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Two samples comparing means
Two samples comparing means

confidence interval
confidence interval

homeworke_ch3
homeworke_ch3

... 4. A set of ordinal, interval or ratio level data may only have one mode. 5. If a variable is measured at the interval or ratio level, all the values are included when computing the mean. 6. A variable measured at the interval or ratio level can have more than one arithmetic mean. 7. The mode is the ...
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... amounts to 16%. Therefore 84% of the intervals actually did contain the true parameter which suggests that these were 80% intervals (though they could have been 90%). 8.10 The figure shows that all of the 25 confidence intervals did contain the true mean. This suggests that the confidence level was ...
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... spanning space and time. Goldstein claims that ‘social statisticians are pretty much forced to adopt the notion of a “superpopulation” when attempting to generalise the results of an analysis’ (Camilli 1996, p,7). There is insufficient space here to contest this peculiar position in full (see Gorard ...
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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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