|
Binomial Test
Binomial test is an exact test of the statistical significance of deviations from a theoretically expected distribution of observations into two categories using sample data. Usage A binomial test is a statistical hypothesis test used to determine whether the proportion of successes in a sample differs from an expected proportion in a binomial distribution. It is useful for situations when there are two possible outcomes (e.g., success/failure, yes/no, heads/tails), i.e., where repeated experiments produce binary data. If one assumes an underlying probability \pi_0 between 0 and 1, the null hypothesis is : H_0\colon\pi=\pi_0 For a sample of size n, we would expect n\pi_0 successes. The formula of the binomial distribution gives the probability of those n samples instead producing k successes: : \Pr(X=k)=\binom\pi_0^k(1-\pi_0)^ Suppose that we want to test the alternative hypothesis : H_\colon\pi\pi_0 using the summation of the range from k to n instead. Calculating a p-val ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exact Test
An exact (significance) test is a statistical test such that if the null hypothesis is true, then all assumptions made during the derivation of the distribution of the test statistic are met. Using an exact test provides a significance test that maintains the type I error rate of the test (\alpha) at the desired significance level of the test. For example, an exact test at a significance level of \alpha = 5\%, when repeated over many samples where the null hypothesis is true, will reject at most 5\% of the time. This is in contrast to an ''approximate test'' in which the desired type I error rate is only approximately maintained (i.e.: the test might reject > 5% of the time), while this approximation may be made as close to \alpha as desired by making the sample size sufficiently large. Exact tests that are based on discrete test statistics may be conservative, indicating that the actual rejection rate lies below the nominal significance level \alpha. As an example, this is th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Mass Function
In probability and statistics, a probability mass function (sometimes called ''probability function'' or ''frequency function'') is a function that gives the probability that a discrete random variable is exactly equal to some value. Sometimes it is also known as the discrete probability density function. The probability mass function is often the primary means of defining a discrete probability distribution, and such functions exist for either scalar or multivariate random variables whose domain is discrete. A probability mass function differs from a continuous probability density function (PDF) in that the latter is associated with continuous rather than discrete random variables. A continuous PDF must be integrated over an interval to yield a probability. The value of the random variable having the largest probability mass is called the mode. Formal definition Probability mass function is the probability distribution of a discrete random variable, and provides the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lady Tasting Tea
In the design of experiments in statistics, the lady tasting tea is a randomized experiment devised by Ronald Fisher and reported in his book '' The Design of Experiments'' (1935). The experiment is the original exposition of Fisher's notion of a null hypothesis, which is "never proved or established, but is possibly disproved, in the course of experimentation".OED quote: 1935 R. A. Fisher, '' The Design of Experiments'' ii. 19, "We may speak of this hypothesis as the 'null hypothesis' ..the null hypothesis is never proved or established, but is possibly disproved, in the course of experimentation." The example is loosely based on an event in Fisher's life. The woman in question, phycologist Muriel Bristol, claimed to be able to tell whether the tea or the milk was added first to a cup. Her future husband, William Roach, suggested that Fisher give her eight cups, four of each variety, in random order. One could then ask what the probability was for her getting the specific ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
P-value
In null-hypothesis significance testing, the ''p''-value is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct. A very small ''p''-value means that such an extreme observed outcome would be very unlikely ''under the null hypothesis''. Even though reporting ''p''-values of statistical tests is common practice in academic publications of many quantitative fields, misinterpretation and misuse of p-values is widespread and has been a major topic in mathematics and metascience. In 2016, the American Statistical Association (ASA) made a formal statement that "''p''-values do not measure the probability that the studied hypothesis is true, or the probability that the data were produced by random chance alone" and that "a ''p''-value, or statistical significance, does not measure the size of an effect or the importance of a result" or "evidence regarding a model or hypothesis". That ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Microsoft Excel
Microsoft Excel is a spreadsheet editor developed by Microsoft for Microsoft Windows, Windows, macOS, Android (operating system), Android, iOS and iPadOS. It features calculation or computation capabilities, graphing tools, pivot tables, and a macro (computer science), macro programming language called Visual Basic for Applications (VBA). Excel forms part of the Microsoft 365 and Microsoft Office suites of software and has been developed since 1985. Features Basic operation Microsoft Excel has the basic features of all spreadsheets, using a grid of ''cells'' arranged in numbered ''rows'' and letter-named ''columns'' to organize data manipulations like arithmetic operations. It has a battery of supplied functions to answer statistical, engineering, and financial needs. In addition, it can display data as line graphs, histograms and charts, and with a very limited three-dimensional graphical display. It allows sectioning of data to view its dependencies on various factors ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stata
