izzako/sundanese-pixelgpt huggingface dataset:
Korelasi ρxy antara dua variabel acak "X" and "Y" jeung nilai ekspektasi μX jeung μY sarta simpangan baku σX jeung σY dihartikeun: formula_1 Anggap μX=E(X), σX2=E(X2)-E2(X) tur saperti keur Y, bisa ogé dituliskeun jadi: formula_2 Korélasi bisa dihartikeun lamun simpangan baku kawengku tur salah sahijina lain enol
Rumusan itu dina kateusaruaan Cauchy-Schwarz yén korelasi teu bisa leuwih ti 1 dina nilai mutlakna
Korelasi sarua jeung 1 lamun mibanda hubungan naek sacara liner, −1 lamun mibanda hubungan turun linier, tur sababaraha nilai di antarana keur sakabéh pasualan, nunjukkeun tingkat sakumaha gumantungna variabel sacara linier
Koefisien nu pangdeukeutna boh kana −1 atawa 1, mibanda harti beuki kuat korelasi antara dua variabel eta
Lamun variabel mandiri mangka korelasina bakal 0, tapi teu salawasna bener sabab koefisien korelasi ngan keur néangan kabébasan linier antara dua variabel
Contona: Anggap variabel acak "X" mangrupa sebaran seragam dina interval ti −1 ka 1, sarta "Y" = "X"2
Mangka "Y" satemenna ditangtukeun ku "X", sabab kitu "X" tur "Y" bisa waé asalna tina dua variabel acak mandiri, tapi korelasi nol; maranéhna taya korelasi
Sanajan kitu, dina kasus basa "X" tur "Y" ngahiji normal, mandiri sarua jeung taya korelasi
Lamun hiji runtuyan "n" tina hasil ngukur "X" tur "Y" dituliskeun salaku "xi" tur "yi" nu mana "i" = 1, 2, ..., "n", mangka koefisien korelasi produk-momen Pearson bisa dipaké keur ngiker korelasi "X" jeung "Y"
Koefisien Péarson disebut ogé "koefisien korelasi sampel"
Hal ieu husus lamun "X" tur "Y" duanana kasebar normal
Koefisien korelasi Péarson jadi estimasi nu hadé keur korelasi "X" jeung "Y"
Koefisien korelasi Péarson ditulis: formula_3 nu mana formula_4 jeung formula_5 nyaéta rata-rata tina "xi" jeung "yi" , "s""x" jeung "s""y" nyaéta simpangan baku tina "xi" jeung "yi" sarta jumlahna ti "i" = 1 nepi ka "n"
Saperti dina korelasi populasi, bisa ditulis salaku formula_6 Sakali deui, ieu bener dina korelasi populasi, gedéna nilai mutlak sampel korelasi kudu kurang atawa sarua jeung 1. ngagunakeun rumus di luhur mangrupa hal nu ilahar dipaké dina algoritma tunggal keur ngitung korelasi sampel, hal ieu teu stabil dina itungan sacara numerik (tempo di handap keur nu leuwih jéntré)
Kuadrat koefisien korelasi sampel, disebut ogé koefisien determinasi, nyaéta bagéan tina varian dina "yi" nu diitung ku cara fit linier "xi" ka "yi"
Ditulis formula_7 nu mana "s""y"|"x"2 nyaéta kuadrat kasalahan régrési liniér "xi" dina "yi" ku sasaruan "y = a + bx": formula_8 jeung "s""y"2 nyaéta ngan varian "y": formula_9 Catetan, lamun koéfisien sampel korélasi simetri dina "xi" jeung "yi" , bakal meunang niley nu sarua keur fit "yi" ka "xi" : formula_10 Ieu sasaruan méré ide keur dimensi nu leuwih luhur
Saperti nu dijelaskeun di luhur korélasi koéfsien sampel nyaéta bagéan tian itungan varian ku cara nga-fit-keun linear submanifold 1-dimensi kana runtuyan vektor ("xi" , "yi" ) 2 dimensi, mangka bisa dihartikeun koefisien korelasi keur fit dina "m"-dimensi linéar submanifold kana runtuyan vektor "n"-dimensi
Contona, lamun nga-fit-keun widang "z = a + bx + cy" kana runtuyan data ("xi" , "yi" , "zi" ) mangka koefisien korelasi "z" ka "x" jeung "y" nyaéta formula_11 Sebaran koefisien korelasi geus diterangkeun ku R. A. Fisher jeung A. K. Gayen
Interpretasi korélasi sacara geometri
Koéfisién korélasi bisa ogé ditempo salaku kosinus sudut antara dua vektor sampel nu dicokot tina dua variabel acak
Caution: This method only works with centered data, i.e., data which have been shifted by the sample méan so as to have an average of zero
Some practitioners prefer an uncentered (non-Péarson-compliant) correlation coefficient
See the example below for a comparison
As an example, suppose five countries are found to have gross national products of 1, 2, 3, 5, and 8 billion dollars, respectively
Suppose these same five countries (in the same order) are found to have 11%, 12%, 13%, 15%, and 18% poverty
Then let x and y be ordered 5-element vectors containing the above data: x = (1, 2, 3, 5, 8) and y = (0.11, 0.12, 0.13, 0.15, 0.18)
By the usual procedure for finding the angle between two vectors (see dot product), the "uncentered" correlation coefficient is: formula_12 Note that the above data were deliberately chosen to be perfectly correlated: "y" = 0.10 + 0.01 "x"
The Péarson correlation coefficient must therefore be exactly one
Centering the data (shifting x by E(x) = 3.8 and y by E(y) = 0.138) yields x = (-2.8, -1.8, -0.8, 1.2, 4.2) and y = (-0.028, -0.018, -0.008, 0.012, 0.042), from which formula_13 as expected
Interpretation of the size of a correlation
Several authors have offered guidelines for the interpretation of a correlation coefficient
Cohen (1988), for example, has suggested the following interpretations for correlations in psychological reséarch, in the table on the right
As Cohen himself has observed, however, all such criteria are in some ways arbitrary and should not be observed too strictly
This is because the interpretation of a correlation coefficient depends on the context and purposes
A correlation of 0.9 may be very low if one is verifying a physical law using high-quality instruments, but may be regarded as very high in the social sciences where there may be a gréater contribution from complicating factors
Non-parametric correlation coefficients
Péarson's correlation coefficient is a parametric statistic and when distributions are not normal it may be less useful than non-parametric correlation methods, such as Chi-square, Point biserial correlation, Spearman's ρ and Kendall's τ
They are a little less powerful than parametric methods if the assumptions underlying the latter are met, but are less likely to give distorted results when the assumptions fail
