Sample size
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This document discusses sample size and determining an appropriate sample size for evaluation purposes. It introduces the concepts of a sample, population size, precision level, confidence level, and variability in determining sample size. Several sampling strategies are presented, including probability and non-probability sampling. Formulas are provided for calculating sample size, such as Slovin's formula and Cochran's formula which take into account factors like margin of error, population size, and degree of variability. Guidelines are given for selecting an appropriate sample size based on the purpose of the study and available population.
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Sample size
- 1. SAMPLE SIZE/CED 246/092314 SAMPLE SIZE CED 246-Evaluation in Rural Development ANNA MERLINNA T. FONTANILLA MS DEVCOM, 1998-38359
- 2. SAMPLE SIZE/CED 246/092314 What’s in this presentation • Introduction • What is a SAMPLE? • Determining/selecting a sample • Other sampling strategies • Using formulas to determine sample size
- 3. SAMPLE SIZE/CED 246/092314 Introduction Phase I: Understanding your program Phase II: Planning your evaluation Phase III: Implementing your evaluation Collecting data Analyzing Data Reporting Results
- 4. SAMPLE SIZE/CED 246/092314 Information Introduction DATA Limitations on ALL important variables SAMPLE
- 5. SAMPLE SIZE/CED 246/092314 What is a SAMPLE?
- 6. SAMPLE SIZE/CED 246/092314 Determining a sample Factors affecting sample size Purpose of the study Population size Precision level or sampling error Confidence level Degree of variability
- 7. SAMPLE SIZE/CED 246/092314 Determining a sample PROBABILITY SAMPLING NON-PROBABILITY SAMPLING NON-BIASED/based on chance BIASED/based on chance Generalization Not really appropriate Statistical methods for result analysis Not appropriate
- 8. SAMPLE SIZE/CED 246/092314 Selecting a sample
- 9. SAMPLE SIZE/CED 246/092314 Other strategies Census Sample size of similar study Published tables Formulas
- 10. SAMPLE SIZE/CED 246/092314 Slovin’s Formula n = 푁 (1 + 푁푒2) n, n0 = sample size e, e2 = margin of error N = population size Cochran’s Formula 푛0 = 푍2푝푞 푒2 푍2 = abscissa of the normal curve that cuts off an area α at the tails 푝 = degree of variability 푞 = 1- 푝
- 11. SAMPLE SIZE/CED 246/092314 Finite population correction n = 푛0 1 + (푛0 − 1) 푁 Cochran’s Formula 푛0 = 푍2푝푞 푒2 n, n0 = sample size N = population size
Editor's Notes
- Selecting samples i.e. sampling methods
- Before I start with my report, let’s take a look where we are now in our evaluation process. So per MEERA’s model, we’re done with the reports for Phases I and II. And we are now in Phase III, where we are implementing our evaluation. In this phase, we have three steps according to Nou Yang. And my report is one aspect of collecting data.
- According to Grace, we need data for our evaluation to arrive at a result and we can get these data from various sources. What we will be more concerned with is the primary data we will get from the program participants. According to Stufflebeam, evaluators should obtain data and information on all the important variables of the program. Our criteria and indicators which Ate Tess discussed during our previous meeting, will guide us on what data and information we have to obtain. Stufflebeam also said that for each source of information, evaluators cannot collect all of the potentially relevant information since evaluation is mainly a time-constrained enterprise or business that functions under real-world complexities. In other words, the evaluation is faced with many limitations particularly time, money, manpower and other resources. For example if we will look at the growth of fish in the ocean and how it relates to climate change, we cannot observe every fish in the sea. There are millions of fishes in the sea and we cannot for the life of us, take each fish and observe it. Other examples: Family Planning Program, Newspaper Readership, Happiness Index, etc. So this is why evaluators or researchers often collect information from only a sample of all the elements or objects of the evaluation or study. In our example, a sample of fishes, a sample of families, a sample of newspapers, etc.
