Exact Method Algorithm
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An Exact Method Algorithm is a Statistical Hypothesis Testing Algorithm that is used to compute an Exact Test.
- AKA: Exact Method, Exact Test Algorithm, Exact Significance Test Algorithm.
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- Example(s)
- Counter-Example(s):
- See: Statistical Modeling Task, Underdispersion, Statistical Dispersion, Variance.
References
2009
- http://en.wikipedia.org/wiki/Exact_statistics
- Exact statistics, such as that described in exact test, is a branch of statistics that was developed to provide more accurate results pertaining to statistical testing and interval estimation by eliminating procedures based on asymptotic and approximate statistical methods. The main characteristic of exact methods is that statistical tests and confidence intervals are based on exact probability statements that are valid for any sample size.
- When the sample size is small, asymptotic results given by some traditional methods may not be valid. In such situations, the asymptotic p-values may differ substantially from the exact p-values. Hence asymptotic and other approximate results may lead to unreliable and misleading conclusions.
- Exact statistical methods help avoid some of the unreasonable assumptions of traditional statistical methods, such as the assumption of equal variances in classical ANOVA. They also allow exact inference on variance components of mixed models.
- When exact p-values 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 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 regression analysis, and mixed models, only exact parametric methods are available.
2007
- http://support.sas.com/rnd/app/da/new/daexactmethods91.html
- Exact methods can be useful in situations where the asymptotic assumptions are not met. Standard asymptotic methods are based on the assumption that the test statistic follows a particular distribution when the sample size is sufficiently large. When the sample size is not large, asymptotic results may not be valid, with the asymptotic p-values differing perhaps substantially from the exact p-values. Asymptotic results may also be unreliable when the distribution of the data is sparse, skewed, or heavily tied.
- SAS/STAT software provides exact computations for the following analysis:
- One-Sample Tests
- Two-Sample Tests
- k-Sample Tests
- Two-Way Table Tests
- Measures of Association
- Measures of Agreement
- Logistic Regression
- Power of Tests and Sample