LESSON 3 Elem Stat and Prob

Elementary Statistics and Probability for College Students
LESSON 3: COLLECTION OF DATA
Learning Outcomes
At the end of this lesson, the students will be able to:

 Compute the sample size using the Slovin’s Formula;
 Determine the different probability sampling techniques; and
 Identify the different nonprobability sampling techniques as
counterparts to the probability sampling techniques.
The collection of data can be done directly, using questionnaires, interviews

or experiments, or indirectly, from written or electronic records and documents.
Data can be collected from a population or a sample. Most often using the
population is impractical, or impossible if it is too large. This is time consuming and
it requires too much effort and money and it is difficult to handle. In this case,
sampling method is used. The sample is the representative part of the population
which is used to describe the population from which it was drawn. The various
Sampling Techniques are as follows:
Slovin’s Formula
It is the most common formula in finding the sample size.
𝑁
𝑛=
1 + 𝑁𝑒 2
where n = sample size
N = Population size
e = is the margin of error
3.1 Probability Sampling Techniques
Probability sampling is a sampling technique where the samples are

gathered in a process that gives all the individuals in the population equal chances
of being selected.
The objective of a sample survey is to make an inference about the

population of interest based on information contained in s sample. The procedure
for selecting the sample is called the sample survey design.
MARLON S. FRIAS, Ph.D. | BUKIDNON STATE UNIVERSITY 1

a. If a sample of size n is drawn from a population of size N in such a way that every
possible sample of size n has the same chance of being selected, the sampling
procedure is called SIMPLE RANDOM SAMPLING. The sample thus obtained is
called a SIMPLE RANDOM SAMPLE.
For example, let’s say you have a population of 1,000 people and you wish
to choose a simple random sample of 50 people. First, each person is numbered
1 through 1,000. Then, you generate a list of 50 random numbers (typically with
a computer program) and those individuals assigned those numbers are the
ones you include in the sample.
b. Systematic Random Sampling. A sample obtained by randomly selecting one

element from the first k elements in the frame and every kth element thereafter
is called a ONE-IN-K SYSTEMATIC SAMPLE. This procedure is called
SYSTEMATIC RANDOM SAMPLING.
Note: A frame is a list of sampling units.
In a systematic sample, the elements of the population are put into a list and
then every kth element in the list is chosen (systematically) for inclusion in the
sample. Note that the first kth element is chosen randomly.
𝑁
𝑘=
𝑛
For example, if the population of study contained 2,000 students at a high

school and the researcher wanted a sample of 100 students, the students would
be put into list form and then every 20th student would be selected for inclusion
in the sample. To ensure against any possible human bias in this method, the
researcher should select the first individual at random. This is technically called
a systematic sample with a random start.
NOTE:
1. Systematic sampling is easier to perform and hence is less subject to interviewer

errors than simple random sampling.
2. Systematic sampling often provides greater information per unit cost than does
simple random sampling.
c. Stratified Random Sampling. A STRATIFIED RANDOM SAMPLE is one

obtained by separating the population elements into nonoverlapping groups,
called strata, and then selecting a simple random sample from each stratum, the
sampling procedure is called STRATIFIED RANDOM SAMPLING.

NOTE:
1. This type of sampling is used when the researcher wants to highlight specific
subgroups within the population. For example, to obtain a stratified sample of
university students, the researcher would first organize the population by
college class and then select appropriate numbers of freshmen, sophomores,
juniors, and seniors. This ensures that the researcher has adequate amounts of
subjects from each class in the final sample.
2. The data within each stratum are more homogeneous than in the population as a
whole.
3. The cost of conducting the actual sampling tends to be less for stratified random
sampling than for simple random sampling because of administrative
convenience.
Sample sizes for Proportional Allocation
If we divide a population of size N into K strata of sizes N1, N2,…,Nk, and select
samples of size n1, n2,…nk, respectively, from the k strata, the allocation is
proportional if
𝑁
𝑛𝑖 = ( 𝑁𝑖 ) ∙ 𝑛 for i = 1, 2, 3, …,k
where n is the total size of the stratified random sample.
Example:
At a small private college the students may be classified according to the

following scheme:
NUMBER OF
CLASSIFICATION
STUDENTS
Senior 150
Junior 163
Sophomore 195
Freshman 220
If we use proportional allocation to select a stratified random sample of size n = 40,

how large a sample must we take from each stratum?