Stata (, , alternatively , occasionally stylized as STATA) is a general-purpose Statistics, statistical software package developed by StataCorp for data manipulation, visualization, statistics, and automated reporting. It is used by researchers in many fields, including biomedicine, economics, epidemiology, and sociology. Stata was initially developed by Computing Resource Center in California and the first version was released in 1985. In 1993, the company moved to College Station, Texas and was renamed Stata Corporation, now known as StataCorp. A major release in 2003 included a new graphics system and dialog boxes for all commands. Since then, a new version has been released once every two years. The current version is Stata 19, released in April 2025. Technical overview and terminology User interface From its creation, Stata has always employed an integrated command-line interface. Starting with version 8.0, Stata has included a graphical user interface which uses Menu ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MATLAB
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities. An additional package, Simulink, adds graphical multi-domain simulation and model-based design for dynamic and embedded systems. , MATLAB has more than four million users worldwide. They come from various backgrounds of engineering, science, and economics. , more than 5000 global colleges and universities use MATLAB to support instruction and research. History Origins MATLAB was invented by mathematician and computer programmer Cleve Moler. The idea for MATLAB was base ... [...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] |
Python (programming Language)
Python is a high-level programming language, high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation. Python is type system#DYNAMIC, dynamically type-checked and garbage collection (computer science), garbage-collected. It supports multiple programming paradigms, including structured programming, structured (particularly procedural programming, procedural), object-oriented and functional programming. It is often described as a "batteries included" language due to its comprehensive standard library. Guido van Rossum began working on Python in the late 1980s as a successor to the ABC (programming language), ABC programming language, and he first released it in 1991 as Python 0.9.0. Python 2.0 was released in 2000. Python 3.0, released in 2008, was a major revision not completely backward-compatible with earlier versions. Python 2.7.18, released in 2020, was the last release of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SPSS
SPSS Statistics is a statistical software suite developed by IBM for data management, advanced analytics, multivariate analysis, business intelligence, and criminal investigation. Long produced by SPSS Inc., it was acquired by IBM in 2009. Versions of the software released since 2015 have the brand name IBM SPSS Statistics. The software name originally stood for Statistical Package for the Social Sciences (SPSS), reflecting the original market, then later changed to Statistical Product and Service Solutions. Overview SPSS is a widely used program for statistics, statistical analysis in social science. It is also used by market researchers, health researchers, survey companies, government, education researchers, industries, marketing organizations, data miners, and others. The original SPSS manual (Nie, Bent & Hull, 1970) has been described as one of "sociology's most influential books" for allowing ordinary researchers to do their own statistical analysis. In addition to statist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SAS (software)
SAS (previously "Statistical Analysis System") is a statistical software suite developed by SAS Institute for data management, advanced analytics, multivariate analysis, business intelligence, and predictive analytics. SAS was developed at North Carolina State University from 1966 until 1976, when SAS Institute was incorporated. SAS was further developed in the 1980s and 1990s with the addition of new statistical procedures, additional components and the introduction of JMP. A point-and-click interface was added in version 9 in 2004. A social media analytics product was added in 2010. SAS Viya, a suite of analytics and artificial intelligence software, was introduced in 2016. Technical overview and terminology SAS is a software suite that can mine, alter, manage and retrieve data from a variety of sources and perform statistical analysis on it. SAS provides a graphical point-and-click user interface for non-technical users and more through the SAS language. SAS programs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apache Commons
The Apache Commons is a project of the Apache Software Foundation, formerly under the Jakarta Project. The purpose of the Commons is to provide reusable, Open-source software, open source Java (software platform), Java software. The Commons is composed of three parts: proper, sandbox, and dormant. Commons Proper The Commons Proper is dedicated to creating and maintaining reusable Java (software platform), Java components. The Commons Proper is a place for collaboration and sharing, where developers from throughout the Apache community can work together on projects to be shared by Apache projects and Apache users. Commons developers will make an effort to ensure that their components have minimal dependencies on other Library (computer science), software libraries, so that these components can be Software deployment, deployed easily. In addition, Commons components will keep their Interface (computer science), interfaces as stable as possible, so that Apache users, as well as other ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
