Analysis (
: analyses) is the process of breaking a
complex topic or
substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
and
logic since before
Aristotle
Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of ...
(384–322
B.C.), though ''analysis'' as a formal concept is a relatively recent development.
The word comes from the
Ancient Greek ἀνάλυσις (''analysis'', "a breaking-up" or "an untying;" from ''ana-'' "up, throughout" and ''lysis'' "a loosening"). From it also comes the word's plural, ''analyses''.
As a formal concept, the method has variously been ascribed to
Alhazen,
René Descartes
René Descartes ( or ; ; Latinized: Renatus Cartesius; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science. Ma ...
(''
Discourse on the Method''), and
Galileo Galilei
Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He ...
. It has also been ascribed to
Isaac Newton, in the form of a practical method of physical discovery (which he did not name).
The converse of analysis is synthesis: putting the pieces back together again in new or different whole.
Applications
Science
The field of
chemistry
Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, proper ...
uses analysis in three ways: to identify the components of a particular
chemical compound (qualitative analysis), to identify the proportions of components in a
mixture (quantitative analysis), and to break down
chemical processes and examine
chemical reactions between
elements of
matter. For an example of its use, analysis of the concentration of elements is important in managing a
nuclear reactor, so
nuclear scientists will analyze
neutron activation to develop discrete measurements within vast samples. A
matrix
Matrix most commonly refers to:
* ''The Matrix'' (franchise), an American media franchise
** '' The Matrix'', a 1999 science-fiction action film
** "The Matrix", a fictional setting, a virtual reality environment, within ''The Matrix'' (franchi ...
can have a considerable effect on the way a chemical analysis is conducted and the quality of its results. Analysis can be done manually or with a
device.
Types of Analysis:
A) Qualitative Analysis: It is concerned with which components are in a given sample or compound.
Example: Precipitation reaction
B) Quantitative Analysis: It is to determine the quantity of individual component present in a given sample or compound.
Example: To find concentration by uv-spectrophotometer.
Isotopes
Chemists can use
isotope analysis to assist analysts with issues in
anthropology,
archeology,
food chemistry,
forensics,
geology, and a host of other questions of
physical science. Analysts can discern the origins of natural and man-made isotopes in the study of
environmental radioactivity.
Business
*
Financial statement analysis – the analysis of the accounts and the economic prospects of a firm
*
Financial analysis – refers to an assessment of the viability, stability, and profitability of a
business, sub-business or
project
*
Gap analysis – involves the comparison of actual performance with potential or desired performance of an organization
*
Business analysis – involves identifying the needs and determining the solutions to business problems
*
Price analysis – involves the breakdown of a price to a unit figure
*
Market analysis – consists of suppliers and customers, and price is determined by the interaction of
supply and demand
In microeconomics, supply and demand is an economic model of price determination in a Market (economics), market. It postulates that, Ceteris paribus, holding all else equal, in a perfect competition, competitive market, the unit price for a ...
*
Sum-of-the-parts analysis – method of valuation of a
multi-divisional company
* Opportunity analysis – consists of customers trends within the industry, customer demand and experience determine purchasing behavior
Computer science
*
Requirements analysis – encompasses those tasks that go into determining the needs or conditions to meet for a new or altered product, taking account of the possibly conflicting requirements of the various stakeholders, such as beneficiaries or users.
*
Competitive analysis (online algorithm) Competitive analysis is a method invented for analyzing online algorithms, in which the performance of an online algorithm (which must satisfy an unpredictable sequence of requests, completing each request without being able to see the future) is co ...
– shows how online algorithms perform and demonstrates the power of randomization in algorithms
*
Lexical analysis – the process of processing an input sequence of characters and producing as output a sequence of symbols
*
Object-oriented analysis and design – à la
Booch
*
Program analysis (computer science)
In computer science, program analysis is the process of automatically analyzing the behavior of computer programs regarding a property such as correctness, robustness, safety and liveness.
