Analysis

Analysis (pl.: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. People have used this technique in the study of mathematics and logic since long before Aristotle, even though the idea of analysis as a special method is relatively new.

The word analysis comes from the Ancient Greek word ἀνάλυσις, meaning "a breaking-up" or "an untying." This idea also gives us the plural form, analyses.

Famous thinkers like René Descartes in his Discourse on the Method, Galileo Galilei, and Isaac Newton helped shape how we think about analysis today. The opposite of analysis is synthesis, which means putting the pieces back together again in a new or different whole.

Academic analysis

Academic analysis is a careful and organized way to study ideas, texts, data, or systems in school and research. It helps us understand things better, question our ideas, and add new knowledge by looking closely and thinking carefully. This way of studying is important in schools and research, and it follows rules for each subject area, uses checking by other experts, and uses special ideas and ways of thinking.

Different subjects use analysis in different ways. In subjects like history and literature, it often means looking at what something means, its background, and its ideas in texts and objects. In subjects like psychology and sociology, analysis might use words to describe patterns (like thematic analysis) or numbers to study how people act and societies work (like statistical analysis). In science, analysis often means testing ideas with math and checking real information again and again.

A key part of academic analysis is thinking about how our own ideas and ways of thinking might affect what we find. The result of academic analysis is usually a detailed argument written in a book, article, or long school paper, which other experts check to see if it makes sense and adds to what we know.

Humanities and social sciences

Linguistics

Linguistics is the scientific study of language. It looks at how languages are structured and used, including how we think and communicate with words. Linguists break down language into smaller parts to understand it better. They study how sounds are made and heard, how words are built, how sentences are formed, and what words mean.

Linguistics also looks at how languages change over time and how they are used in different cultures and social groups. It uses tools from computer science to model language and also studies how the brain processes language.

Literature

Literary criticism is the analysis of literature. One common way to study literature is called close reading. This method looks closely at small pieces of writing, like short poems, to understand how they work. It examines the patterns of sounds, the way sentences are built, and the figures of speech used to create effects.

Music

Musical analysis tries to understand how music is put together. It looks at how composers use notes to create pieces of music. Different composers and cultures have different ways of making music, and musical analysis helps simplify these ideas.

Schenkerian analysis is a way to study how music is structured graphically. It looks at all the chords and tones in a piece of music to understand its overall shape.

Philosophy

Philosophical analysis is a way philosophers study ideas. It clarifies the meanings of words and concepts. Philosophical analysis looks at what is real, what is right, and how we know things. It focuses on questions that cannot be answered just by looking or measuring but need deep thinking.

Analysis is also the name of a well-known philosophy journal.

Science and technology

Chemistry

See also: Analytical chemistry and List of chemical analysis methods

In chemistry, analysis helps us understand substances by breaking them into smaller parts. We can identify what a substance is made of (qualitative analysis), measure how much of each part exists (quantitative analysis), and study how chemicals react with each other. This is important in many areas, such as managing nuclear reactors, where scientists analyze elements to keep everything safe.

Types of Analysis

Qualitative Analysis
This helps us find out which parts are in a sample.

Quantitative Analysis
This helps us measure how much of each part is in a sample.

Isotopes

See also: Isotope analysis and Isotope geochemistry

Chemists use isotope analysis to study questions in many fields, like anthropology, archeology, food science, forensics, geology, and physical science. This helps us learn about the origins of natural and human-made materials.

Computer science

• Requirements analysis – figuring out what needs to be done for a new product
• Competitive analysis (online algorithm) – studying how computer programs perform
• Lexical analysis – turning letters into symbols a computer can understand
• Object-oriented analysis and design – planning how to build software using objects
• Program analysis (computer science) – studying how computer programs behave
• Semantic analysis (computer science) – checking meaning in code
• Static code analysis – checking code without running it
• Structured systems analysis and design methodology – planning software systems
• Syntax analysis – checking the structure of code
• Worst-case execution time – finding the longest time a program might take

Engineering

See also: Engineering analysis and Systems analysis

Engineers use analysis to study requirements, structures, systems, and designs. They look at how electrical systems work, how products last over time, and why systems might fail.

Mathematics

Main article: Mathematical analysis

Modern mathematical analysis studies endless processes and includes calculus. It helps us understand classic ideas like real numbers, complex numbers, and trigonometric functions, as well as newer ideas like infinity and vectors.

Florian Cajori explains the difference between modern and ancient mathematical analysis. In ancient times, analysis meant assuming something to find a truth, while synthesis proved it. The Greeks often used both methods to make sure their solutions were correct.

Psychotherapy

• Psychoanalysis – studying connections in a person's mind
• Transactional analysis
  Transactional analysis helps therapists understand behavior by looking at unconscious thoughts.

Signal processing

• Finite element analysis – a computer method used in engineering
• Independent component analysis
• Link quality analysis – checking signal quality
• Path quality analysis
• Fourier analysis

Statistics

In statistics, analysis means using methods to study data. Some common methods include:

• Analysis of variance (ANOVA) – comparing averages by splitting data
• Boolean analysis – finding links between variables
• Cluster analysis – grouping similar items together
• Factor analysis – building models with hidden factors
• Meta-analysis – combining results from many studies
• Multivariate analysis – studying many variables together
• Principal component analysis – simplifying data into main parts
• Regression analysis – studying links between variables
• Scale analysis (statistics) – scoring survey answers
• Sensitivity analysis – seeing how changes affect results
• Sequential analysis – checking data as it comes in
• Spatial analysis – studying geographic patterns
• Time-series analysis – studying data over time

Business

Business analysis is about understanding how a company works and finding ways to improve it. This can include looking at financial reports to see how well a business is doing, checking if a project is likely to succeed, or studying what customers want and how much they are willing to pay.

There are many types of analysis used in business, such as comparing current performance to goals, figuring out the best price for products, and looking at how different parts of a large company fit together. All these help businesses make smart decisions and solve problems.

Economics

Analysis in economics helps us understand how different parts of a system work together. For example, Agroecosystem analysis looks at how farming affects the environment. An Input–output model can show how changes in one area, like making more products, can impact other areas, such as jobs and services, in a specific region. This is often called the Regional Impact Multiplier System.

Government

Intelligence

See also: Intelligence analysis

Intelligence analysts help break down big questions to understand what’s happening. They use many tools like thinking through problems step-by-step, looking at how people are connected, and discussing ideas together. Military intelligence might look at strategies and plans in a structured way. Signals intelligence works to understand secret messages by studying patterns and codes. Business intelligence helps companies understand their competitors and the market. Law enforcement uses analysis to study crime patterns.

Policy

• Policy analysis – Using data to guess how government choices will work out
  • Policy analysis looks for the best way to solve problems using careful steps.
• Qualitative analysis – Using stories and examples to guess how decisions will work out or shape decisions

Other

Here are a few special ways people use the idea of analysis:

• Aura analysis – a special way some people think they can study the body’s energy field, though scientists don’t support it.
• Bowling analysis – looking at how cricket players do during games.
• Lithic analysis – studying old stone tools with science to learn about history.
• Protocol analysis – a way to understand what people are thinking while they do something.