This document discusses factors to consider when determining the appropriate sample size for a research study, including population size, margin of error, confidence level, and standard deviation. It provides formulas for calculating sample size for both known and unknown populations. The key aspects are that sample size must be large enough to represent the population and yield valid results, but not so large as to greatly increase time and costs. Formulas shown allow researchers to calculate the minimum required sample size based on the desired confidence level and margin of error.

1. Determining Sample Size for a
Research Study

2.  number of individuals included in a research study to represent a
population
 Determining the appropriate sample size is one of the most important
factors in statistical analysis
 If the sample size is too small, it will not yield valid results or
adequately represent the realities of the population being studied
 On the other hand, while larger sample sizes yield smaller margins
of error and are more representative, a sample size that is
too large may significantly increase the cost and time taken to
conduct the research.
Sample size

3.  The entire group that you want to
draw conclusions about or the total
number of people within your
demographic
 It is from the population that a
sample is selected, using probability
or non-probability sampling
techniques
POPULATION

4. MARGIN OF ERROR
For example, if your confidence interval is 5 and 60% percent of your sample picks
A as an answer, you can be confident that if you will ask the entire population,
between 55% (60-5) and 65% (60+5) would pick the same answer as A.
 Sometimes called “confidence interval” which indicates how
much error you wish to allow in your research results. How
far your sample mean differ from the population mean
 margin of error is a percentage that indicates how close your
sample results will be to the true value of the overall population
 It’s often expressed alongside statistics as a plus-minus (±) figure,
indicating a range
which you can be relatively certain about.

5. CONFIDENCE LEVEL
 measures the degree of certainty regarding how well a sample represents the
overall
population within the chosen margin of error
 expressed as percentage and represents how often the percentage of the
population who would pick an answer lies within the confidence interval
 The most common confidence levels are 90%, 95%, and 99%. Researchers
most often
employ a 95% confidence level
For example, if your confidence interval is 5 and 60% percent of your sample picks
A as an answer, you can be confident that if you will ask the entire population,
between 55% (60-5) and 65% (60+5) would pick the same answer as A.
Setting Confidence level of 95% mean that you are 95% certain that 55 – 65% of the
concerned population would select option A as answer

6. It indicates the "standard
normal score," or the number
of standard deviations
between any selected value
and the average/mean of the
population
confidence level
corresponds to something
called a "z-score."
Z-SCORE
Confidence level z-score
80% 1.28
85% 1.44
90% 1.65
95% 1.96
99% 2.58

7. Standard Deviation
measures how much individual sample data
points deviate/vary from the
average population
In calculating the sample size, the standard deviation is useful in
estimating how much the responses received will vary from each
other and from the mean and the standard deviation of a sample
can be used to approximate the standard deviation of a population
Since this value is difficultto determine you give the
actual survey, most
researchers set this value at 0.5 (50%)

8. 1.Define the population size (if known).
2.Designate the confidence interval (margin of error).
3.Determine the confidence level.
4.Determine the standard deviation (a standard deviation of
0.5 is a safe choice where the figure is unknown)
5.Convert the confidence level into a Z-Score
How to Calculate Sample Size
Andrew Fisher’s Formula

9. Sample size for known population
N - 500 with a 5% margin of
error and confidence level of 95%
n = 197 respondents

10. EXAMPLE
Determine the ideal sample size for a population of 425
people. Use a 99% confidence level, a 50% standard of
deviation, and a 5% margin of error
 For 99% confidence, you would have a z-score
of 2.58.
 This means
that:  N = 425
 z = 2.58
 e = 0.05
 p = 0.5

11. Using the standard formula
= [2.582 * 0.5(1-0.5)] / 0.052
/ 2 2
1 + [2.58 * 0.5(1-0.5)] / 0.05 * 425]
= [6.6564 * 0.25] / 0.0025 / 1 + [6.6564 * 0.25] / 1.0625
= 665 / 2.5663
= 259.39

12. Sample size for unknown population
If you have a very large
population or an unknown
one, you'll need to use a
secondary formula
Note: the equation is merely the
top
half of the full formula

13. EXAMPLE
 Determine the necessary sample size for an unknown population
with a 90% confidence level, 50% standard of deviation, a 3%
margin of error.
• For 90% confidence, use the z-score would be 1.65
• This means that:
z = 1.65
e = 0.03
p = 0.5

14. Using the secondary formula
= [1.652 * 0.5(1-0.5)] / 0.032
= [2.7225 * 0.25] / 0.0009
= 0.6806 / 0.0009
= 756.22 or 756

15. Using Slovin's Formula
Sample Size = N / (1 + N*e2)
N = population size
e = margin of error
Note that this is the least accurate formula and, as such, the least ideal.
You should only use this if circumstances prevent you from determining
an appropriate standard of deviation and/or confidence level

16. EXAMPLE
Calculate the necessary survey sample size
for a population of 240, allowing for a 4%
margin of error
 N = 240
 e = 0.04
Sample Size = N / (1 + N*e2)
= 240 / (1 + 240 * 0.042)
= 240 / (1 + 240 * 0.0016)
= 240 / (1 + 0.384}
= 240 / (1.384)
= 173.41 or 173

17. SAMPLE PROBLEM
School Population Sample
School 1 345
School 2 298
School 3 436
School 4 195
Total N=1274 n =
Determine the ideal sample size for a population of 1274 people. Use a
99% confidence level, a 50% standard of deviation, and
a 5% margin of error

18. = [2.582 * 0.5(1-0.5)] / 0.052
/ 2 2
1 + [2.58 * 0.5(1-0.5)] / 0.05 * 1274]
= [6.6564 * 0.25] / 0.0025 / 1 + [6.6564 * 0.25] / 3.185
= 665 / 1.5224
= 436.81 or 437
SAMPLE PROBLEM
N = 1274 people
Confidence level = 99%
SD = 50% (0.5)
Margin of error = 5%

19. SAMPLE PROBLEM
School Population Sample
School 1 345
School 2 298
School 3 436
School 4 195
Total N=1274 n = 437
Determine the ideal sample size for a population of 1274 people. Use a
99% confidence level, a 50% standard of deviation, and
a 5% margin of error

20. PROPORTIONALALLOCATION
Proportional allocation sets the sample size in
each stratum equal to be proportional to the
number of sampling units in that stratum
It ensure that respondents are equally
distributed among all groups where they are
coming

21. SAMPLE PROBLEM
School Population Sample
School 1 345 118
School 2 298 102
School 3 436 150
School 4 195 67
Total N=1274 n = 437
Determine the ideal sample size for a population of 1274 people. Use a
99% confidence level, a 50% standard of deviation, and
a 5% margin of error