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Unformatted text preview: SUNY at Albany  Department of Economics Eco 320 Economic Statistics Student tDistribution SUNY at Albany  Department of Economics Eco 320 Economic Statistics SUNY at Albany  Department of Economics SUNY at Albany  Department of Economics Eco 320 Economic Statistics 1. t Distribution A. SUNY at Albany  Department of Economics Eco 320 Economic Statistics SUNY at Albany  Department of Economics Eco 320 Economic Statistics Degrees of Freedom A. Degrees of freedom means the number of independent observations available to compute a statistics, such as the sample variance. B. If we use the same sample to compute the sample mean, around which we measure the sample variance, we lose one degree of freedom; that is, we have only (n 1) independent observations. SUNY at Albany  Department of Economics Eco 320 Economic Statistics 1. t Distribution A. X ~ t (k) There is a different t distribution for each sample size. It is completely determined by the degrees of freedom (d.f.), k. The mean is zero. Its variance = k/(k 2), which is defined for d.f. greater than 2. Its PDF curves are symmetric around the mean. [Recall: The symmetry implies that F(t) = 1 F(t).] Its PDF curves are flatter than the normal distribution and with thicker tails. As the d.f. (or the sample size) increase, the t distribution approaches to the normal distribution. SUNY at Albany  Department of Economics Eco 320 Economic Statistics 2. History and Story B. William Gosset discovered the tdistribution in 1908 while working for the Guinness Brewery in Dublin. Because his employer prevented employees from publishing papers, Gosset published his research under the pseudonym Student . Thats why his distribution is often called Students tdistribution....
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 Spring '11
 Chan
 Economics

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