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StatisticsStatistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
is the mathematical science involving the collection, analysis and interpretation of data. A number of specialties have evolved to apply statistical theory and methods to various disciplines. Certain topics have "statistical" in their name but relate to manipulations of probability distributions rather than to statistical analysis.
 Actuarial science
Actuarial science is the discipline that applies mathematical and statistical methods to assess risk in the insurance and finance industries. Actuaries are professionals who are qualified in this field through education and experience...
is the discipline that applies mathematical and statistical methods to assess risk in the insuranceIn law and economics, insurance is a form of risk management primarily used to hedge against the risk of a contingent, uncertain loss. Insurance is defined as the equitable transfer of the risk of a loss, from one entity to another, in exchange for payment. An insurer is a company selling the...
and finance"Finance" is often defined simply as the management of money or “funds” management Modern finance, however, is a family of business activity that includes the origination, marketing, and management of cash and money surrogates through a variety of capital accounts, instruments, and markets created...
industries.
 Biostatistics
Biostatistics is the application of statistics to a wide range of topics in biology...
is a branch of biologyBiology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. Biology is a vast subject containing many subdivisions, topics, and disciplines...
that studies biological phenomena and observations by means of statistical analysis, and includes medical statisticsMedical statistics deals with applications of statistics to medicine and the health sciences, including epidemiology, public health, forensic medicine, and clinical research...
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 Business Analytics
Business analytics refers to the skills, technologies, applications and practices for continuous iterative exploration and investigation of past business performance to gain insight and drive business planning. Business analytics focuses on developing new insights and understanding of business...
is a rapidly developing business process that applies statistical methods to data sets (often very large) to develop new insights and understanding of business performance & opportunities
 Chemometrics
Chemometrics is the science of extracting information from chemical systems by datadriven means. It is a highly interfacial discipline, using methods frequently employed in core dataanalytic disciplines such as multivariate statistics, applied mathematics, and computer science, in order to...
is the science of relating measurements made on a chemicalChemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....
system or process to the state of the system via application of mathematical or statistical methods.
 Demography
Demography is the statistical study of human population. It can be a very general science that can be applied to any kind of dynamic human population, that is, one that changes over time or space...
is the statistical study of all populationA population is all the organisms that both belong to the same group or species and live in the same geographical area. The area that is used to define a sexual population is such that interbreeding is possible between any pair within the area and more probable than crossbreeding with individuals...
s. It can be a very general science that can be applied to any kind of dynamic population, that is, one that changes over time or space.
 Econometrics
Econometrics has been defined as "the application of mathematics and statistical methods to economic data" and described as the branch of economics "that aims to give empirical content to economic relations." More precisely, it is "the quantitative analysis of actual economic phenomena based on...
is a branch of economics that applies statistical methods to the empirical study of economic theories and relationships.
 Environmental statistics
Environmental statistics is the application of statistical methods to environmental science. It covers procedures for dealing with questions concerning both the natural environment in its undistrurbed state and the interaction of humanity with the environment...
is the application of statistical methods to environmental scienceEnvironmental science is an interdisciplinary academic field that integrates physical and biological sciences, to the study of the environment, and the solution of environmental problems...
. Weather, climate, air and water quality are included, as are studies of plant and animal populations.
 Epidemiology
Epidemiology is the study of healthevent, healthcharacteristic, or healthdeterminant patterns in a population. It is the cornerstone method of public health research, and helps inform policy decisions and evidencebased medicine by identifying risk factors for disease and targets for preventive...
is the study of factors affecting the health and illness of populations, and serves as the foundation and logic of interventions made in the interest of public health and preventive medicine.
 Geostatistics
Geostatistics is a branch of statistics focusing on spatial or spatiotemporal datasets. Developed originally to predict probability distributions of ore grades for mining operations, it is currently applied in diverse disciplines including petroleum geology, hydrogeology, hydrology, meteorology,...
is a branch of geographyGeography is the science that studies the lands, features, inhabitants, and phenomena of Earth. A literal translation would be "to describe or write about the Earth". The first person to use the word "geography" was Eratosthenes...
that deals with the analysis of data from disciplines such as petroleum geologyPetroleum geology refers to the specific set of geological disciplines that are applied to the search for hydrocarbons .Sedimentary basin analysis:...
, hydrogeologyHydrogeology is the area of geology that deals with the distribution and movement of groundwater in the soil and rocks of the Earth's crust, . The term geohydrology is often used interchangeably...
, hydrologyHydrology is the study of the movement, distribution, and quality of water on Earth and other planets, including the hydrologic cycle, water resources and environmental watershed sustainability...
, meteorologyMeteorology is the interdisciplinary scientific study of the atmosphere. Studies in the field stretch back millennia, though significant progress in meteorology did not occur until the 18th century. The 19th century saw breakthroughs occur after observing networks developed across several countries...
