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e388_08_Spr_Exam1
e388_08_Spr_Exam1

Notes on the chi-squared distribution
Notes on the chi-squared distribution

Statistics 2014, Fall 2001
Statistics 2014, Fall 2001

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... Normal as long as the sample size is large enough. The larger the sample used, the more closely the Normal approximates the sampling distribution. When creating a sampling distribution, we need: 1. a random sample of quantitative data 2. the true population standard deviation,  If we don’t have  ( ...
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13.1.1 Steps of ANOVAs - University of Northern Colorado

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Two-proportion z

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4-03-08 -- t-distributions and t-test

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Worksheet - Math.utah.edu

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Statistics and computer

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1.5 - One Way Analysis of variance

... groups (how far apart are the means?) to the variability within the groups (how much natural variation is there in our measurements?). This is why it is called analysis of variance. ANOVA is based on two assumptions. Therefore, before we carry out ANOVA, we need to check that these are met: 1) The o ...
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... different values of x will produce different mean responses. The statistical model for simple linear regression states that the observed response yi when the explanatory variable takes the value xi is y i   0  1xi   i where i  1,2,..., n . The  i are assumed to be independent and normally di ...
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Confidence Intervals and Tests of Significance

... The first confidence interval for µ1 − µ2 is the two-sample t procedure. If we can assume that the two samples have a common standard deviation, then we pool the data to compute sp , the pooled standard deviation. Matched pair procedures use a one sample procedure on the difference in the observed v ...
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... 1) Which number could replace the x in both 6x and 4x + 2x to produce the same value? a) any number b) a positive number c) a negative number d) 0 only 2) Which survey question could be asked to generate data that will have a mean and range? a) Are you the youngest person in your family? b) Are you ...
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Chapter 5

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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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