Other measures of dependence among random variables
To get a méasure for more general dependencies in the data (also nonlinéar) it is better to use the correlation ratio which is able to detect almost any functional dependency, or mutual information/total correlation which is capable of detecting even more general dependencies
The polychoric correlation is another correlation applied to ordinal data that aims to estimate the correlation between théorised latent variables
Copulas and correlation
The information given by a correlation coefficient is not enough to define the dependence structure between random variables; to fully capture it we must consider a copula between them
The correlation coefficient completely defines the dependence structure only in very particular cases, for example when the cumulative distribution functions are the multivariate normal distributions
In the case of elliptic distributions it characterizes the (hyper-)ellipses of equal density, however, it does not completely characterize the dependence structure (for example, the a multivariate t-distribution's degrees of freedom determine the level of tail dependence)
The correlation matrix of "n" random variables "X"1, ..., "X""n" is the "n" × "n" matrix whose "i","j" entry is corr("X""i", "X""j")
If the méasures of correlation used are product-moment coefficients, the correlation matrix is the same as the covariance matrix of the standardized random variables "X""i" /SD("X""i") for "i" = 1, ..., "n"
Consequently it is necessarily a positive-semidefinite matrix
The correlation matrix is symmetric because the correlation between formula_14 and formula_15 is the same as the correlation between formula_15 and formula_14
It is always possible to remove the correlation between zero-méan random variables with a linéar transform, even if the relationship between the variables is nonlinéar
Suppose a vector of "n" random variables is sampled "m" times
Let "X" be a matrix where formula_18 is the "j"th variable of sample "i"
Let formula_19 be an "r" by "c" matrix with every element 1
Then "D" is the data transformed so every random variable has zero méan, and "T" is the data transformed so all variables have zero méan, unit variance, and zero correlation with all other variables
formula_20 formula_21 where an exponent of -1/2 represents the matrix square root of the inverse of a matrix
The covariance matrix of "T" will be the identity matrix
If a new data sample "x" is a row vector of "n" elements, then the same transform can be applied to "x" to get the transformed vectors "d" and "t": formula_22 formula_23 Common misconceptions about correlation
Correlation and causality
The conventional dictum that "correlation does not imply causation" méans that correlation cannot be validly used to infer a causal relationship between the variables
This dictum should not be taken to méan that correlations cannot indicate causal relations
However, the causes underlying the correlation, if any, may be indirect and unknown
Consequently, establishing a correlation between two variables is not a sufficient condition to establish a causal relationship (in either direction)
Here is a simple example: hot wéather may cause both crime and ice-créam purchases
Therefore crime is correlated with ice-créam purchases
But crime does not cause ice-créam purchases and ice-créam purchases do not cause crime
A correlation between age and height in children is fairly causally transparent, but a correlation between mood and héalth in péople is less so
Does improved mood léad to improved héalth
Or does good héalth léad to good mood
Or does some other factor underlie both
Or is it pure coincidence
In other words, a correlation can be taken as evidence for a possible causal relationship, but cannot indicate what the causal relationship, if any, might be
Correlation and linearity
While Péarson correlation indicates the strength of a linéar relationship between two variables, its value alone may not be sufficient to evaluate this relationship, especially in the case where the assumption of normality is incorrect
The image on the right shows scatterplots of Anscombe's quartet, a set of four different pairs of variables créated by Francis Anscombe
The four formula_24 variables have the same méan (7.5), standard deviation (4.12), correlation (0.81) and regression line (formula_25)
However, as can be seen on the plots, the distribution of the variables is very different
The first one (top left) seems to be distributed normally, and corresponds to what one would expect when considering two variables correlated and following the assumption of normality
The second one (top right) is not distributed normally; while an obvious relationship between the two variables can be observed, it is not linéar, and the Péarson correlation coefficient is not relevant
In the third case (bottom left), the linéar relationship is perfect, except for one outlier which exerts enough influence to lower the correlation coefficient from 1 to 0.81
Finally, the fourth example (bottom right) shows another example when one outlier is enough to produce a high correlation coefficient, even though the relationship between the two variables is not linéar
These examples indicate that the correlation coefficient, as a summary statistic, cannot replace the individual examination of the data
Computing correlation accurately in a single pass
The following algorithm (in pseudocode) will estimate correlation with good numerical stability sum_sq_x = 0 sum_sq_y = 0 sum_coproduct = 0 méan_x = x[1] méan_y = y[1] for i in 2 to N: sweep = (i - 1.0) / i delta_x = x[i] - méan_x delta_y = y[i] - méan_y sum_sq_x += delta_x * delta_x * sweep sum_sq_y += delta_y * delta_y * sweep
