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Boschloo's Test
Boschloo's test is a statistical hypothesis test for analysing 2x2 contingency tables. It examines the association of two Bernoulli distributed random variables and is a uniformly more powerful alternative to Fisher's exact test. It was proposed in 1970 by R. D. Boschloo. Setting A 2 × 2 contingency table visualizes \ n\ independent observations of two binary variables \ A\ and \ B\ : : \begin & B = 1 & B = 0 & \mbox\\ \hline A = 1 & x_ & x_ & n_1 \\ A = 0 & x_ & x_ & n_0 \\ \hline \mbox & s_1 & s_0 & n\\ \end The probability distribution of such tables can be classified into three distinct cases. # The row sums \ n_1\ , n_0\ and column sums \ s_1\ , s_0\ are fixed in advance and not random. Then all \ x_\ are determined by \ x_ ~. If \ A\ and \ B\ are independent, \ x_\ follows a hypergeometric distribution with parameters \ n\ , n_1\ , s_1\ : \ x_\ \sim\ \mbox(\ n\ , n_1\ , s_1\ ) ~. # The row sums \ n_1\ , n_0\ are fixed in advance but the column sums \ s_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Hypothesis Testing
A statistical hypothesis test is a method of statistical inference used to decide whether the data provide sufficient evidence to reject a particular hypothesis. A statistical hypothesis test typically involves a calculation of a test statistic. Then a decision is made, either by comparing the test statistic to a Critical value (statistics), critical value or equivalently by evaluating a p-value, ''p''-value computed from the test statistic. Roughly 100 list of statistical tests, specialized statistical tests are in use and noteworthy. History While hypothesis testing was popularized early in the 20th century, early forms were used in the 1700s. The first use is credited to John Arbuthnot (1710), followed by Pierre-Simon Laplace (1770s), in analyzing the human sex ratio at birth; see . Choice of null hypothesis Paul Meehl has argued that the epistemological importance of the choice of null hypothesis has gone largely unacknowledged. When the null hypothesis is predicted by the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
One- And Two-tailed Tests
In statistical significance testing, a one-tailed test and a two-tailed test are alternative ways of computing the statistical significance of a parameter inferred from a data set, in terms of a test statistic. A two-tailed test is appropriate if the estimated value is greater or less than a certain range of values, for example, whether a test taker may score above or below a specific range of scores. This method is used for null hypothesis testing and if the estimated value exists in the critical areas, the alternative hypothesis is accepted over the null hypothesis. A one-tailed test is appropriate if the estimated value may depart from the reference value in only one direction, left or right, but not both. An example can be whether a machine produces more than one-percent defective products. In this situation, if the estimated value exists in one of the one-sided critical areas, depending on the direction of interest (greater than or less than), the alternative hypothesis is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Barnard's Test
In statistics, Barnard’s test is an exact test used in the analysis of contingency tables with one margin fixed. Barnard’s tests are really a class of hypothesis tests, also known as unconditional exact tests for two independent binomials. These tests examine the association of two categorical variables and are often a more powerful alternative than Fisher's exact test for contingency tables. While first published in 1945 by G.A. Barnard, the test did not gain popularity due to the computational difficulty of calculating the value and Fisher’s specious disapproval. Nowadays, even for sample sizes ''n'' ~ 1 million, computers can often implement Barnard’s test in a few seconds or less. Purpose and scope Barnard’s test is used to test the independence of rows and columns in a contingency table. The test assumes each response is independent. Under independence, there are three types of study designs that yield a table, and Barnard's test applies to the second t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
StatXact
StatXact is a statistical software package for analyzing data using exact statistics. It calculates exact p-values and confidence intervals for contingency table In statistics, a contingency table (also known as a cross tabulation or crosstab) is a type of table in a matrix format that displays the multivariate frequency distribution of the variables. They are heavily used in survey research, business int ...s and non-parametric procedures. It is marketed by Cytel Inc. References * External links StatXact homepage at Cytel Inc. Statistical software Windows-only proprietary software {{statistics-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
R (programming Language)
R is a programming language for statistical computing and Data and information visualization, data visualization. It has been widely adopted in the fields of data mining, bioinformatics, data analysis, and data science. The core R language is extended by a large number of R package, software packages, which contain Reusability, reusable code, documentation, and sample data. Some of the most popular R packages are in the tidyverse collection, which enhances functionality for visualizing, transforming, and modelling data, as well as improves the ease of programming (according to the authors and users). R is free and open-source software distributed under the GNU General Public License. The language is implemented primarily in C (programming language), C, Fortran, and Self-hosting (compilers), R itself. Preprocessor, Precompiled executables are available for the major operating systems (including Linux, MacOS, and Microsoft Windows). Its core is an interpreted language with a na ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SciPy
