2. DEFINITION
• Epidemiology is the branch of medical science that focuses on the study of
patterns, causes, and effects of health and disease conditions in specific
populations. Research methods include; qualitative research, observational
studies, experimental studies, ecological studies, sample size determination.
• Sample is a portion of study population to be considered for a particular study
• Sample size determination is the act or process of choosing the number of
observations or replicates to include in statistical sample.
3. REASONS FOR CARRYING OUT SAMPLE SIZE
DETERMINATION
• To allow for appropriate analysis
• To provide the desired level of accuracy
• To allow validity of significance test
4. SAMPLE SIZE DETERMINATION
• The required samples can be determined by:
Census (using the entire population)
Using a sample size of a similar study
Using published sample sizes from published tables
Manual (using formula)
5. USING CENSUS
Here the entire study population is included into the study
All participants/persons/patients in a given study group/community/hospital are
interviewed or given questionnaires
It is usually used when the study population is small (50-300)
The sample size is equal to the sample population
6. USING A SAMPLE SIZE OF FROM A SIMILAR EARLIER
STUDY.
A sample from the earlier identical study design, setting, content and population
can be adopted and used in a new study.
It is more advantageous especially when such sample size had errors or didn’t
cater for factors like non-response, or change in the study setting or study
population.
This method is rarely recomended
7. USING PUBLISHED TABLES OF PRE- ESTIMATED
SAMPLES.
These are pre-calculated sample sizes using standard formulas and are done for a
wide range of study population size.
The tables indicate the required sample size for the corresponding study
populations
The most commonly used table of samples is the Morgan & Krejcie table
established by Daryle Moegan and Robert Krejcie in 1970.
8.
9. USE OF SAMPLE SIZE FORMULAE
• Formulate a research question
• Select appropriate study design, statistical significance
• Use the appropriate formula to calculate the sample size.
10. EXAMPLES OF FORMULAE FOR ESTIMATING SAMPLE
SIZE
For large populations:
Yamane (1967)
Cochran(1975)
Rao(1985)
Modified kish and Leslie formula in 2009
For smaller populations:
Finite population corrections for small proportions(Cochran,1975)
11. EXAMPLES OF FORMULAE FOR ESTIMATING SAMPLE
SIZE
Yamane, n=
𝑁
1+𝑁(𝑒2)
• Where n=required sample size, N=population size, e=level of precision
Cochran,𝑛0=
𝑍2𝑃𝑄
𝑒2
• Where 𝑛0=required sample size, Z= z value on the normal distribution that’s cuts off an area ∝ at the tails, e=the desired level of precision then P= estimated proportion of an
attribute in the population then Q=1-P
Rao, n=4(
𝑃𝑄
𝐿2 )
• Where P=approximate prevalence rate, Q is 1-P, L is the permissible error in the estimate and n is the required sample size
For research on numerical variables/data, n=
𝑡2∝𝑠2
𝜀2
• Where t∝ is the t-value at 5% level of significancy, s is the SD, the ε= permissible in the estimate of mean and n is the required sample size
Modified kish and Leslie formula, n=
𝑍∝+𝑍𝛽
2
1−𝑃 𝑃
𝐷2
Where 𝑍∝ is the Z value at specified level of confidence, 𝑍𝛽 is the Z value at the specified power, P is estimated proportion of an attribute in the population, D is the degree of precision and n is
the desired sample size
Finite population correction for small proportions, n=
𝑛0
1+
𝑛0−1
𝑁
Where 𝑛0= sample size obtained from CLP formula, N=study population and n is the sample size required for a population
12. SAMPLE SIZE IN QUANTITATIVE STUDIES
• The larger the sample, the more representative, and the smaller the sampling
error.
• Descriptive studies and correlational studies require large samples.
• Quasi-experimental studies use smaller samples than descriptive and co-
relational studies.
13. GENERAL INSTRUCTIONS
• - First, the need for considering sample size will be
• reviewed.
• - Second, the study design parameters
• size will be identified.
• - Third, formulae for calculating appropriate sample
• sizes for some common study designs will be defined.
• - Sample size should be estimated early in the design
• phase of the study.
14. STEPS TO USE SAMPLE SIZE FORMULAE
• 1. 1st Formulate a research question
• 2. 2nd Select appropriate study design, statistical
• significance.
• 3. 3rd use the appropriate formula to calculate the sample
• size
15. SAMPLE SIZE IN QUANTITATIVE STUDIES (NON-
EXPERIMENTAL/
DESCRIPTIVE STUDIES)
• Level of confidence
• Probability of value of parameters will fall within
• specified range, closely connected with the level of
• significance for statistical tests.
• For example, we can be ‘95% confident’ that the true
• mean value lies somewhere within a valid 95%
• confidence level, corresponds to significance testing at
• the 5% level (P < 0.05) of significance.
• Likewise, we can be ‘99% confident’ that the true mean
• value lies somewhere within a valid 99% confidence
• level, corresponds to significance testing at the 1% level
• (P < 0.01) of significance
16. PRECISION
• A measure of how close an estimate is to the true value of a population parameter.
• Degree of Precision
• - This is presented in the form of a confidence interval
• (Range of values within which confidence lies). For
• example, a survey of a sample of patients indicates that
• 35 per cent smoke.
• - We can accept that the figure for the wider population
• lies between 25 and 45 per cent, (allowing a margin for
• random error (MRE) of 10% either way) of precision is presented in the form of a confidence
interval.
17. MORE FORMULAE: MEAN E.G. HOW LARGE MUST A
SAMPLE BE TO ESTIMATE THE MEAN
VALUE OF THE POPULATION?
• - Suppose we wish to measure the number of times that the average patient with
asthma consults her/his general practitioner for treatment?
• The formula to calculate the sample size for a mean estimate is:
• N =(SD/SE) 2
• Where N = the required sample size,
• SD = the standard deviation, and
• SE = the standard error of the mean
• The standard deviation could be estimated either by looking at
• some previous study or by carrying out a pilot study.
18. - Suppose that previous data showed that the standard
deviation of the number of visits made in a year was 20.
First, the SE (standard error) is calculated by deciding
upon the accuracy level which you require.
If you want a 95% confidence level, then divide the
maximum acceptable MRE (margin for random error) by
1.96 to calculate the SE.
If instead you want a 99% confidence level, then divide
the maximum acceptable MRE by 2.56 to calculate the
SE.
b) the standard error is 5 divided by 1.96 = 2.55
The formula as follows:
N=(SD/SE) 2
(20/2.55)2 = (7.84)2
=61.4 =61
19. PERCENTAGE: EXAMPLE; HOW LARGE MUST A SAMPLE BE
TO ESTIMATE A
PROPORTION / PERCENTAGE?
- You want to conduct a survey of the proportion of men
over 65 who have cardiac symptoms
• - Your significance level is 95%
• - Your acceptable margin for random error is plus or
• minus 2 per cent
• - From previous studies work you estimate that the
• proportion is about 20 per cent
20. CONTINUATION
• a) Calculate the SE = ...MRE/1.96...............
• b) Using the formula for the sample sizes for a proportion,
• calculate:
• N=P(100%-P)/(SE)2
• First, the SE can be calculated by dividing the confidence
• interval by 1.96
• SE=2/1.96=1.02
• We then calculate:
• N=P(100%-P)/(SE)2
• With P = 20% and SE = 1.02,
• We have N=20(100-20)/(1.02)2
