In several textbooks and research papers, I've come across the phrase "Large sample size" (for example, an estimator is consistant for large sample size). However, what is meant by a large sample size is unclear. I mean, where does a large sample begin? Is there a formula or a criteria for determining that a sample size is large or small, especially in case of infinite population?
data analysis, testing of hypothesis, statistical inference, probability, survey sampling.
Consistent for large sample size is another way of saying that the estimator is consistent in the limit as n goes to infinity. Thus the larger n is the closer the estimate is to being consistent. For a treatment you might see the attached screenshot of a book I recommend. Available in the z-library. Best wishes David Booth.
The sample size is an indicator of how we are close or far to reality. There is no formula, estimator, or criteria for determining whether the sample size is large or small. But, the small sample size may hide many facts of this reality.
Dear Syed Abdul Rehman
Larger samples are more representative of the population. Because the fundamental purpose of inferential statistics is to generalize from a sample to a population, a greater sample size is less of an inference.
The usage of sample size calculation has a direct impact on study outcomes. Small sample sizes jeopardize a study's internal and external validity. Small differences in very large samples tend to be transformed into statistically significant differences, even though they are clinically inconsequential.
Even in a population of 200,000 individuals, sampling 1000 persons will usually get a reasonably accurate answer. Given the additional time and money required, sampling more than 1000 people will not improve accuracy significantly.
Best Regards
Dr. Fatemeh Khozaei
Formulas and even tables exist for sample size determination.
Hi
i think the sample size is an important feature of any emprical study in which the goal is to make inferences about a population from a sample...Maximum sample size is 10% as long as it does not exceed 1000, but when it exceeds 5000 ...under such situation 10% would be 500
Fatemeh Khozaei, this appears to be one of your sources of wording:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4296634/. Was it?
Everyone should site their sources/references when closely paraphrasing someone like that.
Thanks.
Syed -
You asked "Is there a formula or a criteria for determining that a sample size is large or small...."
That depends on your goal. You generally want sample statistics to be expected to be 'close' to the population statistics. Sample size alone does not guarantee that. A great deal of work has been done using a model-based ('prediction') approach, or model-assisted probability sampling approaches, for inference, because auxiliary or regressor data can help tell you something about your population.
But staying here with the probability-of-selection-based approach, as long as you know enough about the population to stratify properly, if needed, or do whatever other complication is advisable, and none of the population is hidden, one needs a sample that covers all segments of the population well enough according to their standard deviations, that standard error needs will be met with the sample size which is thus derived.
So generally, we assume that no kind of bias is a problem, and determine under the method used and the standard deviation(s) inherent to the population, what sample size (used in what way, based on the method) will achieve a desired standard error(s). Of course you may have some other goal than to achieve a certain standard error or less. Maybe you just want to know how many modes a population has. So a large (shall we say, 'adequate for our purposes') sample size would be one, used in a particular way, say by strata or subpopulations, or clusters, or involving stages, which would likely tell you what you want to know. For an hypothesis, one often can look to meet a certain desired standard error also, considering effect size, as a lone p-value is virtually useless.
So it depends, but in most cases, variance is an important consideration, along with mean, though skewness, etc, may matter. Simply put, there is no number which would always be large or always small, because at the very least, you have to consider variance.
Cheers - Jim
PS -
There certainly are 'formula' for adequate sample sizes, depending upon methodology. Note the following:
Consider this paper on finding sample size requirements for a single population, or subpopulation under classical ratio estimator prediction:
https://www.researchgate.net/publication/261947825_Projected_Variance_for_the_Model-based_Classical_Ratio_Estimator_Estimating_Sample_Size_Requirements.
In that paper, I compare the 'formula' I derive for this simple model-based approach, to the formula found in Cochran's Sampling Techniques, 3rd ed, 1977, Wiley, for simple random sampling, with continuous data, to estimate a sample size requirement. The formats are similar, but the execution differs.
But for complex cases, one might use simulation rather than a closed form solution ('formula').
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