Program analysis focuses on two major areas: program o ...
– the process of automatically analysing the behavior of computer programs
*
Semantic analysis (computer science) – a pass by a compiler that adds semantical information to the parse tree and performs certain checks
*
Static code analysis – the analysis of computer software that is performed without actually executing programs built from that
*
Structured systems analysis and design methodology – à la
Yourdon
*
Syntax analysis
In linguistics, syntax () is the study of how words and morphemes combine to form larger units such as phrases and sentences. Central concerns of syntax include word order, grammatical relations, hierarchical sentence structure (constituency) ...
– a process in compilers that recognizes the structure of programming languages, also known as parsing
*
Worst-case execution time – determines the longest time that a piece of software can take to run
Economics
*
Agroecosystem analysis Agroecosystem analysis is a thorough analysis of an agricultural environment which considers aspects from ecology, sociology, economics, and politics with equal weight. There are many aspects to consider; however, it is literally impossible to a ...
*
Input–output model
In economics, an input–output model is a quantitative economic model that represents the interdependencies between different sectors of a national economy or different regional economies.Thijs Ten Raa, Input–Output Economics: Theory and Ap ...
if applied to a region, is called Regional Impact Multiplier System
Engineering
Analysts in the field of
engineering look at
requirements,
structures, mechanisms,
systems and
dimensions.
Electrical engineers analyse
systems in
electronics.
Life cycles and
system failures are broken down and studied by engineers. It is also looking at different factors incorporated within the design.
Intelligence
The field of
intelligence employs analysts to break down and understand a wide array of questions.
Intelligence agencies may use
heuristics,
inductive and
deductive reasoning,
social network analysis,
dynamic network analysis,
link analysis, and
brainstorming to sort through problems they face.
Military intelligence may explore issues through the use of
game theory,
Red Teaming, and
wargaming.
Signals intelligence applies
cryptanalysis and
frequency analysis to break
codes and
ciphers.
Business intelligence applies theories of
competitive intelligence analysis and
competitor analysis to resolve questions in the
marketplace.
Law enforcement intelligence applies a number of theories in
crime analysis.
Linguistics
Linguistics
Linguistics is the scientific study of human language. It is called a scientific study because it entails a comprehensive, systematic, objective, and precise analysis of all aspects of language, particularly its nature and structure. Ling ...
explores individual languages and
language in general. It breaks language down and analyses its component parts:
theory,
sounds and their meaning,
utterance usage,
word origins, the
history of words, the meaning of
words and
word combinations,
sentence construction,
basic construction beyond the sentence level,
stylistics
Stylistics, a branch of applied linguistics, is the study and interpretation of texts of all types and/or spoken language in regard to their linguistic and tonal style, where style is the particular variety of language used by different individu ...
, and
conversation. It examines the above using
statistics and modeling, and
semantics. It analyses language in context of
anthropology,
biology,
evolution,
geography,
history,
neurology,
psychology, and
sociology. It also takes the
applied approach, looking at
individual language development and
clinical issues.
Literature
Literary criticism is the analysis of
literature
Literature is any collection of Writing, written work, but it is also used more narrowly for writings specifically considered to be an art form, especially prose fiction, drama, and poetry. In recent centuries, the definition has expanded to ...
. The focus can be as diverse as the analysis of
Homer or
Freud. While not all literary-critical methods are primarily analytical in nature, the main approach to the teaching of literature in the west since the mid-twentieth century, literary formal analysis or close reading, is. This method, rooted in the academic movement labelled
The New Criticism, approaches texts – chiefly short poems such as
sonnets, which by virtue of their small size and significant complexity lend themselves well to this type of analysis – as units of discourse that can be understood in themselves, without reference to biographical or historical frameworks. This method of analysis breaks up the text linguistically in a study of
prosody (the formal analysis of meter) and phonic effects such as
alliteration
Alliteration is the conspicuous repetition of initial consonant sounds of nearby words in a phrase, often used as a literary device. A familiar example is "Peter Piper picked a peck of pickled peppers". Alliteration is used poetically in various ...
and
rhyme, and cognitively in examination of the interplay of syntactic structures, figurative language, and other elements of the poem that work to produce its larger effects.