d. Cluster Sampling. A CLUSTER SAMPLE is a simple random sample in which

each sampling unit is a collection, or cluster, of elements. The sampling
procedure is called CLUSTER SAMPLING.
NOTE:
1. Cluster sampling may be used when it is either impossible or impractical to

compile an exhaustive list of the elements that make up the target population.
Usually, however, the population elements are already grouped into
subpopulations and lists of those subpopulations already exist or can be created.
2. Cluster sampling is less costly than simple or stratified random sampling if the
cost of obtaining a frame which lists all population elements is very high or if the
cost of obtaining observations increases as the distance separating the elements
increases.
For example, let’s say the target population in a study was church
members in the Philippines. There is no list of all church members in the
country. The researcher could, however, create a list of churches in the
Philippines, choose a sample of churches, and then obtain lists of members from
those churches.
3.2 Non-probability Sampling Techniques
Non-probability sampling is a sampling technique where the samples are

gathered in a process that does not give all the individuals in the population equal
chances of being selected.
The following are types of non-random or judgment sampling:

1. Purposive (Judgment) Sampling. The researcher selects particular
elements from the population that are informative or representative about
the topic of interest.
2. Quota Sampling. The researcher is unable to take a probability sample but

is still able to select subjects on the basis of characteristics of the population.
3. Convenience Sampling. The most common but least desirable technique.

This is often used when it is virtually impossible to select a random sample.
In this method, a group is selected at will or researcher uses subjects who
happen to be accessible or who may represent certain types of
characteristics.

4. Network (Snowballing) Sampling. This uses social networks to identify

populations which are difficult to find. Examples are when one is interested
with drug users, alcoholics and ex-prisoners as their respondent.

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Elementary Statistics and Probability for College Students

LESSON 3: COLLECTION OF DATA

At the end of this lesson, the students will be able to:

The collection of data can be done directly, using questionnaires, interviews

3.1 Probability Sampling Techniques

Probability sampling is a sampling technique where the samples are

The objective of a sample survey is to make an inference about the

MARLON S. FRIAS, Ph.D. | BUKIDNON STATE UNIVERSITY 1

b. Systematic Random Sampling. A sample obtained by randomly selecting one

Note: A frame is a list of sampling units.

For example, if the population of study contained 2,000 students at a high

1. Systematic sampling is easier to perform and hence is less subject to interviewer

c. Stratified Random Sampling. A STRATIFIED RANDOM SAMPLE is one

MARLON S. FRIAS, Ph.D. | BUKIDNON STATE UNIVERSITY 2

Sample sizes for Proportional Allocation

where n is the total size of the stratified random sample.

At a small private college the students may be classified according to the

If we use proportional allocation to select a stratified random sample of size n = 40,

MARLON S. FRIAS, Ph.D. | BUKIDNON STATE UNIVERSITY 3

d. Cluster Sampling. A CLUSTER SAMPLE is a simple random sample in which

1. Cluster sampling may be used when it is either impossible or impractical to

3.2 Non-probability Sampling Techniques

Non-probability sampling is a sampling technique where the samples are

The following are types of non-random or judgment sampling:

2. Quota Sampling. The researcher is unable to take a probability sample but

3. Convenience Sampling. The most common but least desirable technique.

MARLON S. FRIAS, Ph.D. | BUKIDNON STATE UNIVERSITY 4

4. Network (Snowballing) Sampling. This uses social networks to identify

MARLON S. FRIAS, Ph.D. | BUKIDNON STATE UNIVERSITY 5

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