Seems to me, Sampling and fixing sample size are the inevitable tasks of any research study. Researchers should have clear insights about the terms. Common and simple method of calculating sample size is expected.
There are lots. Google computing needed sample size. best, David Booth
The Cochran formula is:
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Where:
- e is the desired level of precision (i.e. the margin of error),
- p is the (estimated) proportion of the population which has the attribute in question,
- q is 1 – p.
The z-value is found in a Z tabl
Cochran's sample size formula for categorical data for an alpha level a priori at .05 (error of 5%) = n0=(t)2*(p)(q)/(d)2=384
Please refer the book given below.
Sekaran, U., 2003. Research methods for business: A skill building approach. John Wiley & Sons.
Sekaran (20013) wrote:
"Roscoe (1975) proposes the following rules of thumb for determining sample size:
1. Sample sizes larger than 30 and less than 500 are appropriate for most research.
2. Where samples are to be broken into sub-samples; (male/females, juniors/seniors, etc.), a minimum sample size of 30 for each category is necessary.
3. In multivariate research (including multiple regression analyses), the sample size should be several times (preferably 10 times or more) as large as the number of variables in the study.
4. For simple experimental research with tight experimental controls (matched pairs, etc.), successful research is possible with samples as small as 10 to 20 in size."
Reference
Sekaran, U., 2003. Research methods for business: A skill building approach. John Wiley & Sons.
The key is basically what estimated standard errors you find acceptable. There are a number of factors which determine those estimates: data type (continuous, yes/no), sampling methodology (modeling, probability of selection sample design which can include multiple stages), method of determining standard deviation(s) to use, estimation (or for regression, prediction) method, and if you have multiple items/questions/variables, you need to determine sample size need for each, or at least each important one.
Beware of online calculators which have limited use, generally only good for worst case yes/no data. The finite population correction (fpc) factor may be omitted by most online calculators as well.
Cochran (1977), 3rd ed, Sampling Techniques, Wiley, has a chapter on sample size estimation that is just for simple random sampling. Then he has other chapters on other sample designs with more information on sample sizes which is not always a simple formula. Some involve tradeoffs in the design.
Model Assisted Survey Sampling by Särndal, Swensson, and Wretman provides other information, and I have a paper on sample size needed using a model for one stratum. There, predicted totals (meaning use of regression) are important.
So you see, the basic idea behind sample size selection is not too involved: standard deviation, sample size, and methodology to obtain a given standard error. However, the more complex the methodology, the more difficult the application, which might sometimes involve simulations. Often a pilot study is needed to obtain a preliminary estimate for standard deviation(s). Cochran also discussed preliminary standard deviations.
The estimation of sample size needs can get quite complicated except in the simplest cases. The simplest cases can be inefficient in terms of sample size needs or resources from a logistics/data collection viewpoint, so complications are often unavoidable. They also may be more successful because use of more complex methods may mean more is known about the data/population, so mistakes and missed opportunities may be fewer.
"Rules of thumb" are often of little or no value.
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