This document discusses sample size determination and sampling procedures in research. It defines key terms like population, sample, and margin of error. It presents Slovin's formula for calculating sample size given the population size and margin of error. Examples are provided to demonstrate how to use the formula. The document also discusses probability sampling methods like simple random sampling, systematic random sampling, and stratified random sampling. It concludes by covering non-probability sampling techniques.

1. DESCRIBING SAMPLE
SIZE AND SAMPLING
PROCEDURES
LESSON 20

2. INTRODUCTION
Determining the correct sample size and how the samples
are selected are crucial in ensuring the accuracy and
precision of an estimate leading to valid research findings.
SAMPLING- is securing some of the elements of a
population.

3. SAMPLE SIZE DETERMINATION
A sample (n) is a selection of respondents for a research
study to represent the total population (N). Making a
decision about a sample size for a survey is important.
Too large sample may mean a waste of resources, both
human and financial.
Too small sample decreases the utilization of the results.

4. Reasons for the use of samples
1. A sample saves time compared to doing a complete census which
requires more time.
2. A sample saves money because it is less costly than conducting a
complete census.
3. A sample allows more particular attention to be given to a number of
elements than when doing a census.
4. There is a greater error in reporting results of a census caused by
inexperienced interviewers. There is less sampling error in survey.
5. Some research studies in the industry may only be performed on a
sample of items.

5. Slovin’s formula in Determining the
Sample Size
Population (N) consists of members of a group that a
researcher is interested in studying the members of a group
that usually have common characteristics.
Margin of error is the allowable error margin in research. A
confidence interval of 95% gives a margin of error of 5%; a
98% confidence interval gives a margin of error of 2%; a
confidence interval of 99% gives 1% margin of error.

6. SLOVIN’S FORMULA
𝑛 =
𝑁
1+𝑁𝑒2 where: n= sample size
◦ N= total population
◦ e = margin of error

7. Example 1:
A researcher wants to conduct a survey. If the
population of a big university is 35,000, find the sample
size if the margin of error is 5%.
Solution: 𝑛 =
𝑁
1+𝑁𝑒2=
35000
1+ 35000 (0.05)2
=395

8. Example 2:
Suppose you plan to conduct a study among 1500 Grade
11 students enrolled in the STEM track. How many
respondents are needed using a margin of error of 2%?
Solution: 𝑛 =
𝑁
1+𝑁𝑒2=
1500
1+ 1500 (0.02)2
=938

9. Exercises: Find the sample needed given the
following data.
No. N E n
1 560 5% ?
2 880 2% ?
3 3500 1% ?
4 5600 5% ?
5 85000 2% ?
6 95000 5% ?
7 98, 876 1% ?
8 100, 256 2% ?
9 250,000 5% ?
10 550, 245 2% ?

10. SAMPLING PROCEDURES
Sampling is a formal process of choosing the correct subgroup called
a sample from a population to participate in a research study. The
subgroup shall be the representative of the large group from where
they selected. To create a sample, you may follow any of the
following categories of sampling techniques: probability sampling
and non-probability sampling schemes.

11. PROBABILTY SAMPLING PROCEDURES
The most important characteristics of probability sampling
procedure is the random selection of the samples.
1. SIMPLE RANDOM SAMPLING –this is characterized by the idea
that the chance of selection is the same for every member of the
population.
2. SYSTEMATIC RANDOM SAMPLING –it follows specific steps and
procedures in doing random selection of samples.
Example: Choosing 500 samples from 5000 population can be done
through the age group, hair color, body weight.

12. 3. STRATIFIED RAMDOM SAMPLING
The population is first divided into two or more mutually
exclusive categories based on your variables of interest in
the research study. The population is organized into
homogenous subsets before drawing the samples.
The population is subdivided into subpopulation called
strata.

13. EXAMPLE in Computing the sample using
stratified sampling
If there are 1200 JHS students and your desired sample size is 300.
Step 1: Identify the population in each strata( year level)
Grade 7 =350
Grade 8 =300
Grade 9 =280;
Grade 10 = 250
Total =1200

14. EXAMPLE in Computing the sample using
stratified sampling
Step 2: Divide each number of students per level by the total
population of 1200 and then multiply by the desired sample size of
300.
Grade 7 =350/1200 x 300= 88
Grade 8 =300/1200 x 300= 75
Grade 9 =280/1200 x 300= 70
Grade 10 = 250 /1200 x 300= 67
Total =300

15. 4. CLUSTER SAMPLING
Cluster sampling is used when the target respondents in a research is
spread across a geographical location.
In this method, the population is divided into groups called clusters
which are heterogenous in nature and are mutually exclusive.
Cluster sampling technique may be classified as either single stage,
two-stage or multi-stage.

16. NON-PROBABILTY SAMPLING
PROCEDURES
There are situations when the researcher cannot employ random
selection.
Convenience Sampling
◦ This is a method of selecting that are available and are capable of
participating in a research study on a current issue.
Snowball Sampling
Snowball sampling is a techniques where the researcher identifies a
key informant about a research of interest and then ask that respondent
to refer or identify another respondent who can participate in the study.
The identification of the samples follows a multiplier effect, that is one
person is asked to the refer the researcher to another respondent and so
on.

17. NON-PROBABILTY SAMPLING
PROCEDURES
Purposive Sampling
◦ Employs a procedure in which samples are chosen for special
purposes.
Quota Sampling
Gathering a representative sample from a group based on
certain characteristics of the population chosen by the researcher.
Usually the population is divided into specific groups.

18. Seatwork # 1 Find the desired samples of the
following.
No. N E n
1 430 5% ?
2 678 2% ?
3 2355 1% ?
4 4567 5% ?
5 12345 2% ?
A.

19. If there are 1800 SHS students in Ateneo de
Maa University and your desired sample size
is 560. Find the number of samples per
strand.
B.
abm 320
humms 345
tvl 578
gas 467
stem 90
Total 1800