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Analysis

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Adriaen van Ostade,"Analysis" (1666)

Analysis(pl.:analyses) is the process of breaking acomplex topicorsubstanceinto smaller parts in order to gain a betterunderstandingof it. The technique has been applied in the study ofmathematicsandlogicsince beforeAristotle(384–322B.C.), thoughanalysisas a formal concept is a relatively recent development.[1]

The word comes from theAncient Greekἀνάλυσις(analysis,"a breaking-up" or "an untying;" fromana-"up, throughout" andlysis"a loosening" ).[2]From it also comes the word's plural,analyses.

As a formal concept, the method has variously been ascribed toRené Descartes(Discourse on the Method), andGalileo Galilei.It has also been ascribed toIsaac Newton,in the form of a practical method of physical discovery (which he did not name).

The converse of analysis issynthesis:putting the pieces back together again in a new or different whole.

Science and technology

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Chemistry

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A clinical chemistry analyzer

The field ofchemistryuses analysis in three ways: to identify the components of a particularchemical compound(qualitative analysis),[3]to identify the proportions of components in amixture(quantitative analysis),[4]and to break downchemical processesand examinechemical reactionsbetweenelementsofmatter.[5]For an example of its use, analysis of the concentration of elements is important in managing anuclear reactor,sonuclear scientistswill analyzeneutron activationto develop discrete measurements within vast samples. Amatrixcan 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 adevice.

Types of Analysis

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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

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Chemists can useisotope analysisto assist analysts with issues inanthropology,archeology,food chemistry,forensics,geology,and a host of other questions ofphysical science.Analysts can discern the origins of natural and man-made isotopes in the study ofenvironmental radioactivity.

Computer science

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Engineering

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Analysts in the field ofengineeringlook atrequirements,structures,mechanisms,systemsanddimensions.Electrical engineersanalysesystemsinelectronics.Life cyclesandsystem failuresare broken down and studied by engineers. It is also looking at different factors incorporated within the design.

Mathematics

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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 asreal numbers,complex variables,trigonometric functions,andalgorithms,or ofnon-classicalconcepts likeconstructivism,harmonics,infinity,andvectors.

Florian Cajoriexplains inA History of Mathematics(1893) the difference between modern and ancient mathematical analysis, as distinct from logical analysis, as follows:

The termssynthesisandanalysisare 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 [appended to]Euclid,XIII. 5, which in all probability was framed byEudoxus:"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 hisA 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 distinguishedtheoreticfromproblematicanalysis. A theoretic analysis is of the following kind. Toprovethat A is B,assumefirst 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 beconvertible,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.

Psychotherapy

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  • 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.[6]

Signal processing

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Statistics

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Instatistics,the termanalysismay refer to any method used fordata 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– 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– 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– methods that attempt to understand a sequence of data points spaced apart at uniform time intervals

Business

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Business

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Economics

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Government

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Intelligence

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The field ofintelligenceemploys analysts to break down and understand a wide array of questions.Intelligence agenciesmay useheuristics,inductiveanddeductive reasoning,social network analysis,dynamic network analysis,link analysis,andbrainstormingto sort through problems they face.Military intelligencemay explore issues through the use ofgame theory,Red Teaming,andwargaming.Signals intelligenceappliescryptanalysisandfrequency analysisto breakcodesandciphers.Business intelligenceapplies theories ofcompetitive intelligence analysisandcompetitor analysisto resolve questions in themarketplace.Law enforcementintelligence applies a number of theories incrime analysis.

Policy

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  • Policy analysis– 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.[7]
  • Qualitative analysis– The use of anecdotal evidence to predict the effects of policy decisions or, more generally, influence policy decisions

Humanities and social sciences

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Linguistics

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Linguisticsexplores individual languages andlanguagein general. It breaks language down and analyses its component parts:theory,sounds and their meaning,utterance usage,word origins,thehistory of words,the meaning ofwordsandword combinations,sentence construction,basic construction beyond the sentence level,stylistics,andconversation.It examines the above usingstatistics and modeling,andsemantics.It analyses language in context ofanthropology,biology,evolution,geography,history,neurology,psychology,andsociology.It also takes theappliedapproach, looking atindividual language developmentandclinicalissues.

Literature

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Literary criticismis the analysis ofliterature.The focus can be as diverse as the analysis ofHomerorFreud.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 labelledThe New Criticism,approaches texts – chiefly short poems such assonnets,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 ofprosody(the formal analysis of meter) and phonic effects such asalliterationandrhyme,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.

Music

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  • 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.[8]
  • 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.[9]Simply put, it analyzes tonal music which includes all chords and tones within a composition.[8]

Philosophy

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  • 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.[10]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.[10]
  • Analysisis the name of a prominent journal in philosophy.

Other

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  • Aura analysis– apseudoscientifictechnique in which supporters of the method claim that the body's aura, or energy field is analysed
  • Bowling analysis– Analysis of the performance ofcricketplayers
  • 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.[11]
  • Protocol analysis– a means for extracting persons' thoughts while they are performing a task

See also

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References

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  1. ^Beaney, Michael (Summer 2012)."Analysis".The Stanford Encyclopedia of Philosophy.Metaphysics Research Lab, Stanford University.Retrieved23 May2012.
  2. ^Douglas Harper (2001–2012)."analysis (n.)".Online Etymology Dictionary.Douglas Harper.Retrieved23 May2012.
  3. ^"Qualitative Analysis"(PDF).Archived(PDF)from the original on 9 October 2022.
  4. ^OpenStaxCollege (2 October 2014)."Quantitative Chemical Analysis".{{cite journal}}:Cite journal requires|journal=(help)
  5. ^"CHEMICAL AND BIOMOLECULAR ENGINEERING"(PDF).Spring 2018.Archived(PDF)from the original on 9 October 2022.
  6. ^Hargaden, Helena; Sills, Charlotte (23 April 2014).Transactional Analysis.doi:10.4324/9781315820279.ISBN9781315820279.
  7. ^"Dye, Dr Christopher",Who's Who,Oxford University Press, 1 December 2012,doi:10.1093/ww/9780199540884.013.256626
  8. ^abWarfield, Scott (November 2014). "Lady in the Dark: Biography of a Musical. By bruce d. mcclung. Oxford: Oxford University Press, 2007. - Oklahoma!: The Making of an American Musical. By Tim Carter. New Haven, CT: Yale University Press, 2007. - South Pacific: Paradise Rewritten. By Jim Lovensheimer. Oxford: Oxford University Press, 2010. - Wicked: A Musical Biography. By Paul R. Laird. Lanham, MD: Scarecrow Press, 2011".Journal of the Society for American Music.8(4): 587–596.doi:10.1017/s1752196314000443.ISSN1752-1963.S2CID232401945.
  9. ^Neumeyer, David (2018)."Guide to Schenkerian Analysis".doi:10.15781/T2D21S443.{{cite journal}}:Cite journal requires|journal=(help)
  10. ^abHospers, John (15 April 2013).An Introduction to Philosophical Analysis.doi:10.4324/9780203714454.ISBN9780203714454.
  11. ^McCall, Grant (March 2012). "In Memory of George H. Odell".Lithic Technology.37(1): 3–4.doi:10.1179/lit.2012.37.1.3.ISSN0197-7261.S2CID108647958.
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