AksaraLLM/aksara-bahasa-daerah-v1 huggingface dataset:
Dina statistik, sampel acak basajan tina hiji populasi nyaéta sampel nu dicokot sacara acak, unggal anggota dina éta populasi mibanda kamungkinan nu sarua pikeun dicokot.  Dina populasi nu saeutik, cara nyokot sampelna digawékeun ku cara "dicokot teu disimpen deui", nyaéta ku cara sacara tarapti milih unggal conto tina populasi.

Sacara konsép, nyokot sampel acak basajan mangrupa téhnik nyokot sampel probibiliti nu pangbasajanna, sanajan kitu langka dipaké sabab loba masalah dina makéna. Nyokot sampel acak basajan lain mangrupa métodeu  nu épéktip. métodeu  ieu merlukeun rohangan sampel nu kacida gedéna sarta hasilna merlukeun waktu ngitung nu lila sarta biaya nu mahal. Lamun panalungtik mibanda informasi nu cukup ngeunaan populasi, métodeu  ieu cukup épisién.

Kauntungannana nyaéta bébas tina klasifikasi kasalahan sarta merlukeun kanyaho nu teu loba ngeunaan populasi. Dua kaayaan nu hadé nu mana populasi ampir sarua sarta saeutikna informasi ngeunaan populasi. Lamun henteu dina kaayaan tadi, mangka leuwih hadé ngagunakeun stratified sampling.

Tempo Ogé 
 Statistik 
 Risét pamasaran 
 Risét pamasaran kuantitatif
 Sampling
 Cluster sampling 
 Multistage sampling 
 Nonprobability sampling 
 Systematic sampling 
 Stratified sampling''

Statistika
Multistage sampling nyaéta bentuk kompleks tina cluster sampling. Ngagunakeun sakabel unsur sampel dina sakabéh klaster nu dipilih teu dimeunangkeun atawa teu penting. Dina kaayaan aturan ieu, nyokot sampel dina sababaraha tingkatan klaster jadi penting. Gantina maké kabéh unsur nu dipiboga ku klaster nu dipilih, panalungtik sacara acak milih unsur tina unggal klaster. Wangun klaster dina léngkah kahiji. Tangtukeun unsur mana nu dina jero klaster éta bakal dipaké, dina léngkah kadua. tehnik ieu remen dipaké lamun runtuyan lengkep sakabéh anggota dina populasi euweuh.

Nyokot sampel Probabilitas-sabanding-kana-ukuran mangrupa salah sahiji tipe nyokot sampel klaster multiléngkah. Dina métodeu  ieu, pamilihan probabilitas unsur anu ditangtukeun dina klaster variasina tibalik jeung ukuran dina klaster.

Sanajan nyokot sampel sacara klaster jeung nyokot sampling ku cara ngabédakeun lapisan sampel meh ampir sarua, tapi sacara substansi duanana béda. Dina nyokot sampel ku cara ngabédakeun lapisan, sampel acak dicokot tina sakabéh lapisan, nu mana dina nyokot sampel sacara klaster ngan tina klaster nu ditalungtik, boh dina saléngkah atawa multiléngkah

Tempo ogé : statistika, marketing research, quantitative marketing research, sampling, cluster sampling, simple random sampling, nonprobability sampling, systematic sampling, stratified sampling

Statistika
Dina statistik, sebaran sampling nyaéta sebaran probabiliti, dina kaayaan sampling dina populasi diulang, tina statistik nu dibérékeun (kuantitas numerik diitung tina nilai data dina sample).

Bentuk (atawa rumus keur) sebaran sampling gumantung kana sebaran populasi, statistik nu ditempo sarta ukuran sampel nu dipaké.

(Catetan yén rumus nu leuwih présisi nyebutkeun yén sebaran statistik bisa dipaké keur sakabeh sampel nu mungkin tina ukuran nu dibérékeun, henteu ngan sakadar "dina kaayaan sampling diulang".)

