Etymology
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analysis (n.)

1580s, "resolution of anything complex into simple elements" (opposite of synthesis), from Medieval Latin analysis (15c.), from Greek analysis "solution of a problem by analysis," literally "a breaking up, a loosening, releasing," noun of action from analyein "unloose, release, set free; to loose a ship from its moorings," in Aristotle, "to analyze," from ana "up, back, throughout" (see ana-) + lysis "a loosening," from lyein "to unfasten" (from PIE root *leu- "to loosen, divide, cut apart").

The meaning "statement presenting results of an analytic process" is from 1660s. The psychological sense is from 1890. English also formerly had a noun analyse (1630s), from French analyse, from Medieval Latin analysis. Phrase in the final (or last) analysis (1844), translates French en dernière analyse.

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statistical (adj.)

"pertaining to statistics," 1787, from statistics + -al (1). Related: Statistically.

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self-analysis (n.)

"analysis by or of oneself," 1860; see self- + analysis.

Trying to define yourself is like trying to bite your own teeth. [attributed to Alan Watts, who did often use the image in this sense in his talks, if not in these exact words]
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analyst (n.)

1650s, "one versed in algebraic analysis, mathematician skilled in algebraic geometry," from French analyste "a person who analyzes," from analyser, from analyse "analysis," from Medieval Latin analysis (see analysis). As a short form of psychoanalyst, attested from 1914; the one analyzed is an analysand (1933). Greek analyter meant "a deliverer."

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psychoanalysis (n.)

"the theory or therapy of treating mental disorders by investigating unconscious elements and bringing repressed fears and conflicts to the patient's awareness," from Psychoanalyse, coined 1896 in French by Freud from Latinized form of Greek psykhē "the soul, mind, spirit; understanding" (see psyche) + German Analyse, from Greek analysis (see analysis). Freud earlier used psychische analyse (1894).

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median (n.)

1540s, "a median part," originally anatomical, from Latin medianus "of the middle" (see median (adj.)). Statistical meaning "middle number of a series" is from 1883.

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emic (adj.)

"of or pertaining to analysis of cultural phenomena from the inside," 1954, from phonemic.

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predictor (n.)

"one who or that which predicts or foretells," 1650s, from Medieval Latin praedictor, agent noun from praedicere "foretell, advise, give notice" (see predict). Statistical sense is from 1950.

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analyze (v.)

c. 1600, of material things, "to dissect, take to pieces," from French analyser, from the noun analyse "analysis" (see analysis). Of literature, "examine critically to get the essence of," from 1610s; the meaning in chemistry ("resolve a compound into elements") dates from 1660s. The general sense of "to examine closely" dates from 1809; the psychological sense is by 1909. Related: Analyzed; analyzing.

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