Mathematics
Modern mathematical analysis is the study of infinite processes. It is the branch of mathematics that includes calculus. It can be applied in the study of
classical concepts of mathematics, such as
real numbers,
complex variables,
trigonometric functions, and
algorithms, or of
non-classical concepts like
constructivism,
harmonics,
infinity, and
vectors.
Florian Cajori explains in
''A History of Mathematics'' (1893) the difference between modern and ancient mathematical analysis, as distinct from logical analysis, as follows:
The terms ''synthesis'' and ''analysis'' are used in mathematics in a more special sense than in logic. In ancient mathematics they had a different meaning from what they now have. The oldest definition of mathematical analysis as opposed to synthesis is that given in ppended to Euclid, XIII. 5, which in all probability was framed by Eudoxus: "Analysis is the obtaining of the thing sought by assuming it and so reasoning up to an admitted truth; synthesis is the obtaining of the thing sought by reasoning up to the inference and proof of it."
The analytic method is not conclusive, unless all operations involved in it are known to be reversible. To remove all doubt, the Greeks, as a rule, added to the analytic process a synthetic one, consisting of a reversion of all operations occurring in the analysis. Thus the aim of analysis was to aid in the discovery of synthetic proofs or solutions.
James Gow uses a similar argument as Cajori, with the following clarification, in hi
''A Short History of Greek Mathematics''(1884):
The synthetic proof proceeds by shewing that the proposed new truth involves certain admitted truths. An analytic proof begins by an assumption, upon which a synthetic reasoning is founded. The Greeks distinguished ''theoretic'' from ''problematic'' analysis. A theoretic analysis is of the following kind. To ''prove'' that A is B, ''assume'' first that A is B. If so, then, since B is C and C is D and D is E, therefore A is E. If this be known a falsity, A is not B. But if this be a known truth and all the intermediate propositions be convertible, then the reverse process, A is E, E is D, D is C, C is B, therefore A is B, constitutes a synthetic proof of the original theorem. Problematic analysis is applied in all cases where it is proposed to construct a figure which is assumed to satisfy a given condition. The problem is then converted into some theorem which is involved in the condition and which is proved synthetically, and the steps of this synthetic proof taken backwards are a synthetic solution of the problem.
Music
*
Musical analysis – a process attempting to answer the question "How does this music work?"
**Musical Analysis is a study of how the composers use the notes together to compose music. Those studying music will find differences with each composer's musical analysis, which differs depending on the culture and history of music studied. An analysis of music is meant to simplify the music for you.
*
Schenkerian analysis
**Schenkerian analysis is a collection of music analysis that focuses on the production of the graphic representation. This includes both analytical procedure as well as the notational style. Simply put, it analyzes tonal music which includes all chords and tones within a composition.
Philosophy
*
Philosophical analysis – a general term for the techniques used by philosophers
**Philosophical analysis refers to the clarification and composition of words put together and the entailed meaning behind them.
Philosophical analysis dives deeper into the meaning of words and seeks to clarify that meaning by contrasting the various definitions. It is the study of reality, justification of claims, and the analysis of various concepts. Branches of philosophy include logic, justification, metaphysics, values and ethics. If questions can be answered empirically, meaning it can be answered by using the senses, then it is not considered philosophical. Non-philosophical questions also include events that happened in the past, or questions science or mathematics can answer.
* ''
Analysis'' is the name of a prominent journal in philosophy.
Psychotherapy
*
Psychoanalysis – seeks to elucidate connections among unconscious components of patients' mental processes
*
Transactional analysis
** Transactional analysis is used by therapists to try to gain a better understanding of the unconscious. It focuses on understanding and intervening human behavior.