Contona, anggap populasi nu kacida gedéna nuturkeun normal (ilaharna disebut kurva bel). Asumsi urang mindo nyokot sampe dina sampel nu dibérékeun tina populasi sarta ngitung sample mean (arithmetic mean nilai data) keur unggal sampel. Sampel nu béda bakal mangaruhan kana bédana sampel méans. Sebaran méan ieu nyaéta "sebaran sampling tina sampel mean" (keur ukuran sampel nu dibérékeun). Sebaran ieu bakal jadi normal saprak populasina normal. (Dumasar kana teorema central limit, lamun populasi teu normal tapi "bentukna cukup hade",
sebaran sampling  tina sampel méan bakal masih kénéh cukup normal sanajan ukuran sampel kacida gedéna).

Simpangan baku tina sebaran sampling ngacu ka standar kasalahan (statistis) sarta di-estimasi maké rumus:

nu mana  mangrupa simpangan baku tina sebaran populasi sarta N nyaéta ukuran sampe (jumlah barang) dina sampel.

Hal nu penting dina rumus ieu nyaéta kudu ngalikeun opat kali ukuran sampel (4X) ngarah ukuran kasalahanna jadi (1/2).  Waktu rarangkay elmu statistik nu mana biaya mangrupa faktor, ieu mangrupa faktor nu kudu dipikaharti ngeunaan pentingna biaya.

Alternatipna, anggap median sampel tina populasi. Ieu mibanda sebaran sampling nu béda sacara umum teu normal (tapi masih kénéh pakait dina aturan ka-normal-an).

Tempo oge
central limit theorem, standard error (statistics)

Statistika
Dina statistik, tes-G nyaéta tes rasio likelihood atawa maximum likelihood nu loba dipaké dina statistical significance sarta saméméhna disarankeun maké tes chi-kuadrat.

Ilaharna maké tes chi-kuadrat keur goodness of fit tina hiji sebaran sarta keur kabébasan dina contingency table nu dina kanyataanna dideukeutan ku log-likelihood ratio keur tes G ieu. Perkiraan ieu diwanohkeun ku Karl Péarson alatan perluna waktu lila keur ngitung log-likelihood. Ku mecenghulna kalkulator sarta komputer pribadi éléktronik, hal ieu henteu jadi masalah deui. Tes-G mucunghul tur loba dipaké, saprak direkomendasikan di édisi 1994 dina sababaraha buku teks statistika ku Sokal sarta Rohlf.

Rumus umum keur tes statistik chi-kuadrat Péarson's nyaéta

nu mana O nyaéta frékuénsi observasi dina sel, E nyaéta ekspektasi frékuénsi dina null hipotesa, sarta jumlah dina sakabéh sel. Rumus pakait nu ilahar dipaké keur G nyaéta 

nu mana ln ngalambangkeun logaritma alami (log dina e) sarta jumlah dina sakabéh sel.

Dina null hipotesa yén hasil frekuesni observasi tina nyokot sampel sacara acak tina hiji sebaran ditangtukeun ku ekspektasi frékuénsi nu dipikanyaho, sebaran G meh sarua jeung chi-kuadrat, nu mana jumlah wilangan tingkat kabebasan saperti dina tes chi-kuadrat.

Keur sampel nu meh sarua, tes-G jeung tes chi kuadrat bakal ngahasilkeun kasimpulan nu sarua. Sanajan kitu, pamarekankana téori sebaran chi-kuadrat keur tes-G leuwih hadé tina tes chi-kuadrat Péarson dina pasualan di mana keur sakabéh sel |O − E| > E, sarta dina sababaraha pasualan tesG geus ilahar dipaké.

Keur sampel nu saeutik tes binomial keur goodness of fit, sarta tes kapastian Fisher keur contingency tables, leuwih hadé maké tes chi-kuadrat atawa tes-G.

Rujukan
Sokal, R. R., & Rohlf, F. J. (1994). Biometry: the principles and practice of statistics in biological research., 3rd edition. New York: Freeman. ISBN 0-7167-2411-1.

