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and confidence intervals are computed under a certain distribution, such as the normal distribution, then the underlying methods are referred to as exact parametric methods. The exact methods that do not make any distributional assumptions are referred to as exact nonparametric methods. The latter
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All classical statistical procedures are constructed using statistics which depend only on observable random vectors, whereas generalized estimators, tests, and confidence intervals used in exact statistics take advantage of the observable random vectors and the observed values both, as in
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has the advantage of making fewer assumptions whereas, the former tend to yield more powerful tests when the distributional assumption is reasonable. For advanced methods such as higher-way ANOVA
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Classical statistical methods do not provide exact tests to many statistical problems such as testing
Variance Components and ANOVA under unequal variances. To rectify this situation, the
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552:{\displaystyle R={\frac {{\overline {x}}S}{s\sigma }}-{\frac {{\overline {X}}-\mu }{\sigma }}={\frac {\overline {x}}{s}}{\frac {\sqrt {U}}{\sqrt {n}}}~-~{\frac {Z}{\sqrt {n}}}}
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50:. Exact statistical methods help avoid some of the unreasonable assumptions of traditional statistical methods, such as the assumption of equal variances in classical
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Mehta CR, Patel NR and Gray R. 1985. On computing an exact confidence interval for the common odds ratio in several 2 x 2 contingency tables.
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When the sample size is small, asymptotic results given by some traditional methods may not be valid. In such situations, the asymptotic
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but without having to treat constant parameters as random variables. For example, in sampling from a normal population with mean
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Mehta CR and Patel NR. 1983. A network algorithm for performing Fisher's exact test in rxc contingency tables.
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and approximate statistical methods. The main characteristic of exact methods is that statistical tests and
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721:-values so that one can perform tests based on exact probability statements valid for any sample size.
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are possible because its distribution and the observed value are both free of nuisance parameters.
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Generalized
Inference in Repeated Measures: Exact Methods in MANOVA and Mixed Models
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405:. Then, we can easily perform exact tests and exact confidence intervals for
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are the sample mean and the sample variance. Then, defining Z and U thus:
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Now suppose the parameter of interest is the coefficient of variation,
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279:{\displaystyle Z={\sqrt {n}}({\overline {X}}-\mu )/\sigma \sim N(0,1)}
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that was developed to provide more accurate results pertaining to
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are based on exact probability statements that are valid for any
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360:{\displaystyle U=nS^{2}/\sigma ^{2}\sim \chi _{n-1}^{2}}
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Mehta, C. R. 1995. SPSS 6.1 Exact test for
Windows.
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583:{\displaystyle {\overline {x}}}
168:{\displaystyle {\overline {X}}}
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44:confidence intervals
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75:regression analysis
56:variance components
36:interval estimation
32:statistical testing
758:. Oliver and Boyd.
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65:When exact
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28:statistics
24:exact test
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234:¯
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841:Category
725:See also
715:-values
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52:ANOVA
831:XPro
617:and
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