SciPy (pronounced "sigh pie") is a free and open-source Python library used for scientific computing and technical computing. SciPy contains modules for optimization, linear algebra, integration, interpolation, special functions, fast Fourier transform, signal and image processing, ordinary differential equation solvers and other tasks common in science and engineering. SciPy is also a family of conferences for users and developers of these tools: SciPy (in the United States), EuroSciPy (in Europe) and SciPy.in (in India). Enthought originated the SciPy conference in the United States and continues to sponsor many of the international conferences as well as host the SciPy website. The SciPy library is currently distributed under the BSD license, and its development is sponsored and supported by an open community of developers. It is also supported by NumFOCUS, a community foundation for supporting reproducible and accessible science. Components The SciPy package is at the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Critical Value (statistics)
A statistical hypothesis test is a method of statistical inference used to decide whether the data provide sufficient evidence to reject a particular hypothesis. A statistical hypothesis test typically involves a calculation of a test statistic. Then a decision is made, either by comparing the test statistic to a critical value or equivalently by evaluating a ''p''-value computed from the test statistic. Roughly 100 specialized statistical tests are in use and noteworthy. History While hypothesis testing was popularized early in the 20th century, early forms were used in the 1700s. The first use is credited to John Arbuthnot (1710), followed by Pierre-Simon Laplace (1770s), in analyzing the human sex ratio at birth; see . Choice of null hypothesis Paul Meehl has argued that the epistemological importance of the choice of null hypothesis has gone largely unacknowledged. When the null hypothesis is predicted by theory, a more precise experiment will be a more severe test of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Test Statistic
Test statistic is a quantity derived from the sample for statistical hypothesis testing.Berger, R. L.; Casella, G. (2001). ''Statistical Inference'', Duxbury Press, Second Edition (p.374) A hypothesis test is typically specified in terms of a test statistic, considered as a numerical summary of a data-set that reduces the data to one value that can be used to perform the hypothesis test. In general, a test statistic is selected or defined in such a way as to quantify, within observed data, behaviours that would distinguish the null from the alternative hypothesis, where such an alternative is prescribed, or that would characterize the null hypothesis if there is no explicitly stated alternative hypothesis. An important property of a test statistic is that its sampling distribution under the null hypothesis must be calculable, either exactly or approximately, which allows ''p''-values to be calculated. A ''test statistic'' shares some of the same qualities of a descriptive stat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decision Rule
In decision theory, a decision rule is a function which maps an observation to an appropriate action. Decision rules play an important role in the theory of statistics and economics, and are closely related to the concept of a strategy in game theory. In order to evaluate the usefulness of a decision rule, it is necessary to have a loss function detailing the outcome of each action under different states. Formal definition Given an observable random variable ''X'' over the probability space \scriptstyle (\mathcal,\Sigma, P_\theta), determined by a parameter ''θ'' ∈ ''Θ'', and a set ''A'' of possible actions, a (deterministic) decision rule is a function ''δ'' : \scriptstyle\mathcal→ ''A''. Examples of decision rules * An estimator is a decision rule used for estimating a parameter. In this case the set of actions is the parameter space, and a loss function details the cost of the discrepancy between the true value of the parameter and the e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power (statistics)
In frequentist statistics, power is the probability of detecting a given effect (if that effect actually exists) using a given test in a given context. In typical use, it is a function of the specific test that is used (including the choice of test statistic and significance level), the sample size (more data tends to provide more power), and the effect size (effects or correlations that are large relative to the variability of the data tend to provide more power). More formally, in the case of a simple hypothesis test with two hypotheses, the power of the test is the probability that the test correctly rejects the null hypothesis (H_0) when the alternative hypothesis (H_1) is true. It is commonly denoted by 1-\beta, where \beta is the probability of making a Type I and type II errors#Type II error, type II error (a false negative) conditional probability, conditional on there being a true effect or association. Background Statistical testing uses data from Sampling (statisti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nuisance Parameter
In statistics, a nuisance parameter is any parameter which is unspecified but which must be accounted for in the hypothesis testing of the parameters which are of interest. The classic example of a nuisance parameter comes from the normal distribution, a member of the location–scale family. For at least one normal distribution, the variance(s), ''σ2'' is often not specified or known, but one desires to hypothesis test on the mean(s). Another example might be linear regression with unknown variance in the explanatory variable (the independent variable): its variance is a nuisance parameter that must be accounted for to derive an accurate interval estimate of the regression slope, calculate p-values, hypothesis test on the slope's value; see regression dilution. Nuisance parameters are often scale parameters, but not always; for example in errors-in-variables models, the unknown true location of each observation is a nuisance parameter. A parameter may also cease to be a " ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
