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One-Way Analysis of Variance: Comparing Several Means
One-Way Analysis of Variance: Comparing Several Means

Measures of Variability
Measures of Variability

Economics 102: Analysis of Economic Data Cameron Fall 2004
Economics 102: Analysis of Economic Data Cameron Fall 2004

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Learning the Language of the Statistician
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... will be using in this class. These are the symbols we will be using in formulas. While I do not require you to memorize all of the formulas, it is important that you know what these symbols mean. You will be expected to memorize a few of the simpler formulas for the departmental final. • To do respo ...
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... viewed as a known constant  i are independent N(0, 2) [normally distributed with mean 0 and variance 2]  This is the same model as (1.1) except that it assumes i are normally distributed. As a consequence, assumption that i are uncorrelated becomes assumption of independence.  The assumption ...
Notes from Lecture 13
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... In most cases we are testing whether a relationship is positive or negative, so we test the coefficients in a regression with H0= 0. Most statistical programs (including SPSS) will automatically perform a t test on each coefficient in the regression, using 0 as the null ...


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... variance above—The difference is that you divide by “N” in the denominator to find population variance, which is equal to the total number of members of your population, whereas you divide by n-1 to find the ESTIMATED population variance ...
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... Obtaining a point estimate of a parameter is just one problem in statistical inference ...
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... scores, then each score has a placement either above, or below the mean. If the score lies above the mean, this directionality is identified with a “+” sign in front o the score. If the score lies below the mean, it is indicated with a “ - ” in front of the score. To find the average deviation score ...
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Test Code: RSI/RSII (Short Answer Type) 2008 Junior Research
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Notes 9 - Wharton Statistics Department

... average test score would be of decreasing student-teacher ratio and keeping everything else in the world fixed. • Lurking variable: A variable that is associated with both average test score and student-teacher ratio. • In order to figure out whether a drop in studentteacher ratio causes higher test ...
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Degrees of freedom (statistics)

In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary.The number of independent ways by which a dynamic system can move, without violating any constraint imposed on it, is called number of degrees of freedom. In other words, the number of degrees of freedom can be defined as the minimum number of independent coordinates that can specify the position of the system completely.Estimates of statistical parameters can be based upon different amounts of information or data. The number of independent pieces of information that go into the estimate of a parameter are called the degrees of freedom. In general, the degrees of freedom of an estimate of a parameter are equal to the number of independent scores that go into the estimate minus the number of parameters used as intermediate steps in the estimation of the parameter itself (i.e. the sample variance has N-1 degrees of freedom, since it is computed from N random scores minus the only 1 parameter estimated as intermediate step, which is the sample mean).Mathematically, degrees of freedom is the number of dimensions of the domain of a random vector, or essentially the number of ""free"" components (how many components need to be known before the vector is fully determined).The term is most often used in the context of linear models (linear regression, analysis of variance), where certain random vectors are constrained to lie in linear subspaces, and the number of degrees of freedom is the dimension of the subspace. The degrees of freedom are also commonly associated with the squared lengths (or ""sum of squares"" of the coordinates) of such vectors, and the parameters of chi-squared and other distributions that arise in associated statistical testing problems.While introductory textbooks may introduce degrees of freedom as distribution parameters or through hypothesis testing, it is the underlying geometry that defines degrees of freedom, and is critical to a proper understanding of the concept. Walker (1940) has stated this succinctly as ""the number of observations minus the number of necessary relations among these observations.""
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