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Jamovi
Jamovi (stylized in all lower-case as jamovi) is a free and open-source computer program for data analysis and performing statistical tests. The core developers of Jamovi are Jonathon Love, Damian Dropmann, and Ravi Selker who are developers for the JASP project. Software Jamovi is an open source graphical user interface for the R programming language. It is used in statistical research, especially as a tool for ANOVA (analysis of variance) and to understand statistical inference. It also can be used for linear regression, mixed models and Bayesian models. Data is entered into a spreadsheet interface that can be imported into Jamovi. The analyses produced by the software are automatically updated to reflect changes made to the raw data. The software includes a multinomial test to determine whether observed data differs from researchers' predictions. Extendibility Users can modify the base program and extend its functionality using community created open source add-on modu ...
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R (programming Language)
R is a programming language for statistical computing and graphics supported by the R Core Team and the R Foundation for Statistical Computing. Created by statisticians Ross Ihaka and Robert Gentleman, R is used among data miners, bioinformaticians and statisticians for data analysis and developing statistical software. Users have created packages to augment the functions of the R language. According to user surveys and studies of scholarly literature databases, R is one of the most commonly used programming languages used in data mining. R ranks 12th in the TIOBE index, a measure of programming language popularity, in which the language peaked in 8th place in August 2020. The official R software environment is an open-source free software environment within the GNU package, available under the GNU General Public License. It is written primarily in C, Fortran, and R itself (partially self-hosting). Precompiled executables are provided for various operating systems. R ...
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Statistical Inference
Statistical inference is the process of using data analysis to infer properties of an underlying probability distribution, distribution of probability.Upton, G., Cook, I. (2008) ''Oxford Dictionary of Statistics'', OUP. . Inferential statistical analysis infers properties of a Statistical population, population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is Sampling (statistics), sampled from a larger population. Inferential statistics can be contrasted with descriptive statistics. Descriptive statistics is solely concerned with properties of the observed data, and it does not rest on the assumption that the data come from a larger population. In machine learning, the term ''inference'' is sometimes used instead to mean "make a prediction, by evaluating an already trained model"; in this context inferring properties of the model is referred to as ''training'' or ''learning'' (rather than ''inference''), and using a model for ...
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Survival Analysis
Survival analysis is a branch of statistics for analyzing the expected duration of time until one event occurs, such as death in biological organisms and failure in mechanical systems. This topic is called reliability theory or reliability analysis in engineering, duration analysis or duration modelling in economics, and event history analysis in sociology. Survival analysis attempts to answer certain questions, such as what is the proportion of a population which will survive past a certain time? Of those that survive, at what rate will they die or fail? Can multiple causes of death or failure be taken into account? How do particular circumstances or characteristics increase or decrease the probability of survival? To answer such questions, it is necessary to define "lifetime". In the case of biological survival, death is unambiguous, but for mechanical reliability, failure may not be well-defined, for there may well be mechanical systems in which failure is partial, a matter of ...
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Structural Equation Models
Structural equation modeling (SEM) is a label for a diverse set of methods used by scientists in both experimental and observational research across the sciences, business, and other fields. It is used most in the social and behavioral sciences. A definition of SEM is difficult without reference to highly technical language, but a good starting place is the name itself. SEM involves the construction of a ''model'', to represent how various aspects of an observable or theoretical phenomenon are thought to be causally structurally related to one another. The ''structural'' aspect of the model implies theoretical associations between variables that represent the phenomenon under investigation. The postulated causal structuring is often depicted with arrows representing causal connections between variables (as in Figures 1 and 2) but these causal connections can be equivalently represented as equations. The causal structures imply that specific patterns of connections should appe ...
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Psychometrics
Psychometrics is a field of study within psychology concerned with the theory and technique of measurement. Psychometrics generally refers to specialized fields within psychology and education devoted to testing, measurement, assessment, and related activities. Psychometrics is concerned with the objective measurement of latent constructs that cannot be directly observed. Examples of latent constructs include intelligence, introversion, mental disorders, and educational achievement. The levels of individuals on nonobservable latent variables are inferred through mathematical modeling based on what is observed from individuals' responses to items on tests and scales. Practitioners are described as psychometricians, although not all who engage in psychometric research go by this title. Psychometricians usually possess specific qualifications such as degrees or certifications, and most are psychologists with advanced graduate training in psychometrics and measurement theory. I ...
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GitHub
GitHub, Inc. () is an Internet hosting service for software development and version control using Git. It provides the distributed version control of Git plus access control, bug tracking, software feature requests, task management, continuous integration, and wikis for every project. Headquartered in California, it has been a subsidiary of Microsoft since 2018. It is commonly used to host open source software development projects. As of June 2022, GitHub reported having over 83 million developers and more than 200 million repositories, including at least 28 million public repositories. It is the largest source code host . History GitHub.com Development of the GitHub.com platform began on October 19, 2007. The site was launched in April 2008 by Tom Preston-Werner, Chris Wanstrath, P. J. Hyett and Scott Chacon after it had been made available for a few months prior as a beta release. GitHub has an annual keynote called GitHub Universe. Organizational ...