, oceanographyOceanography , also called oceanology or marine science, is the branch of Earth science that studies the ocean...
, geochemistryThe field of geochemistry involves study of the chemical composition of the Earth and other planets, chemical processes and reactions that govern the composition of rocks, water, and soils, and the cycles of matter and energy that transport the Earth's chemical components in time and space, and...
, geographyGeography is the science that studies the lands, features, inhabitants, and phenomena of Earth. A literal translation would be "to describe or write about the Earth". The first person to use the word "geography" was Eratosthenes...
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 Operations research
Operations research is an interdisciplinary mathematical science that focuses on the effective use of technology by organizations...
(or Operational Research) is an interdisciplinary branch of applied mathematics and formal science that uses methods such as mathematical modeling, statistics, and algorithms to arrive at optimal or near optimal solutions to complex problems.
 Population ecology
Population ecology is a subfield of ecology that deals with the dynamics of species populations and how these populations interact with the environment. It is the study of how the population sizes of species living together in groups change over time and space....
is a subfield of ecologyEcology is the scientific study of the relations that living organisms have with respect to each other and their natural environment. Variables of interest to ecologists include the composition, distribution, amount , number, and changing states of organisms within and among ecosystems...
that deals with the dynamics of species populations and how these populations interact with the environmentThe biophysical environment is the combined modeling of the physical environment and the biological life forms within the environment, and includes all variables, parameters as well as conditions and modes inside the Earth's biosphere. The biophysical environment can be divided into two categories:...
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 Quantitative psychology
Research in quantitative psychology develops psychological theory in relation to mathematics and statistics. Psychological research requires the elaboration of existing methods and the development of new concepts, so that quantitative psychology requires more than "applications" of statistics and...
is the science of statistically explaining and changing mental processes and behaviors in humans.
 Psychometrics
Psychometrics is the field of study concerned with the theory and technique of psychological measurement, which includes the measurement of knowledge, abilities, attitudes, personality traits, and educational measurement...
is the theory and technique of educational and psychological measurement of knowledge, abilities, attitudes, and personality traits.
 Quality control
Quality control, or QC for short, is a process by which entities review the quality of all factors involved in production. This approach places an emphasis on three aspects:...
reviews the factors involved in manufacturing and production; it can make use of statistical samplingIn statistics and survey methodology, sampling is concerned with the selection of a subset of individuals from within a population to estimate characteristics of the whole population....
of product items to aid decisions in process controlProcess control is a statistics and engineering discipline that deals with architectures, mechanisms and algorithms for maintaining the output of a specific process within a desired range...
or in accepting deliveries.
 Statistical finance
Statistical finance, sometimes called econophysics, is an empirical attempt to shift finance from its normative roots to a positivist framework using exemplars from statistical physics with an emphasis on emergent or collective properties of financial markets...
, sometimes called econophysicsEconophysics is an interdisciplinary research field, applying theories and methods originally developed by physicists in order to solve problems in economics, usually those including uncertainty or stochastic processes and nonlinear dynamics...
, is an empirical attempt to shift finance from its normativeNormative economics is that part of economics that expresses value judgments about economic fairness or what the economy ought to be like or what goals of public policy ought to be....
roots to a positivist framework using exemplars from statistical physics with an emphasis on emergent or collective properties of financial markets.
 Statistical mechanics
Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...
is the application of probabilityProbability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
theory, which includes mathematical tools for dealing with large populations, to the field of mechanicsMechanics is the branch of physics concerned with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment....
, which is concerned with the motion of particles or objects when subjected to a force.
 Statistical physics
Statistical physics is the branch of physics that uses methods of probability theory and statistics, and particularly the mathematical tools for dealing with large populations and approximations, in solving physical problems. It can describe a wide variety of fields with an inherently stochastic...
is one of the fundamental theories of physicsPhysics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, and uses methods of probabilityProbability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
theory in solving physical problems.
 Statistical thermodynamics is the study of the microscopic behaviors of thermodynamic system
A thermodynamic system is a precisely defined macroscopic region of the universe, often called a physical system, that is studied using the principles of thermodynamics....
s using probability theory and provides a molecular level interpretation of thermodynamic quantities such as workIn thermodynamics, work performed by a system is the energy transferred to another system that is measured by the external generalized mechanical constraints on the system. As such, thermodynamic work is a generalization of the concept of mechanical work in mechanics. Thermodynamic work encompasses...
, heatIn physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...
, free energyThe thermodynamic free energy is the amount of work that a thermodynamic system can perform. The concept is useful in the thermodynamics of chemical or thermal processes in engineering and science. The free energy is the internal energy of a system less the amount of energy that cannot be used to...
, and entropyEntropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
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