2. • The population is very large, making a
census or a complete enumeration of all
the values in the population is either
impractical or impossible.
• Elements of a sample:
• Sample points
• Sampling units
• observations
• The data sample may be drawn from:
• Subset of a population
• Multi-subset
What is sample and Why are samples are
used in statistics?
6. What size sample do I need?
The answer to this question is influenced by a
number of factors, including:
1. Whether undertaking a qualitative or
quantitative study.
2. Purpose of the study
3. Population size
4. Risk of selecting a “bad” sample
5. Allowable sampling error.
7. Sample size determination in
Qualitative Study
• Probability sampling not appropriate
• Sample should have represent salient
characteristics of the population.
• Until point of theoretical saturation
• Sample size is usually small
• A matter of judgement and expertise in
evaluating the quality of information
• A flexible, pragmatic approach.
8. Sample size determination in
Qualitative Study
• Researcher actively selects the most
productive sample
• Developing a framework of the variables
that might influence an individual's
contribution
• If the subjects are known to the researcher,
they may be stratified according to known
public attitudes or beliefs
9. Sample size determination in
Qualitative Study
• It may be advantageous to study a broad
range of subjects :
• maximum variation sample
• outliers (deviant sample)
• subjects who have specific experiences
(critical case sample)
• subjects with special expertise (key
informant sample).
10. Sample size determination in
Qualitative Study
• The iterative process of qualitative study
design
• Theoretical sampling necessitates building
interpretative theories
• grounded theoretical approach
11. Some suggestions of sample
size in qualitative studies
• The smallest number of participants could be 15
• Number of participants Should lie under 50
• 6-8 participants for FGDs AND at least 2 FGDs per
population group
• Attainment of saturation
• Justification of choice of number
12. Sample size determination in
quantitative study
Level of
precision
Range in which the true
value of the population is
estimated to be
This range is often
expressed in percentage
points (e.g., ±5 percent).
Level of
confidence or
risk
based on ideas
encompassed under the
Central Limit Theorem
E.g. a 95% confidence
level is selected
Degree of variability in
the attributes being
measured ( prevalence)
refers to the distribution
of attributes in the
population
The more heterogeneous
a population, the larger
the sample size required
The more homogeneous a
population, the smaller
the sample size.
13. Sample size determination in
quantitative study
• A proportion of 50 % indicates a greater level of
variability than either 20% or 80%
• proportion of 0.5
• Sample size affects accuracy of representation
• Minimum suggested sample is 30 and upper limit
is 1,000
14. Strategies for Determining
Sample Size
1. Using a census for small populations
2. Imitating a sample size of similar studies
3. Using published tables
4. Applying formulas to calculate a sample size
15. 1. Using a Census for Small
Populations
• One approach is to use the entire population as
the sample
• Cost considerations make this impossible for
large populations
• Attractive for small populations (e.g., 200 or
less).
• Eliminates sampling errorand provides data on all
the individuals
• Some costs are “fixed”
• the entire population would have to be sampled
in small populations to achieve a desirable level
of precision
16. 2. Imitating a sample size of
similar studies
• Use the same sample size as those of studies
similar to the one you plan( Cite reference)
• Procedures employed in these studies should be
reviewed
• A review of the literature in your discipline can
provide guidance about “typical” sample sizes
17. 3. Using published tables
• Published tables provide the sample size for a
given set of criteria.
• Necessary for given combinations of precision,
confidence levels and variability.
• The sample sizes presume that the attributes
being measured are distributed normally or
nearly so.
• you may need to calculate the necessary sample
size for a different combination of levels of
precision, confidence, and variability.
18. 3. Using published tables
Size of
Population
Sample Size (n) for Precision (e) of:
±5% ±7% ±10%
100 81 67 51
125 96 78 56
150 110 86 61
175 122 94 64
200 134 101 67
225 144 107 70
250 154 112 72
275 163 117 74
300 172 121 76
325 180 125 77
350 187 129 78
375 194 132 80
400 201 135 81
425 207 138 82
450 212 140 82
• Sample Size for ±5%, ±7% and ±10%
Precision Levels
where Confidence Level Is 95% and P=.5.
