled), the secondary sampling unit within the primary sampling, etc.

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Suppose the provinces are the primary sampling units, the towns are the
secondary sampling units and the barangay are the final sampling units.
These are called natural clusters
2. Since the sample is 20%, 20% of 9 provinces equals to 1.8 or 2 provinces.
Select these two ( 20 provinces either by pure or systematic random
sampling)
3. Within each of these two provinces, select 20% of the towns either by pure
random or systematic random sampling method.
4. Within each town selected, choose 20% of the barangays. Since there are
only one elementary school in one barrio or barangay, this is the final
sampling unit. The respondents may be stratified into teachers, parents and
pupils. The respondents have to be taken from these stratified groups either
pure random or systematic random sampling.
Example:

Desired sample : 50
Population : 100 with 10 clusters

Step1 . Number 10 clusters 1-10
Step2. Use simple random sampling
. Step3. Identify the groups represented by the numbers drawn

e. Multi-stage Sampling – selection of sample is accomplished in two or more stages.
Example:
Desired sample : 50
Population : all men with 0-6 yrs old children in province

Stage1 . Draw sample towns in the province. List all the names in the province and use
random sampling to draw the three sample towns.
Stage2. Draw sample barangays in the sample towns. Secure a list of all barangays in
each of the sample towns and using simple random sampling, draw 3 sample
barangays in each of the three sample towns.
Stage3. Draw a sample of married men in the sample barangays.List their names per
sample barangays from the 3sample towns then use random sampling to select
the men with 0-6 yrs old children.
Guidelines with regards to the minimum number of items needed for a representative
sample (Gay,1976):

 Descriptive studies – a minimum number of 100, 10 percent of the population. for
smaller population, a minimum of 20% may be required
 Co-relational studies – a sample of at least 50 is deemed necessary to establish the
existence of a relationship
 Ex post facto research of causal comparative studies-15 subjects or groups can be
defended if they are very tightly controlled
 Experimental studies – minimum of 30 per group or 15 subjects per group Sometimes
experimental studies with only 15 items in each group can be defended if they are very
tightly controlled
 If the sample is randomly selected and is sufficiently large, an accurate view of the
population can be had, provided that no bias enters the selection process

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Sampling

THE RESEARCH SAMPLING

NAME: __________________________________________ SCORE: ___________________

YEAR & SECTION: _________________________________ DATE: _____________________

Instructions: Restate your research problem, research objectives and identify
your population. Determine the most appropriate sampling technique that you will
use then solve for your sample size.

Research Title:
_____________________________________________________
_____________________________________________________

The Sampling Technique that I will use is: ____________________________
because__________________________________________________________
_________________________________________________________________
_________________________________________________________________
_______________

To compute for the sample size, I will use
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________

Chapter 9 sampling and statistical tool

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Chapter 9 sampling and statistical tool