Analysis

Analysis (pl.: analyses) is the process of breaking a complex topic or substance into smaller parts to better understand it. People have used this way of thinking in mathematics and logic for a long time, even before Aristotle.

Adriaen van Ostade, "Analysis" (1666)

The word analysis comes from the Ancient Greek word ἀνάλυσις, which means "a breaking-up" or "an untying." 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.

Academic analysis

Academic analysis is a careful way to study ideas, books, information, or systems in school and research. It helps us understand things better, ask questions about our ideas, and learn new facts by looking closely and thinking well. This way of studying is important in schools and research. It has rules for each subject, 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 books and objects. In subjects like psychology and sociology, analysis might use words to find 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 many times.

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

Humanities and social sciences

Linguistics

Linguistics is the study of language. It looks at how languages are made and used. Linguists study how sounds are made, how words are built, and how sentences are formed. They also look at how languages change over time and how they are used in different places and groups.

Literature

Literary criticism is the study of literature. One way to study literature is called close reading. This looks closely at small pieces of writing, like short poems, to see how they work. It checks the sounds, sentence structures, and figures of speech used.

Music

Musical analysis helps us understand how music is made. It looks at how composers use notes to create music. Different composers and cultures have different styles, and musical analysis helps explain these ideas.

Schenkerian analysis is a way to study music by looking at its chords and tones to see the overall shape of a piece.

Philosophy

Philosophical analysis is how philosophers study ideas. It helps make the meanings of words and concepts clearer. It looks at questions about what is real, what is right, and how we know things. These questions need deep thinking, not just looking or measuring.

Analysis is also the name of a famous philosophy journal.

Science and technology

Chemistry

In chemistry, analysis helps us understand substances by breaking them into smaller parts. We can see what a substance is made of (qualitative analysis) and measure how much of each part exists (quantitative analysis). 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

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

A clinical chemistry analyzer

Engineering

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.

Psychotherapy

Psychoanalysis – studying connections in a person's mind
Transactional analysis

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 learning how a company works and finding ways to make it better. This can mean looking at money reports to see how well a business is doing, checking if a project will work well, or finding out what customers want and how much they will pay.

There are many ways to analyze business, such as comparing what a company is doing now to its goals, deciding the best price for products, and seeing how different parts of a big company work together. These all help businesses make good choices and fix 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.

Government

Intelligence

Policy

Policy analysis – Using data to guess how government choices will work out
- Policy analysis finds the best way to solve problems with 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.