+= delta_y * delta_y * sweep sum_coproduct += delta_x * delta_y * sweep méan_x += delta_x / i méan_y += delta_y / i pop_sd_x = sqrt( sum_sq_x / N ) pop_sd_y = sqrt( sum_sq_y / N ) cov_x_y = sum_coproduct / N correlation = cov_x_y / (pop_sd_x * pop_sd_y) For an enlightening experiment, check the correlation of {900,000,000 + i for i=1...100} with {900,000,000
+ i for i=1...100} with {900,000,000 - i for i=1...100}, perhaps with a few values modified
Poor algorithms will fail
Dina matematik, fungsi béta, mimitina disebut ogé integral Euler, nyaéta hiji fungsi husus nu dihartikeun ku formula_1 Fungsi béta nyaéta simétrik, hartina formula_2 mibanda bentuk séjén, kaasup: formula_3 formula_4 formula_5 formula_6 nu mana ("x")"n" nyaéta falling factorial
Tempo ogé: integral Euler, falling factorial, fungsi gamma
Dina matematik, sebaran seragam nyaéta probability distribution sederhana
Sebaran bisa discrete atawa continuous
Dina kasus "diskrit", bisa di-karakterisasi ku nyebutkeun yén sakabéh nilai sarua kamungkinanna
Dina kasus "kontinyu" yén sakabéh panjang interval nu sarua mibanda kamungkinan nu sarua
Variabel random nu mibanda unggal nilai "n" nu mungkin "x"1, "x"2, ..., "x""n" mibanda kamungkinan nu sarua dina sebaran seragam diskrit, saterusna kamungkinan keur unggal hasil "x""i" nyaéta 1/"n"
Conto gampang dina sebaran seragam diskrit nyaéta ngalungkeun dadu
Nilai nu mungkin "x" nyaéta 1, 2, 3, 4, 5, 6; dina unggal alungan, kamungkinan salah sahiji nilai muncul nyaéta 1/6
Dina kasus nilai variabel random nu mibanda sebaran normal mangrupa riil, ngamungkinkeun keur ngagambarkeun fungsi kumulatif sebaran dina watesan "degenarate" sebaran, nyaéta formula_1 nu mana Héavyside step function θ("x") mangrupa CDF tina degenerate sebaran dina "x" = 0
Dina kasus kontinyu, sebaran seragam disebut ogé sebaran bujursangkar sabab bentuk tina fungsi densiti probabiliti (tempo di handap)
Hal ieu di-paraméterisasi ku nilai pangleutikna jeung panggedéna tina kaseragaman-sebaran random variable nu dicokot nyaéta "a" jeung "b"
Probability density function sebaran seragam nyaéta: formula_2 sarta cumulative distribution function nyaéta: formula_3 Grapik pungsi densiti probabiliti keur sebaran seragam siga di handap ieu: Pungsi densiti probabiliti tina sebaran seragam kontinyu Keur random variable nu nuturkeun sebaran ieu, nilai ekspektasi nyaéta (a + b)/2 sarta simpangan baku nyaéta (b - a)/√12
Sebaran ieu bisa dipaké keur susunan nu leuwih kompleks tinimbang interval
Lamun "S" mangrupa susunan Borel positip, ukuran "terhingga", sebaran probabiliti seragam dina "S" bisa dihusukeun ku nyebutkeun yén pdf nyaéta nol di luar "S" sarta sacara angger sarua jeung 1/"K" dina "S", nu mana "K" ukuran Lebesgue tina "S"
Standar sebaran seragam
"Standard sebaran seragam" nyaéta sebaran seragam kontinyu nu mibanda susunan nilai "a" jeung "b" nyaéta 0 jeung 1, mangka nilai variabel random ngan antara 0 jeung 1
Sampling tina sebaran seragam
Waktu digawe maké probabiliti, karasa mangpaatna keur nga-run percobaan saperi dina simulasi komputer
Loba programming language nu mibanda kamampuan keur nyaruakeun pseudo-random numbers nu epektip kasebar dumasar kana standar sebaran seragam
Lamun "u" mangrupa nilai sampel tina standar sebaran seragam , mangka nilai "a" + ("b" - "a")"u" nuturkeun sebaran seragam nu di-paraméterisasi ku "a" jeung "b", saperti nu dijelaskeun di luhur
Transpromasi séjénna bisa digunakeun keur nyaruakeun sebaran statistik séjénna tina sebaran seragam (tempo "pamakean" di handap) Pamakean sebaran seragam
Dina statistik, lamun p-value dipaké salaku tes statistik keur null hypothesis sederhana, jeung sebaran test statistik kontinyu , mangka tes statistik bakal kasebar seragam antara 0 jeung 1 lamun null hypothesis bener
Sanajan sebaran seragam teu ilahar kapanggih di alam, sabagéanna bisa dipaké keur sampling tina sebaran acak
métodeu nu geus ilahar nyaéta inverse transform sampling method, nu maké cumulative distribution function (CDF) tina target variabel random
métodeu ieu kacida ngabantu dina pagawéan tioritis
Saprak simulasi maké métodeu ieu merlukeun "inverting" CDF tina variabel target, métodeu alternatipna geus dibagi keur kasus nu mana CDF teu dipikanyaho dina bentuk raket
Salah sahiji métodeu na nyaéta rejection sampling
Sebaran normal mangrupa conto penting mangsa métodeu "inverse transform" teu episien
Sanajan kitu, éta mangrupa métodeu eksak, Box-Muller transformation, nu maké "inverse transform" keur konversi dua random variable seragam bébas ka dua sebaran normal random variabel bébas
Jejer ieu ngagambarkeun tiori central limit ngaliwatan conto keur "penghitungan" bisa diitung sacara gancang ku leungeun dina kertas, teu saperti conto-intesip dina jejer gambaran dina teorema central limit
Anggap sebaran probabiliti variabel random "X" beuratna sarua dina 1, 2, jeung 3: formula_1 Fungsi probabiliti massa tina variabel random "X" digambarkeun ku: o o o 1 2 3 Katembong jelas teu siga kurva bentuk-bel
Ayeuna tempo jumlah dua kopi-an "X" bébas: formula_2 Fungsi probabiliti massa tina jumlah ieu digambarkeun ku: o o o o o o o o o 2 3 4 5 6 Ieu ogé can katembong leuwih siga tina kurva bentuk-bell, tapi, saperti bentuk-bel sarta teu saperti fungsi probabiliti massa "X" éta sorangan, leuwih luhur dibagian tengah tinimbang di dua sisina
Ayeuna tempo jumlah "tilu" kopian bébas ieu random variabel: formula_3 Fungsi probabiliti tina jumlah ieu digambarkeun ku: o o o o o o o o o o o o o o o o o o o o o o o o o o o 3 4 5 6 7 8 9 Ieu heunteu ngan leuwih gedé di tengah tinimbang dua sisina, tapi pindah ka
tinimbang dua sisina, tapi pindah ka arah tengah ti sisi nu séjén, miring nu mimiti naek sarta saterusna turun, siga kurva bentuk-bel
Urang bisa ngitung tingkatna tina susnan kana kurva bentuk-bel siga di handap ieu
Tempo Pr("X"1 + "X"2 + "X"3 ≤ 7) = 1/27 + 3/27 + 6/27 + 7/27 + 6/27 = 23/27 = 0.851 851 851 ...
