Lecture3_Part5

Lecture3_Part5 - SUNY at Albany - Department of Economics...

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Unformatted text preview: SUNY at Albany - Department of Economics Eco 320 Economic Statistics Student t-Distribution 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 t-distribution 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 t-distribution....
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Lecture3_Part5 - SUNY at Albany - Department of Economics...

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