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Statistical Power
In statistics, the power of a binary hypothesis test is the probability that the test correctly rejects the null hypothesis (H_0) when a specific alternative hypothesis (H_1) is true. It is commonly denoted by 1-\beta, and represents the chances of a true positive detection conditional on the actual existence of an effect to detect. Statistical power ranges from 0 to 1, and as the power of a test increases, the probability \beta of making a type II error by wrongly failing to reject the null hypothesis decreases. Notation This article uses the following notation: * ''β'' = probability of a Type II error, known as a "false negative" * 1 − ''β'' = probability of a "true positive", i.e., correctly rejecting the null hypothesis. "1 − ''β''" is also known as the power of the test. * ''α'' = probability of a Type I error, known as a "false positive" * 1 − ''α'' = probability of a "true negative", i.e., correctly not rejecting the null hypothesis Description For a ty ...
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Meta-analysis
A meta-analysis is a statistical analysis that combines the results of multiple scientific studies. Meta-analyses can be performed when there are multiple scientific studies addressing the same question, with each individual study reporting measurements that are expected to have some degree of error. The aim then is to use approaches from statistics to derive a pooled estimate closest to the unknown common truth based on how this error is perceived. Meta-analytic results are considered the most trustworthy source of evidence by the evidence-based medicine literature.Herrera Ortiz AF., Cadavid Camacho E, Cubillos Rojas J, Cadavid Camacho T, Zoe Guevara S, Tatiana Rincón Cuenca N, Vásquez Perdomo A, Del Castillo Herazo V, & Giraldo Malo R. A Practical Guide to Perform a Systematic Literature Review and Meta-analysis. Principles and Practice of Clinical Research. 2022;7(4):47–57. https://doi.org/10.21801/ppcrj.2021.74.6 Not only can meta-analyses provide an estimate of the un ...
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Mediation (statistics)
In statistics, a mediation model seeks to identify and explain the mechanism or process that underlies an observed relationship between an independent variable and a dependent variable via the inclusion of a third hypothetical variable, known as a mediator variable (also a mediating variable, intermediary variable, or intervening variable). Rather than a direct causal relationship between the independent variable and the dependent variable, a mediation model proposes that the independent variable influences the mediator variable, which in turn influences the dependent variable. Thus, the mediator variable serves to clarify the nature of the relationship between the independent and dependent variables. Mediation analyses are employed to understand a known relationship by exploring the underlying mechanism or process by which one variable influences another variable through a mediator variable.Cohen, J.; Cohen, P.; West, S. G.; Aiken, L. S. (2003) ''Applied multiple regression/c ...
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Multinomial Test
In statistics, the multinomial test is the test of the null hypothesis that the parameters of a multinomial distribution equal specified values; it is used for categorical data. Beginning with a sample of ~ N ~ items each of which has been observed to fall into one of k categories. It is possible to define ~ \mathbf = (x_1, x_2, \dots, x_k) ~ as the observed numbers of items in each cell. Hence ~ \sum_^k x_ = N ~. Next, defining a vector of parameters ~ H_0: \boldsymbol = (\pi_, \pi_, \ldots, \pi_) ~, where: ~ \sum_^k \pi_ = 1 ~. These are the parameter values under the null hypothesis. The exact probability of the observed configuration ~ \mathbf ~ under the null hypothesis is given by :~ \operatorname\mathbb\left( \mathbf\right )_0 = N! \, \prod_^k \frac ~. The significance probability for the test is the probability of occurrence of the data set observed, or of a data set less likely than that observed, if the null hypothesis is true. Using an exact test, this is calculate ...
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Bayesian Models
Bayesian statistics is a theory in the field of statistics based on the Bayesian interpretation of probability where probability expresses a ''degree of belief'' in an event. The degree of belief may be based on prior knowledge about the event, such as the results of previous experiments, or on personal beliefs about the event. This differs from a number of other interpretations of probability, such as the frequentist interpretation that views probability as the limit of the relative frequency of an event after many trials. Bayesian statistical methods use Bayes' theorem to compute and update probabilities after obtaining new data. Bayes' theorem describes the conditional probability of an event based on data as well as prior information or beliefs about the event or conditions related to the event. For example, in Bayesian inference, Bayes' theorem can be used to estimate the parameters of a probability distribution or statistical model. Since Bayesian statistics treats pr ...
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Mixed Model
A mixed model, mixed-effects model or mixed error-component model is a statistical model containing both fixed effects and random effects. These models are useful in a wide variety of disciplines in the physical, biological and social sciences. They are particularly useful in settings where repeated measurements are made on the same statistical units (longitudinal study), or where measurements are made on clusters of related statistical units. Because of their advantage in dealing with missing values, mixed effects models are often preferred over more traditional approaches such as repeated measures analysis of variance. This page will discuss mainly linear mixed-effects models (LMEM) rather than generalized linear mixed models or nonlinear mixed-effects models. History and current status Ronald Fisher introduced random effects models to study the correlations of trait values between relatives. In the 1950s, Charles Roy Henderson provided best linear unbiased estimates of ...
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