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Tuesday, January 14, 2014

Sample size for Central Limit Theorem

The general rule in using central limit theorem is based on the sample size which is greater or equal to 30. However, the sample size would need to be greater than 30 or even smaller sample size would be enough to apply the central limit theorem. For instance, if a population distribution was bell-shaped, the distribution of sample means would become normal even with small sample size. On the other hand, in the case where the distribution is extremely skewed or has more than one mode, more samples may be required to obtain the normality of the distribution of sample means. For small samples size which is less than 30, a t-distribution can be assumed for the distribution of the sample means, if the population is normal. Note that the t-distribution approaches the normal distribution, as the number of degrees of freedom grows. Because of the fatter tails of the t-distribution, it assumes more outliers in the distribution.

http://ijims.ms.tku.edu.tw/PDF/M17N33.pdf
http://people.virginia.edu/~rwm3n/pdf/When%20do%20you%20use%20the%20t%20distribution.pdf
http://statistics.ucla.edu/system/resources/BAhbBlsHOgZmSSJVMjAxMi8wNS8zMC8xNV8zMV80Ml82MzFfUm9idXN0X1N0YXRpc3RpY2FsX01vZGVsaW5nX1VzaW5nX3RoZV90X0Rpc3RyaWJ1dGlvbi5wZGYGOgZFVA/Robust%20Statistical%20Modeling%20Using%20the%20t-%20Distribution.pdf

http://www.talkstats.com/showthread.php/24275-I-am-not-sure-how-Central-Limit-Theorem-and-the-t-distribution-fit-together.

http://www.stat.wisc.edu/~st571-1/07-normal-4.pdf

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