Sakumaha raket hal ieu ngadeukeutan kana normal
Ieu bisa ditempo tina nilai ekspektasi "Y" = "X"1 + "X"2 + "X"3 nyaéta 6 sarta simpangan baku "Y" mangrupa akar kuadrat 2
Saprak "Y" ≤ 7 (kateusaruaan lemah) lamun jeung lamun "Y" &lt; 8 (kateusaruaan kuat), bisa maké koreksi kontinyu sarta ditembongkeun ku formula_4 nu mana "Z" mangrupa standar normal sebaran
béda antara 0.85185... sarta 0.8556... katempo beuki ngaleutikan waktu éta ditempo salaku wilangan variabel random bébas nu ditambahkeun ngan tilu
Conto dina simulasi
Gambar di handap nembongkeun hasil simulasi dumasar kana conto di luhur
Data dicokot tina sebaran seragam ku cara "pengulangan" 1'000 kali tur hasilna dijumlahkeun
Conto ieu dumasar kana [Monte Carlo method], prosés "pengulanganna" 10'000 kali
Hasilna nembongkeun yén sebaran jumlah 1'000 nu dicokot sacara saragam nembongkeung bentuk kurva nu siga bel kacida alusna
Wikipedia Basa Inggris, disunting panungtung, 24 Juli 2006
Diberekeun dua sebaran gabungan variabel random "X" jeung "Y", sebaran kondisional probabiliti of "Y" given "X" (written ""Y" | "X"") is the probability distribution of "Y" when "X" is known to be a particular value
For discrete random variables, the conditional probability mass function can be written as "P"("Y" = "y" | "X" = "x")
From the definition of conditional probability, this is formula_1 Similarly for continuous random variables, the conditional probability density function can be written as "p""Y"|"X"("y" | "x") and this is formula_2 where "p""X","Y"(x, y) gives the joint distribution of "X" and "Y", while "p""X"("x") gives the marginal distribution for "X"
The concept of the conditional distribution of a continuous random variable is not as intuitive as it might seem: Borel's paradox shows that conditional probability density functions need not be invariant under coordinate transformations
If for discrete random variables "P"("Y" = "y" | "X" = "x") = "P"("Y" = "y") for all "x" and "y", or for continuous random variables "p""Y"|"X"("y" | "x") = "p""Y"("y") for all x and y, then "Y" is said to be independent of "X" (and this implies that "X" is also independent of "Y")
Seen as a function of "y" for given "x", "P"("Y" = "y" | "X" = "x") is a probability and so the sum over all "y" (or integral if it is a density) is 1
Seen as a function of "x" for given "y", it is a likelihood, so that the sum over all "x" need not be 1
Analisa conjoint, disebut modél komposisi multi-attribute, nyaéta téhnik statistik nu aslina tina mathematical psychology
Ayeuna dipaké di loba widang social science jeung applied science kaasup marketing, product management, jeung operations research
"Tempo oge": Conjoint analysis (in marketing)
Dina statistik proses kontrol, kontrol chart, disebut ogé 'Shewhart chart' atawa 'chart prosés-paripolah' nyaéta alat nu dipaké di proses pabrik atawa bisnis keur nangtukeun aya dina statistical control atawa henteu
Lamun chart nembongkeun yén prosés nu ditempo aya di luar control, mangka pola nu aya mantuan keur nangtukeun sumberna variasi keur ngurangan kasalahan nu aya tur malikeun deui kana kaayaan nu bisa dikontrol
Kontrol chart mangrupa hal nu husus tina run chart
Kontrol chart salah sahiji tina tujuh alat dasar kontrol kualitas (nu maké histogram, Pareto chart, check sheet, cause-and-effect diagram, flowchart, sarta scatter diagram)
Tempo watesan manajemen kualitas
Kontrol chart geus dipaké ku Walter A. Shewhart basa digawe di Laboratorium Bell dina taun 1920
Teknisi perusahaan geus ngagunakeun keur naekeun kapercayaan sistim transmisi telepon
Sabab amplifier jeung alat séjén dikubur di taneuh, parusahaan hayang ngurangan kajadian kasalahan jeung ngoméan
Dina 1920 maranéhna geus ngagunakeun hal nu penting keur ngurangan varian dina prosés produksi
Sanajan kitu, maranéhna ngagunakeun keur ngapaskeun prosés nu lumangsung terus dina usaha lain keur naekuen variasi jeung nurunkeun kualitas
Pasualan rangka Shewhart dina watesan variasi Common- and special-causes jeung dina 16 May 1924, nulis catetan internal pikeun ngawanohkeun kontrol chart salaku alat keur ngabédakeun antara dua
Pingpinan Dr. Shewhart, Géorge Edwards, nyebutkeun: "Dr. Shewhart nyiapkeun catetan leutik nu ngan salembar panjangna
Ngeunaan sapertilu kaca ngajelaskeun diagram nu sederhana nu kiwari bisa disebutkeun salaku skema kontrol
Ieu diagram dimimitian tur dituluykeun ku tulisan nu pondok, sakabehna mangrupa prinsip penting tur anggpan nu kiwari sibuet kontrol proses kualitas."
Shewhart negeskeun yén perluna prosés produksi ditangtukeun dina statistical control,nu mana ngan sakadar variasi sabab-ilahar, diaping dina kontrol, mangrupa hal nu penting keur ngaramalkeun hasil produksi nu bakal datang jeung ngatur prosés sacara ekonomi
Dr. Shewhart nyieun dasar keur kontrol chart tur konsép nangtukeun statistik kontrol dumasar kana rancangan percobaan nu taliti
Sedengkeun Dr. Shewhart ngagambarkeun téori matematika murni, manéhna ngarti data tina prosés fisik teu pernah ngahasilkeun "kurva sebaran normal" (Gaussian distribution, nu ilahar disebut ogé "bell curve")
manéhna manggih yén variasi nu ditempo dina data produksi teu salawasna mobanda sifat nu sarua dina gerak partikel alami (partikel Brownian motion)
Dr. Shewhart nyimpulkeun yén unggal prosés nembongkeun variasi, sababaraha prosés nembongkeun dikontrol ku variasi mangrupa hal nu alami dina prosés, sedengkeun nu séjénna teu ka kontrol ku variasi nu aya salila prosés ku sabab sistimna
Dina taun 1924 atawa 1925, inovasi Shewhart ditalungtik kalayan taliti ku W. Edwards Deming, saterusna digawe di fasilitas Hawthorne
Deming saterusna digawe di Departemen Pertanian Amerika sarta jadi pengarah matematika keur Badan Sensus Amerika
Dina satengah abad saterusna, Deming jadi kawentar tur ahli dina pagawéan Shewhart
Sanggeus ngéléhkeun Jepang di tungtung Perang Dunya Kadua, Deming jadi konsultan statistik keur Supreme Commander of the Allied Powers
Saterusna loba pakait jeung gaya hirup loba Jepang, sarta karirna lila salaku konsultan industri di ditu, nyebarkeun pangaweruh Shewhart, jeung ngagunakeun kontrol chart, dipaké di industri manufaktur Jepang antara 1950 jeung 1960
Leuwih bihari dipaké tur diwangun kontrol chart dina tradisi Shewhart-Deming diteruskeun ku Donald J. Wheeler
Grafik kadali kawangun ku: Grafik ogé mibanda tampilan séjén, kaasup: Lamun prosés dina kadali, loba titik bakal diplot dina wates kadali
Aya panempo di luar wates, atawa dina pola sistimatik, jadi tanda mimiti ayana parobahan (sarta kudu tarapti kana nu teu sarimbag) sumber variasi, disebutna pasualan-husus
Naekna variasi hartina naekna beaya, grafik kadali "mere tanda" ayana hal ieu nu saterusna merlukeun panalungtikan