19. Normal Distribution
The normal distribution is the most important and most widely used distribution in
statistics. It is sometimes called the "bell curve," although the tonal qualities of such a
bell would be less than pleasing
20. Central Limit theorem
The theorem says that if we take samples of size n from any arbitrary
population (with any arbitrary distribution) and calculate ,
then sampling distribution of will
approach the normal distribution as
the sample size n increases with mean
μ and standard error
22. Cochran equation
Where n0 is the sample size,
Z2 is the abscissa of the normal curve that cuts off an area α at the tails;
(1 – α) equals the desired confidence level, e.g., 95%);
e is the desired level of precision,
p is the estimated proportion of an attribute that is present in the
population,and q is 1-p.
The value for Z is found in statistical tables which contain the area
under the normal curve. e.g Z = 1.96 for 95 % level of confidence
Finite population
N is the population size
23. A Simplified Formula For Proportions
Yamane (1967:886) provides a simplified formula to calculate sample sizes.
ASSUMPTION:
95% confidence level
P = .5 ;
Where n is the sample size,
N is the population size,
e is the level of precision.
24. Allocation methods in Stratified
sampling
Sample size through proportional allocation method :
In this method, the sampling fraction, is same in all strata.This allocation was used
to obtain a sample that can estimate size of the sample with greater speed and a
higher degree of precision.
25. Allocation methods in Stratified
sampling
The sample size through optimum allocation method :
The allocation of the sample units to the different stratum is determined with a view to
minimize the variance for a specified cost of conducting the survey or to minimize the
cost for a specified value of the variance.The cost function is given by
Where, a is the observed cost which is constant, c i is the average
cost of surveying one unit in the i th stratum.
Therefore, the required sample size in different stratum is given by
Typically, the population is very large, making a census or a complete enumeration of all the values in the population is either impractical or impossible.
The sample usually represents a subset of manageable size.
Random sampling is the purest form of probability sampling. Each member of the population has an equal and known chance of being selected. When there are very large populations, it is often difficult or impossible to identify every member of the population, so the pool of available subjects becomes biased.
Systematic sampling is often used instead of random sampling. It is also called an Nth name selection technique. After the required sample size has been calculated, every Nth record is selected from a list of population members. As long as the list does not contain any hidden order, this sampling method is as good as the random sampling method.
Stratified sampling is commonly used probability method that is superior to random sampling because it reduces sampling error. A stratum is a subset of the population that share at least one common characteristic. resent a good cross section from the population.
Convenience sampling is used in exploratory research where the researcher is interested in getting an inexpensive approximation of the truth. As the name implies, the sample is selected because they are convenient. This nonprobability method is often used during preliminary research efforts to get a gross estimate of the results, without incurring the cost or time required to select a random sample.
Judgment sampling is a common nonprobability method. The researcher selects the sample based on judgment. This is usually and extension of convenience sampling.
Quota sampling is the nonprobability equivalent of stratified sampling. Like stratified sampling, the researcher first identifies the stratums and their proportions as they are represented in the population. Then convenience or judgment sampling is used to select the required number of subjects from each stratum. This differs from stratified sampling, where the stratums are filled by random sampling.
Snowball sampling is a special nonprobability method used when the desired sample characteristic is rare. It may be extremely difficult or cost prohibitive to locate respondents in these situations.
Convenience sampling is used in exploratory research where the researcher is interested in getting an inexpensive approximation of the truth. As the name implies, the sample is selected because they are convenient. This nonprobability method is often used during preliminary research efforts to get a gross estimate of the results, without incurring the cost or time required to select a random sample.
Judgment sampling is a common nonprobability method. The researcher selects the sample based on judgment. This is usually and extension of convenience sampling.
Quota sampling is the nonprobability equivalent of stratified sampling. Like stratified sampling, the researcher first identifies the stratums and their proportions as they are represented in the population. Then convenience or judgment sampling is used to select the required number of subjects from each stratum. This differs from stratified sampling, where the stratums are filled by random sampling.
