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Informally, in frequentist statistics, a confidence interval (CI) is an interval which is expected to typically contain the parameter being estimated. More specifically, given a confidence level γ {\displaystyle \gamma } (95% and 99% are typical values), a CI is a random interval which contains the parameter being estimated γ {\displaystyle ...
Ci – cosine integral function. cis – cos + i sin function. (Also written as expi.) Cl – conjugacy class. cl – topological closure. CLT – central limit theorem. cod, codom – codomain. cok, coker – cokernel. colsp – column space of a matrix. conv – convex hull of a set. Cor – corollary. corr – correlation. cos – cosine ...
¯ = sample mean of differences d 0 {\displaystyle d_{0}} = hypothesized population mean difference s d {\displaystyle s_{d}} = standard deviation of differences
Also confidence coefficient. A number indicating the probability that the confidence interval (range) captures the true population mean. For example, a confidence interval with a 95% confidence level has a 95% chance of capturing the population mean. Technically, this means that, if the experiment were repeated many times, 95% of the CIs computed at this level would contain the true population ...
Random variables are usually written in upper case Roman letters, such as or and so on. Random variables, in this context, usually refer to something in words, such as "the height of a subject" for a continuous variable, or "the number of cars in the school car park" for a discrete variable, or "the colour of the next bicycle" for a categorical variable.
Classically, a confidence distribution is defined by inverting the upper limits of a series of lower-sided confidence intervals. [15] [16] [page needed] In particular, For every α in (0, 1), let (−∞, ξ n (α)] be a 100α% lower-side confidence interval for θ, where ξ n (α) = ξ n (X n,α) is continuous and increasing in α for each sample X n.
In these hypothetical repetitions, independent data sets following the same probability distribution as the actual data are considered, and a confidence interval is computed from each of these data sets; see Neyman construction. The coverage probability is the fraction of these computed confidence intervals that include the desired but ...
Convex hull (red) of a polygon (yellow). The usual set closure from topology is a closure operator. Other examples include the linear span of a subset of a vector space, the convex hull or affine hull of a subset of a vector space or the lower semicontinuous hull ¯ of a function : {}, where is e.g. a normed space, defined implicitly (¯) = ¯, where is the epigraph of a function .