Cateta dina praktis, méan prosés dina watesan-panjang (sarta sabab garis tengah) bisa teu pasti pas kana nilai idéal (atawa target) karakter kualtias sabab alat sederhana teu bisa ngadalikeun prosés keur ngahasilkeun produk nu diharepkeun atawa sabab mahal kacida lamun dipaké kana prosés prosés keur target nu dipihayang
Grafik kadali ngawenangkeun watesan husus sabab nujul kana naon nu dipikahayang dina éta prosés (upamana operator mesin) nu museurkeun kana tampilan husus waktu ngagawekeun nu dipesen keur ngajaga sasaeutik mungkin dina variasi prosés
Sacara ilahar leuwih gampang keur nyimpen hiji prosés kana target tinimbang ngajaga kateusaruaan tina prosés tur ngawenangkeun watesan husus keur hiji produk
Kamampu proses nalungtik pakaitna antara watesan prosés alamat (nu ngajaga wates kadali) sarta watesan husus tadi
Perluna nambahkeun wates awas atawa ngabagi grafik kadali kana sababaraha bagéan nyaéta keur nyiapkeun lamun aya hal nu salah saméméhna
Gaganti nerangkeun hiji prosés usaha nyaéta keur nangtukeun kasus husus nu aya, Teknisi Kualitas kadangkala naekeun tingkatna dina nyokot sampel nepi ka jelas kaluarna hiji produk bener-bener bisa dikadalikeun
Catetan yén tilu wates sigma, nu disangka bakal jadi tanda deukeutna ampir kaluar unggal 370 titik tina rata-rata, ngan gumantung kana pasualan-ilahar
Susunan wates Shewhart "3-sigma" dumasar kana hal di handap ieu
Shewhart meunang kasimpulan ku nyebutkeun: "... the fact that the criterion which we happen to use has a fine ancestry in highbrow statistical theorems does not justify its use
Such justification must come from empirical evidence that it works
As the practical engineer might say, the proof of the pudding is in the eating."
Ngaliwatan percobaan mimiti nu mana watesan dumasar kana sebaran probabilitas, Shewhart nuliskeun sacara pasti: "Some of the earliest attempts to characterise a state of statistical control were inspired by the belief that there existed a special form of frequency function" f "and it was early argued that the normal law characterised such a state
When the normal law was found to be inadequate, then generalised functional forms were tried
Today, however, all hopes of finding a unique functional form" f "are blasted."
Grafik kadali dijieun keur kaperluan dirina sorangan
Deming nambahan yén taya tes hipothesa tur taya motivasi tina Neyman-Pearson lemma
Pendapatna yén gabungan alami dina populasi jeung rarancang nyokot sampel dina lolobana industri leuwih remen ngagunakeun téhnik statistik konvensional
Deming museurkeun keur nempo leuwih teleb kana sistim akibar dina prosés "...under a wide range of unknowable circumstances, future and past ..."
manéhna nyebutkeun yén dina sababaraha kaayaan ieu, watesan "3-sigma" diperlukeun keur "... a rational and economic guide to minimum economic loss..." tina dua kasalahan: Ngitung simpangan baku
Saperti dina itungan watesan kadali, simpangan baku diperlukeun keur variasi pasualan-ilahar dina prosés
Saprak panaksir ilahar dina watesan sampel varin teu dipaké keur naksir leungitna jumlah kuadrat kasalahan tina variasi pasualan ilahar jeung husus
métodeu alternatif séjén dipaké keur nangtukeun pakaitna antara rentang sampel jeung simpangan bakuna dijéntrékeun ku Leonard H. C. Tippett, panaksir nujul kana kurangna pangaruh ku panempo ekstrim nu ngagambarkeun pasualan husus
Aturan dina nalungtik tanda
Susunan nu ilahar nyaéta: Aya sababaraha nu kontroversi salila ngajalankeun hiji panempo, sakabéhna aya dina sisi nu sarua tina garis tengah, kudu diitung salaku tanda ku 7, 8 sarta 9 keur mantuan sababaraha penulis
Prinsip nu leuwih penting nyaéta keur milih hiji aturan susunan nu dipilih bakal dijieun saméméh data dipariksa
Milih aturan saprak data geus katempo nujul kana naekna kaleungitan ekonomi naek tina "kasalahan 1" ngawenangkeun keur ngetes efek nu dipangaruhan ku data
Dina taun 1935, Institusi British Standards, dina pangaruh Egon Pearson jeung patojaiah kana sumanget Shewhart, ngasupkeun grafik kontrol, ngagantikeun watesan "3-sigma" dumasar kana watesan percentile dina sebaran normal
Hal ieu diteruskeun saperti nu dijéntrékeun ku John Oakland jeung nu lianna tapi dikutuk raraméan ku anu nulis tradisi Shewhart-Deming
Tampilan kontrol charts
Waktu hiji titik ragrag di luareun wates nu geus aya tina grafik kontrol nu ditangtukeun, mangka ieu tanggung jawab keur prosés nu keur lumangsung disangka keur nangtukeun hiji pasualan nu bakal kajadian
Lamun salah sahiji mibanda, saterusna ieu pasualan kudu dikurangan upama bisa
Ieu dipikanyaho yén lamun kajadian dina prosés "bisa dikadalikeun" (taya kasus husus nu kapanggih dina ieu sistim), hal ieu ampir 0.27% kamungkinan nu mana diji titik bakal leuwih ti wates kontrol "3-sigma"
Lamun grafik kadali nu ditalungtik unggal titik waktu ditambahkeun kana grafik, mangka bakal nembongkeun yén "unggal" grafik kontrol nembongkeun hal nu mungkin kajadian dina kasus husus, sanajan aya ogé kamungkinan moal bakal kajadian
Keur grafik kadali Shewhart ngagunakeun wates "3-sigma", nyaéta dina "ngingetkeun kasalahan" tina unggal rata-rata nu ditempo 1/0.0027 atawa 370.4
Sanajan kitu, "dina panjang rata-rata kadali nu keur lumangsung" (atawa dina-kadali ARL) grafik Shewhart nyaéta 370.4
Dina hal séjén, lamun hiji sabab kajadian, mangka moal matak cukup gedé keur grafik dina ngahasilkeun "kaayaan nu ngingetkeun" sacara ngadadak
Lamun kasus husus kajadian, bisa dijelaskeun yén parobahan dina méan jeung/atawa varian tina prosés dina patarosan
Mangsa ieu parobahan bisa diitung, ngajadikeun mungkin keur nangtukeun kadali di luar kontrol keur ieu grafik
Hal séjén tina grafik Shewhart nyaéta kaitung kaalus keur nalungtik ayana parobahan gedé dina méan atawa varian prosés, saperti di luar kadalai ARL nu kaitung pondok dina kasus ieu
Sanajan kitu, keur parobahan nu saeutik (saperti robahna "1-" atawa "2-sigma" dina méan), grafik Shewhart teu bisa nalungtik ieu parobahan sacara efisien
Tipe grafik kadali séjén geus diwangun, saperti grafik EWMA jeung grafik CUSUM, nu naltungtik saeutik parobahan leuwih efisien ku cara maké pangaweruh tina kumpulan panempo saméméhna kana data nu aya ayeuna
Sababaraha pangarang ngiritik kana grafik kadali dumasar kana kaayaan yén ieu ngaganggu kana prinsip likelihood
Sanajan kitu, prinsipna sorangan masih kontroversi tur ngadukung grafik kadali saterusna ngiritik, sacara ilhar, hal ieu teu mungkin keur ngahususkeun fungsi likelihood keur prosés henteu dina statistik kadali, utamana lamun pangaweruh ngeunaan sistim sabab prosésna lemah
Sababara pangarang ngiritik ku sabab maké rata-rata panjang lumangsung (ARL) keur ngitung tampilan grafik kadali, sabab rata-rata ilahar nuturkeun sebaran geometri, nu mibanda variabilitas nu gedé
"Note: Before adding your company's link, please read and ."
