Assuming that a researcher does not know the nature of population distribution (the parameters or the type e.g. normal, exponential, etc.), is it possible that the sampling distribution can indicate the nature of the population distribution.
According to the central limit theorem, the sampling distribution is likely to be normal. So, the exact population distribution can not be known. The shape of the distribution for a large sample size is enough? or It has to be inferred logically based on different factors?
Am I missing some points? Any lead or literature will help.
Thank you
You should have as large sample size as possible. Also you should consider a representative sample size in according to the age structure of the population (for instance).For more, please consult the recommended demographic classic book:
Preston, S.H., Heuveline, P., and Gulliot, M. (2001). Demography: Measuring and Modeling Population Processes. Blackwell Publishers Ltd: Oxford. Best
You are misunderstanding the role of the central limit theorem (CLT). The CLT is about the distribution of a sample statistic (that is as summary of several values that are sampled from a distribution, like a sample mean; the CLT says that the sample means will approximate a normal distribution).
To infer the type of the population distribution, you need to look at the values (and not at some summary statistic). The CLT does not play any role here.
If the sampling assures that each value from the population has the same probability to be in the sample, the frequency distribution of the sample will approximate the frequency distribution of the population. The approximation will be better for larger samples. How large a sample should be to provide a sufficiently good approximation depends on the concrete case.
Hello Brajaballav,
Of course samples may be used to make inferences about the nature of a population distribution. How to proceed?
1. Take a probability sample of size n from the population of N cases.
2. Try goodness-of-fit index/indices, comparing the shape of the sample distribution to whatever candidate distribution/s you'd like to consider as possible for the population.
3. The best-fitting (or least mis-fitting) matches are then deemed worthy of further investigation as potential descriptors for the population.
Why probability sample? Because that's the only way to build confidence that your data set will not terribly misrepresent the population.
What sample size (n)? More is better. However, you have to balance that against the cost and time associated with data collection. The usual sample size formulae offered for sampling studies are concerned with the precision with which a specific population parameter (e.g., the mean) are estimated. In your case, you're really trying to identify all the moments of the population distribution, so these formulae are likely to lead to under-estimates of requisite n.
Will all this guarantee that you find the "right" answer? No, but you're far less likely to arrive at a wildly wrong result!
Good luck with your work.
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