Policy
*
Policy analysis
Policy analysis is a technique used in the public administration sub-field of political science to enable civil servants, nonprofit organizations, and others to examine and evaluate the available options to implement the goals of laws and elected ...
– The use of statistical data to predict the effects of policy decisions made by governments and agencies
** Policy analysis includes a systematic process to find the most efficient and effective option to address the current situation.
*
Qualitative analysis – The use of anecdotal evidence to predict the effects of policy decisions or, more generally, influence policy decisions
Signal processing
*
Finite element analysis – a computer simulation technique used in engineering analysis
*
Independent component analysis
*
Link quality analysis – the analysis of signal quality
*
Path quality analysis Path quality analysis: In a communications path, an analysis that (a) includes the overall evaluation of the component quality measures, the individual link quality measures, and the aggregate path quality measures, and (b) is performed by evaluat ...
*
Fourier analysis
Statistics
In
statistics, the term ''analysis'' may refer to any method used
for
data analysis. Among the many such methods, some are:
*
Analysis of variance (ANOVA) – a collection of statistical models and their associated procedures which compare means by splitting the overall observed variance into different parts
*
Boolean analysis Boolean analysis was introduced by Flament (1976).Flament, C. (1976). "L'analyse booleenne de questionnaire", Paris: Mouton. The goal of a Boolean analysis is to detect deterministic dependencies between the items of a questionnaire or similar data- ...
– a method to find deterministic dependencies between variables in a sample, mostly used in exploratory data analysis
*
Cluster analysis – techniques for finding groups (called clusters), based on some measure of proximity or similarity
*
Factor analysis – a method to construct models describing a data set of observed variables in terms of a smaller set of unobserved variables (called factors)
*
Meta-analysis – combines the results of several studies that address a set of related research hypotheses
*
Multivariate analysis
Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable.
Multivariate statistics concerns understanding the different aims and background of each of the diff ...
– analysis of data involving several variables, such as by factor analysis, regression analysis, or principal component analysis
*
Principal component analysis – transformation of a sample of correlated variables into uncorrelated variables (called principal components), mostly used in exploratory data analysis
*
Regression analysis – techniques for analysing the relationships between several predictive variables and one or more outcomes in the data
*
Scale analysis (statistics) – methods to analyse survey data by scoring responses on a numeric scale
*
Sensitivity analysis – the study of how the variation in the output of a model depends on variations in the inputs
*
Sequential analysis – evaluation of sampled data as it is collected, until the criterion of a stopping rule is met
*
Spatial analysis – the study of entities using geometric or geographic properties
*
Time-series analysis
In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. ...
– methods that attempt to understand a sequence of data points spaced apart at uniform time intervals
Other
*
Aura analysis – a technique in which supporters of the method claim that the body's aura, or energy field is analysed
*
Bowling analysis
In cricket, a bowling analysis (sometimes shortened to just analysis, especially in the phrase innings analysis, and also referred to as bowling figures) usually refers to a notation summarising a bowler's performance in terms of overs bowled, h ...
– Analysis of the performance of
cricket players
*
Lithic analysis – the analysis of stone tools using basic scientific techniques
**Lithic analysis is most often used by archeologists in determining which types of tools were used at a given time period pertaining to current artifacts discovered.
*
Protocol analysis – a means for extracting persons' thoughts while they are performing a task
See also
*
Formal analysis
In art history, formalism is the study of art by analyzing and comparing form and style. Its discussion also includes the way objects are made and their purely visual or material aspects. In painting, formalism emphasizes compositional elements ...
*
Metabolism in biology
*
Methodology
*
Scientific method
References
External links
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{{Authority control
Abstraction
Critical thinking skills
Emergence
Empiricism
Epistemological theories
Intelligence
Mathematical modeling
Metaphysics of mind
Methodology
Ontology
Philosophy of logic
Rationalism
Reasoning
Research methods
Scientific method
Theory of mind