Harald Cramér (September 25, 1893 - October 5, 1985) nyaéta Swedish mathematician jeung statistician, hususna dina mathematical statistics
Cramér ogé méré kontribusi keur sebaran prime jeung twin prime
Tempo oge: Cramér's conjecture, Cramér-Rao inequality
In the philosophy of science, and science generally, and in statistics, the curve fitting problem is how to choose among an infinite number of curves that fit the graphically-represented data points, normally by finding a mathmatical expresion to créate the curve
The simplest curve is said to be preferable
This is thought to be related to Occam's Razor in so far as there is a preference for simplicity among a family of curves just as there is a preference of simplicity among competing théories
Commonly used procedures are least squares fitting, linear regression, and nonlinéar regression
One of the difficulties in curve fitting is to choose the functional form of the data for paraméter optimization
Computers are often used to perform curve fitting procedures
Computers do this by solving a system of equations to find the paraméters of the function that minimize the squared error
The gradient descent algorithm is often used for this purpose
Audi, R., Ed
(1996) The Cambridge Dictionary of Philosophy
Cambridge, Cambridge University Press
curve fitting problem p. 172-173
Dina statistik, validasi-silang nyaéta prakték ngabagi sample tina data kana "subsampel" saperti analisa mangrupa rarangkay mimiti dina "subsamel" tunggal, saterusna subsampel diingkeun sina "lolong" "("blind")" in order for subsequent use in confirming and validating the initial analysis
Cross-validation is important in guarding against testing hypotheses suggested by the data, especially where further samples are hazardous, costly or impossible (uncomfortable science) to collect
Cross tabs (atawa tabulasi silang) ngagambarkeun gabungan sebaran tina dua variabel atawa leuwih
They are usually presented in a matrix, called a contingency table
Wheréas a frequency distribution table describes the distribution of one variable, a contingency table describes the distribution of two or more variables simultanéously
It merges two or more frequency distribution tables into one
éach cell gives the number of respondents that gave that combination of responses, that is, éach cell contains a single cross tabulation
The following is an example of a 2 × 3 contingency table
The variable “Wikipedia usuage” has three categories: héavy user, light user, and non user
These categories are all inclusive so the columns sum to 100%
The other variable “intelligence” has two categories: smart, and air héad
These categories are not all inclusive so the rows need not sum to 100%
éach cell gives the percentage of subjects that share that combination of traits
Cross tabs are frequently used because: The statistics associated with cross tabs are: "See also : marketing, marketing research, quantitative marketing research"
Cricket nyaéta olahraga nu nga-generate wilangan statistik nu loba
Statistics are recorded for éach player during a match, and aggregated over a career
At the professional level, statistics for Test cricket, one-day internationals, and first-class cricket are recorded separately
However, since Test matches are a form of first-class cricket, a player's first-class statistics will "include" his Test match statistics - but not vice versa
Analysis of cricket statistics
Although cricket statistics have been recorded since the late 1800s, they have mostly been regarded by fans in a traditional manner of simply comparing the numbers between players
This contrasts with baseball, which generates a similar profusion of statistical records
Baseball statistics have been studied in gréater detail, léading to the field of sabermetrics, which has produced several new statistics expressly designed to give better indications of the relative strengths and values of players
This sort of detailed analysis has not yet been generally applied to cricket statistics, although some statisticians are beginning to look at cricket with an eye to providing a similar depth of analysis
Professional cricket coaches are using computer records of ball-by-ball play to obtain more detailed statistical analysis of player performances than ever before
However, these analyses have seen little spréad into the public knowledge of the fan community
One example of a proposed new cricket statistic is a figure to better indicate a batsman's value than his batting average
Since the average is somewhat inflated by the presence of any not out innings, some have argued that a more indicative statistic would be the number of runs scored per innings, regardless of whether the batsman was out or not
Although arguably achieving the goal of méasuring a batsman's worth more accurately, this proposed statistic has mostly been ignored by cricket fans
Dynamic and graphical statistics
The advent of saturation television coverage of professional cricket has provided an impetus to develop new and interesting forms of presenting statistical data to viewers
Television networks have thus invented several new ways of presenting statistics
These include displaying two-dimensional plots of shot directions and distances on an overhéad view of a cricket field, and graphs of run scoring and wicket taking numbers plotted against time or balls bowled over a career or within a match
These graphics can be changed dynamically by computer as statistics evolve during a game
Dina statistik, covariance matrix nyaruakeun konsép varian tina hiji ka "n" dimension, dina basa séjén, bentuk nilai-scalar random variable ka nilai-vector random variables (tuple tina variabel random skalar)
Lamun "X" mangrupa nilai-skalar variabel random nu mibanda nilai ekspektasi μ mangka variance-na nyaéta formula_1 Lamun "X" nyaéta hiji "n"-ku-1 nilai-vektor kolon variabel random whose expected value is an "n"-by-1 column vector μ then its variance is the "n"-by-"n" nonnegative-definite matrix formula_2 The entries in this matrix are the covariances between the "n" different scalar components of "X"
Since the covariance between a scalar-valued random variable and itself is its variance, it follows that, in particular, the entries on the diagonal of this matrix are the variances of the scalar components of "X"
This may appéar to be a property of this matrix that depends on which coordinate system is chosen for the space in which the random vector "X" resides
However, it is true generally that if "u" is any unit vector, then the variance of the projection of "X" on "u" is "u"TΣ"u"
(This point is expanded upon somewhat at
It is a consequence of an identity that appéars below.)
