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Sample Size Determination
- 1. SAMPLE SIZE DETERMINATIONAND SAMPLING TECHNIQUES Tina Sepehrifar EbrahimAlavi Babak Boghrati Amir Mousavinia
- 2. • The populationis 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?
- 3. Probability Sampling Methods Systematic sampling (Nthname selection) Stratified sampling Random sampling
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- 6. What size sampledo 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 determinationin 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 determinationin 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 determinationin 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 determinationin Qualitative Study • The iterative process of qualitative study design • Theoretical sampling necessitates building interpretative theories • grounded theoretical approach
- 11. Some suggestions ofsample 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 determinationin 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 determinationin 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 SampleSize 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 aCensus 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 asample 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 publishedtables • 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 publishedtables 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 normaldistribution 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 Thetheorem 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
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- 22. Cochran equation Where n0is 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 FormulaFor 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 inStratified 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 inStratified 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
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Editor's Notes
- #3 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.
- #4 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.
- #5 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.
- #6 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.
- #8 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.
- #9 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.
- #10 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.
- #11 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 .
- #12 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 .
- #13 Several criteria will need to be specified to determine the appropriate sample size
- #14 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
- #15 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
- #16 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
- #17 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.
- #18 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
- #19 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