Abstract
Sample size is very important in statistical research because it is not too small or too large. Given significant level α, the sample size is calculated based on the z-value and pre-defined error. Such error is defined based on the previous experiment or other study or it can be determined subjectively by specialist, which may cause incorrect estimation. Therefore, this research proposes an objective method to estimate the sample size without pre-defining the error. Given an available sample X = {X1, X2, ..., Xn}, the error is calculated via the iterative process in which sample X is re-sampled many times. Moreover, after the sample size is estimated completely, it can be used to collect a new sample in order to estimate new sample size and so on.
Highlights
Given a sample of size n, = {X1, X 2, X n} from a normal distribution with theoretical unknown mean μ and known variance σ2, it implies that the sample mean ∑ X 1 n nXi i=1 is normally distributed with mean μ and known variance σ2/n
I invent this method when discussing with the co-author Dr Hang Ho about choice of sample size
Given an available random sample is used to estimate the sample size and such sample size is applied to collect new random sample; after that new sample size is estimated based on the new random sample and so on
Summary
Given a sample of size n, = {X1, X 2 , , X n} from a normal distribution with theoretical unknown mean μ and known variance σ2, it implies that the sample mean. (2015) A Proposed Method for Choice of Sample Size without Pre-Defining Error. N. There is a requirement that how to estimate the sample size n so as to the deviation X − μ is less than or equal to the pre-defined error E at given a 100(1 – α) % confident level. There is a requirement that how to estimate the sample size n so as to the deviation X − μ is less than or equal to the pre-defined error E at given a 100(1 – α) % confident level This is the choice of sample size.
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