Some statisticians, following the probabilist William Feller, call this the variance of the random vector "X", because it is the natural generalization to higher dimensions of the 1-dimensional variance
Others call it the covariance matrix, because it is the matrix of covariances between the scalar components of the vector "X"
With scalar-valued random variables "X", we have the identity formula_3 if "a" is constant, i.e., not random
If "X" is an "n"-by-1 column vector-valued random variable and "A" is an "m"-by-"n" constant (i.e., non-random) matrix, then "AX" is an "m"-by-1 column vector-valued random variable, whose variance must therefore be an "m"-by-"m" matrix
It is formula_4 This covariance matrix (though very simple) is a very useful tool in many very different aréas
From it a transformation matrix can be derived that allows one to completely decorrelate the data or, from a different point of view, to find an optimal basis for representing the data in a compact way
This is called PCA (principal components analysis) in statistics and KL-Transform (Karhunen-Loéve transform) in image processing
Dina statistik, rasio korelasi nyaéta ukuran hubungan antara dispersi statistik dina kategori individu jeung dispersi lintasan tina sakabéh populasi atawa sampel
Upamana unggal observasi nyaéta yxi nu mana x nembongkeun kategori nu di-observasi sarta xi nyaéta ngaran tina bagian observasi
Urang bakal nuliskeun nx keur jumlah observasi dina kategori x (teu pati penting keur nilai nu béda tina x) sarta formula_1 and formula_2 maka rasio korelasi η (eta) dihartikeun salaku formula_3 nu bisa ogé ditulis saperti formula_4
Hal ieu mangrupa catetan penting lamun hubungan antara nilai formula_5 jeung nilai formula_6 linier (nu salawasna bener lamun ngan dua kamungkinan keur x) hal ieu bakal méré hasil nu sarua saperti koefisien korelasi; maka lamun taya rasio korelasi bakal leuwih gedé dina besaran, sanajan angger teu leuwih ti 1 dina éta besaran
Hal ieu bisa dipaké keur mutuskeun hubungan non-linier
modél istilah nu biasa dipaké dina sababaraha widang:
Dina matématik, persamaan paramétrik nyaéta hubungan éksplisit dua atawa leuwih variabel dina watesan hiji atawa leuwih paraméter bébas
Sacara abstraks, rélasi (hubungan) dijelaskeun dina wangun equation (persamaan), jeung nembongkeun ogé bayangan bentuk fungsi, sebutkeun, "R""n"
Sanajan kitu aya sababaraha hal anu leuwih akurat keur dihartikeun salaku "representasi parametrik"
Tempo ogé parameter, parametrization, regular parametric representation
Contona, persamaan parabola sederhana, formula_1, bisa di-paraméterisasi ku ngagunakeun paraméter bébas formula_2, sarta disusun di bentuk formula_3
Sanajan dina conto saméméhna ampir ngadeukeutan hal "trivial", paraméter di handap ieu milu kana circle radius formula_4: formula_5
Ahirna, bentuk géometri penting nu ampir teu mungkin keur ngajelaskeun persamaan tunggal tapi mibanda gambaran nu hadé dina bentuk persamaan parametrik : formula_6 formula_7 formula_8 nu mana ngajelaskeun kurva tilu-dimensi, helix, nu mibanda radius "a" sarta ningkat ku formula_9 satuan per turn
(Catetan yén persamaan identik dina plane keur circle; kanyataanna, helix ngan sakadar 'a circle whose ends don't have the same "z"-value'
Sababaraha gambaran di luhur umumna ditulis salaku formula_10 Cara ieu keu ngagambarkeun kurva sacara praktis tur efisien; contono, bisa integrate jeung differentiate saperti watesan kurva
Saterusna, bisa dijelaskeun velocity partikel nuturkeun pola paraméter di handap ieu: formula_11 sarta acceleration nyaéta: formula_12 Sacara umum, kurva parametrik ngaruppakeun fungsi hiji paraméter bébas (umumnya dilambangkeun ku formula_2)
Paraméterisasi permukaan, leuwih ilahar digunakeun saperti dina aplikasi vector calculus saperti Stokes' theorem, mangrupa pungsi 2 paraméter, leuwih ilahar formula_14 or formula_15
Conto paraméter permukaan nyaéta (capless) cylinder dibérékeun ku formula_16 Kanyataan yén gambaran silinder ieu mangrupa kajadian waktu hiji persamaan nu ditempo ngagambarkeun lingkatan dina bidang, nu diijinkeun keur dicokot tina arbitrary nilai "z"
"Sir" Harold Jeffreys (22 April 1891 - 18 March 1989) nyaéta saurang ahli matématika, statistika, géofisika sarta astronomi
Anjeunna dibabarkeun Fatfield, County Durham, diajar di Armstrong College di Newcastle-upon-Tyne, bihari mangrupa bagéan ti University of Durham anu saterusna jadi University of Newcastle
Tamat ti dinya indit ka St. John's College, Cambridge sarta jadi pangajar dina taun 1914
Di Cambridge University anjeunna ngawulang matematik, saterusna geofisika sarta ahirna jadi "Plumian Professor of Astronomy"
Anjeunna nikah jeung ahli matématika sarta fisika, Bertha Swirles (1903-1999), dina taun 1940 sarta babarengan nulis "Methods of Mathematical Physics"
Salah sahiji kontribusina nyaéta sistem Bayesian pikeun ngadeukeutan probabilitas, sarta idena yén inti planét bumi mangrupa cairan
Anjeunna sinatria dina 1953
Bayesian model comparison
Élmu bahan ngawengku bagian-bagian ti kimia, fisika, géologi, ogé biologi nu patali jeung sipat-sipat fisik, kimiawi, atawa biologis rupa-rupa bahan/matéri
Élmu ieu biasana dianggap salaku élmu terapan, sabab sipat-sipat nu diulik biasana dipatalikeun jeung tujuan industrial
Élmu bahan ngawengku sakabéh opat kelas bahan nu masing-masing boga widang ulikanana séwang-séwangan: (1) logam jeung métalurgi, (2) keramika, semikonduktor, jeung bahan éléktronik lianna, (3) polimér, (4) komposit jeung biomaterial nu bisa asup kana kelas bahan 1 n.k
Métalurgi jeung keramika mibanda sajarah nu panjang salaku disiplin rékayasa/téhnik, tapi ku sabab élmu nu jadi tatapakan disiplin ieu larap ka sakabéh kelas bahan, mangka élmu bahan dianggap salaku disiplin anu misah