Snowball sampling is a special nonprobability method used when the desired sample characteristic is rare. It may be extremely difficult or cost prohibitive to locate respondents in these situations.
Probability sampling not appropriate as sample not intended to be statistically representative
But, sample should have ability to represent salient characteristics in population.
Sample size taken until point of theoretical saturation
Sample size is usually small to allow in-depth exploration and understanding of phenomena under investigation
Ultimately a matter of judgement and expertise in evaluating the quality of information against final use, research methodology , sampling strategy and results is ecessary.
In practice, qualitative sampling usually requires a flexible, pragmatic approach.
The researcher actively selects the most productive sample to answer the research question.
This can involve developing a framework of the variables that might influence an individual's contribution and will be based on the researcher's practical knowledge of the research area, the available literature and evidence from the study itself.
This is a more intellectual strategy than the simple demographic stratification of epidemiological studies, though age, gender and social class might be important variables.
Instead of seeking representativeness through equal probabilities, maximum variation sampling seeks it by including a wide range of extremes. The principle is that if you deliberately try to interview a very different selection of people, their aggregate answers can be close to the whole population's.
Researchers seek out extreme or deviant cases in order to develop a richer, more in-depth understanding of a phenonmenon and to lend credibility to one's research account.
The iterative process of qualitative study design means that samples are usually theory driven ( theoretical sampling) to a greater or lesser extent
Theoretical sampling necessitates building interpretative theories from the emerging data and selecting a new sample to examine and elaborate on this theory.
It is the principal strategy for the grounded theoretical approach .
The iterative process of qualitative study design means that samples are usually theory driven ( theoretical sampling) to a greater or lesser extent
Theoretical sampling necessitates building interpretative theories from the emerging data and selecting a new sample to examine and elaborate on this theory.
It is the principal strategy for the grounded theoretical approach .
Several criteria will need to be specified to determine the appropriate sample size
A proportion of 50 % indicates a greater level of variability than either 20% or 80%. This is because 20% and 80% indicate that a large majority do not or do, respectively, have the attribute of interest.
Because a proportion of 0.5 indicates the maximum variability in a population, it is often used in determining a more conservative sample size, that is, the sample size may be larger than if the true variability of the population attribute were used.
Sample size affects accuracy of representation; Larger sample means less chance of error
Minimum suggested sample is 30 and upper limit is 1,000
A proportion of 50 % indicates a greater level of variability than either 20% or 80%. This is because 20% and 80% indicate that a large majority do not or do, respectively, have the attribute of interest.
Because a proportion of 0.5 indicates the maximum variability in a population, it is often used in determining a more conservative sample size, that is, the sample size may be larger than if the true variability of the population attribute were used.
Sample size affects accuracy of representation; Larger sample means less chance of error
Minimum suggested sample is 30 and upper limit is 1,000
One approach is to use the entire population as the sample.
Although cost considerations make this impossible for large populations.
Attractive for small populations (e.g., 200 or less).
Eliminates sampling error and provides data on all the individuals in the population.
Some costs such as questionnaire design and developing the sampling frame are “fixed,” that is, they will be the same for samples of 50 or 200.
Finally, virtually the entire population would have to be sampled in small populations to achieve a desirable level of precision
Use the same sample size as those of studies similar to the one you plan( Cite reference).
Without reviewing the procedures employed in these studies you may run the risk of repeating errors that were made in determining the sample size for another study.
However, a review of the literature in your discipline can provide guidance about “typical” sample sizes that are used.
Published tables provide the sample size for a given set of criteria.
Necessary for given combinations of precision, confidence levels and variability.
The sample sizes presume that the attributes being measured are distributed normally or nearly so.
Although tables can provide a useful guide for determining the sample size, you may need to calculate the necessary sample size for a different combination of levels of precision, confidence, and variability
Published tables provide the sample size for a given set of criteria.
Necessary for given combinations of precision, confidence levels and variability.
The sample sizes presume that the attributes being measured are distributed normally or nearly so.
Although tables can provide a useful guide for determining the sample size, you may need to calculate the necessary sample size for a different combination of levels of precision, confidence, and variability