- In other words, we take samples to save time, money, labor and other resources when doing our evaluation or any study. And also, there are less errors from handling the data (e.g. encoding) because there are fewer opportunities to make mistakes (Israel, 2013). So what is a sample? In very simple terms, a sample means a smaller quantity taken from much larger group to represent the whole group. Technically, according to MathIsFun.com, a sample is a selection taken from a larger group or the "population", so that you can examine it to find out something about the population. The key words to remember about samples are population and representativeness- the sample should be enough to sufficiently represent the population where it was taken. So we need to be careful about identifying the population and finding out the sample size so we can get reliable evaluation results. A good problem statement is necessary to identify the population relevant to evaluating program impacts (Israel, 2013). We have to be specific about our problem statement. What do we really wanna know? E.g. happiness index, fish, family planning, aerobics The population can be defined in many ways, geographically, demographic, economic, social characteristics, or content of the survey (Israel, 2013).
- So after defining the population, we can now go to determining our sample. There are cases when all the elements or sampling units in a population are included in the evaluation or study. Sometimes because the population is small e.g. evaluating CED 246 class and sometimes, because the evaluation calls for it. The sample size is influenced by (Israel, 2013): Purpose of the study – what do we really wanna know? Population size – if small, all elements can be included as sample; if big, sample size have to be determined Risk of selecting a "bad" sample or the confidence level – e.g. if we use a 95% confidence level, we assume that 95 out of 100 samples will have the true population value within the range of precision Allowable sampling error or level of precision – the range in which the true value of population is estimated to be e.g. if a researcher finds that 60% of the sample adopted a technology within a ±5% precision rate, then he can conclude that between 55% or 65% of the whole population adopted the technology. Degree of variability in the attributes being measured – distribution of attributes in the population; the more heterogeneous or variable the population is, the larger the sample size is required to obtain a given level of precision and vv. 50% is the maximum variability and often used in determining a conservative sample size, 80% means majority has the attribute being measured, 20% means majority do not have the attribute These factors are particularly seen when using mathematical formulas.
- Two categories of doing sampling: non-probability and probability. Nonprobability – use procedures for selection that are not based on chance. There is no way to accurately estimate the chance of any element being selected. The quality of the sample depends on the knowledge, judgement and expertise of the researcher. Convenient and economical. Probability – every element in the population has a known, non-zero probability of selection. Because the probability is known, the sample statistics can be generalized to the population at large (in a given level of precision). Probability samples are generally preferred because the risk of incorrectly generalizing the population is known. You are aware of the error. An important benefit of simple random sampling is that it allows researchers to use statistical methods to analyze sample results. For example, given a simple random sample, researchers can use statistical methods to define a confidence interval around a sample mean. Statistical analysis is not appropriate when non-random sampling methods are used.
- 00:33 The choice of a sample design will be largely determined by the amount of information that is available for the population. If characteristics of the population are known, then a stratified sample can be used to obtain more precise data. If little is known about the population, then a less complex design such as simple random or systematic samples can be used. When a list is unavailable or incomplete, a cluster sample may be the most efficient choice. But methods can be combined.
- Using a census for small populations – small is 200 or less; eliminates sampling error and provides data on all the individuals in the population Using a sample size of a similar study – published studies Using published tables – provides the sample size for a given set of criteria; sample sizes reflect the number of obtained responses not the number of surveys mailed or interviews planned; Table 2 presumes that the attributes being measured are distributed normally or nearly so Using formulas – when different combination of levels of precision, confidence, and variability are used Assumptions for 3 and 4: simple random sample is used Israel, 2013
- Both are used to calculate a sample for proportions Cochran’s formula is used for large populations, finite population Value of Z is found in statistical tables. When Slovin’s formula is used: If you have no idea about a population’s behavior. Using Slovin’s formula restricts the confidence coefficient to 95%.
- If the population is small, the sample size can be reduced slightly Israel (2013) notes that the above approaches have assumed that a simple random sample is the sampling design. More complex designs such as stratified, clustering would require other considerations in the computation. If descriptive statistics are to be used, e.g. mean, frequencies, then nearly any sample size will suffice. A good sample size, e.g. 200-500 is needed for multiple regression, analysis of co-variance or log-linear analysis. The sample size should be appropriate for the analysis that is planned.