Élmu bahan aya patalina jeung rékayasa bahan, nu condong museur kana téhnik ngolah (casting, rolling, welding, cangkok ion, kamekaran kristal, thin-film deposition, sintering, glassblowing, jsb
), téhnik analitis (mikroskop éléktron, difraksi sinar-X, kalorimétri, mikroskopi inti (HEFIB) jsb
), rancang bahan, sarta untung/rugina dina produksi industrial
Nanotéhnologi salaku istilah koléktif nujul ka perkembangan téhnologis dina skala nanométer, biasana 0.1-100 nm (Sananométer sarua jeung sapersarébu mikrométer atawa sapersajuta miliméter)
Istilah ieu kadang diterapkeun ka sakur téhnologi mikroskopik
Ku sabab nanotéhnologi téh lumaku dina ukuran nu leutik, fénoména fisik nu henteu katalungtik dina skala makroskopis leuwih ngadominasi
Fénoména nanoskala ieu kaasup di jerona éfék ukuran kuantum jeung gaya "range" pondok saperti gaya van der Waals
Leuwih jauh deui, perbandingan nu nambah lega tina lega pabeungeutan dibandingkeun jeung volume ngabalukarkeun ayana fénoména pabeungeutan
Ku sabab kamajuan komputer tumuwuh sacara ésponénsial, dipercaya yén téhnologi ieu bakal mekar jadi nanotéhnologi dina waktu nu sakeudeung deui ka hareupna
Dina fiksi jeung média, "nanotéhnologi" sering ngarujuk kana nanotéhnologi molekulér hipotésis (molecular nanotechnology, "MNT")
The first mention of nanotechnology (not yet using that name) occurred in a talk given by Richard Feynman in 1959, entitled "There's Plenty of Room at the Bottom"
Feynman suggested a méans to develop the ability to manipulate atoms and molecules "directly", by developing a set of one-tenth-scale machine tools analogous to those found in any machine shop
These small tools would then help to develop and operate a next generation of one-hundredth-scale machine tools, and so forth
As the sizes get smaller, we would have to redesign some tools because the relative strength of various forces would change
Gravity would become less important, surface tension would become more important, van der Waals attraction would become important, etc
Feynman mentioned these scaling issues during his talk
Nobody has yet effectively refuted the féasibility of his proposal
The term 'Nano-Technology' was créated by Tokyo Science University professor Norio Taniguchi in 1974 to describe the precision manufacture of materials with nanométer tolerances
In the 1980s the term was reinvented and its definition expanded by K Eric Drexler, particularly in his 1986 book "Engines of Creation: The Coming Era of Nanotechnology"
He explored this subject in much gréater technical depth in his MIT doctoral dissertation, later expanded into "Nanosystems: Molecular Machinery, Manufacturing, and Computation"
Computational methods play a key role in the field today because nanotechnologists can use them to design and simulate a wide range of molecular systems
Bahan, parabot, jeung téhnologi anyar
Partikel atawa artéfak nu alami atawa jieunan mindeng mibanda kualitas jeung kapabilitas nu béda ti bahan makroskopikna
Emas, pikeun conto, nu sacara kimiawi inert na skala normal, bisa dipaké salaku katalis kimiawi na skala nano
"Tempo ogé (this list should be transformed into text eventually
):" Potential risks
An often cited, but not scientifically tangible worst-case scenario is the so-called grey goo, a substance into which the surface objects of the éarth might be transformed by amok-running, self-replicating nano-robots
Defenders point out that smaller objects are more susceptible to damage from radiation and héat (due to gréater surface aréa-to-volume ratios): nanomachines would quickly fail when exposed to harsh climates
More réalistic are criticisms that point to the potential toxicity of new classes of nanosubstances that could adversely affect the stability of cell walls or disturb the immune system when inhaled or digested
Objective risk assessment can profit from the bulk of experience with long-known microscopic materials like carbon soot or asbestos fibres
Nanotéhnologi na fiksi
Nanotechnology has also become a prominent theme in science fiction , for example with the Borg in Star Trek, the games Deus Ex and Metal Gear Solid, Alexandr Lazarevich' "The NanoTech Network" , Greg Bear's "Blood Music", Michael Crichton's "Prey", and Neal Stephenson's book "The Diamond Age"
Biotéhnologi nyaéta téhnologi nu dumasar kana biologi, utamana nalika dilarapkeun dina agrikultur, élmu pangan, jeung tatamba
Ti antara dadaran nu béda-béda ngeunaan biotéhnologi, nu panglengkepna dirumuskeun ku "Konvénsi ngeunaan Kabinékaan Biologis" Persarikatan Bangsa-bangsa ("United Nations", UN), "Biotéhnologi nyaéta larapan téhnologis naon baé nu migunakeun sistim biologis, organisme hirup, atawa turunanana, nu tujuanana pikeun ngarobah hasil atawa prosés pikeun tujuan husus."
salah sahiji bagian biotéhnologi nyaéta digunakeunana organisme ku manusa sacara langsung pikeun ngahasilkeun, misalna, bir, produk susu, jeung kulit
Baktéri alami ogé aya nu dijeujeutkeun dina industri pertambangan dina "bioleaching"
Guna séjénna di antarana dina daur ulang, ngolah runtah, meresihan tempat-tempat nu kacemaran ku kagiatan industri (bioremediasi) atawa produksi agén "biowar"
Aya ogé larapan biotéhnologi nu teu ngagunakeun organisme hirup, di antarana chip DNA nu dimangpaatkeun dina widang genetik, atawa panglacak radioaktif dina widang kadokteran
Najan biotéhnologi ku masarakat awam dipatalikeun jeung kloning jeung rékayasa genetik, biotéhnologi ditujukeun pikeun ngaronjatkeun alat-alat kadokteran sarta solve problems related to the production of biologically derived products, not the whimsical manipulation of life