Statistika
Latin square mangrupa tabel n × n nu dieusi ku n lambang nu béda dina sababaraha jalan mangka éta lambang pasti ngan aya sakali dina unggal baris jeung kolom.

Latin squares salaku multiplication table dina quasigroup, ilahar dipaké dina desain percobaan.

Ngaran Latin square asalna ti Leonard Euler nu ngagunakeun simbol ku hurup Latin.

Tempo ogé 
 Graeco-Latin square

Matematika
métodeu  statistik Latin hypercube sampling diwangun sarta dikumpulkeun ku Ronald L. Iman, J. C. Helton, and J. E. Campbell, saparakanca keur nga-generate sebaran koleksi nu asup akal tina nilai paramater dina sebaran multidimensi.

Paperna An approach to sensitivity analysis of computer models, Part I. Introduction, input variable selection and preliminary variable assessment. dina Journal of Quality Technology taun 1981.
Dina statistik, téoréma Lehmann-Scheffé netepkeun yén unggal éstimator anu lengkep, cukup, sarta teu bias mangrupa éstimator teu bias nu unik tina nilai ekspektasi-na.

Cara nu ilahar dipaké keur néangan nilai éstimator nyaéta ngagunakeuntéoréma Rao-Blackwell.

Statistika
Dina statistik modél linier bisa ditembongkeun ku nyebutkeun

 

di mana Y mangrupa nx1 vektor kolom variabel random, X mangrupa matrik kuantitas nxp "dipikanyaho" (contona, bisa di-observasi sarta non-random), vektor baris pakait jeung statistical unit, β mangrupa  px1 vektor paraméter (teu ka-observasi), sarta ε mangrupa  nx1 vektor "error", nu teu pakait ka variabel random nu mibanda nilai ekspektasi 0 sarta varian  σ2.  Salawasna komponen vektor kasalahan nu dicokot bakal independent sarta kasebar normal.  Anggap nilai X sarta Y ka observasi, statistikawan kudu nga-estimate β sarta σ2.  Sacara tipikal paraméter β di-estimasi maké métodeu  least squares.

Tinimbang nyokot varian ε jadi σ2I, nu mana I mangrupa nxn matrik identitas, anggap varian mangrupa σ2M,
nu mana M mangrupa matrik séjén nu dipikanyaho salian ti matrik identitas, mangka estimate β maké métodeu  "generalized least squares", nu mana, ku ngaminimalkeun kuadrat residu, minimalkeun bentuk béda kuadrat dina residu—bentuk kuadrat dibérékeun ku matrik M−1.
Lamun sakabéh diagonal dina matrik M sarua jeung 0, mangka estimasi normal β ku métodeu  "weighted least squares", nu mibanda beurat sarua jeung diagonal asupan.

Linear regression ordiner mangrupa topik nu raket pakait.

Generalisasi

Generalisasi model linier 

Generalized linear models, tinimbang 
 E(Y)=Xβ,
leuwih ilahar
f(E(Y))=Xβ,
di mana f mangrupa "fungsi pakait".  Contona "model regresi Poisson", ku nuliskeun 
Yi mibanda sebaran Poisson nu mibanda nilai ekspektasi eγ+δxi.
Fungsi pakait mangrupa fungsi logaritma natural.
Observasi nu dipiboga xi sarta Yi keur
i=1,...,n, bisa nga-estimasi γ and δ ku métodeu  maximum likelihood.

Model linier general 

General linear model (atawa multivariate regression model) mangrupa modél linier nu mibanda sababara ukuran dina unggal obyek.
Unggal obyek diwakilan dina bentuk vektor.

Statistika
Prediksi linier mangrupa operasi matematik di mana nilai ka hareup tina digital signal mangrupa estimasi minangka fungsi linier sampel saméméhna.

Dina digital signal processing prediksi linier ilahar disebut linear predictive coding (LPC) sarta bisa ditembongkeun minangka sub susunan filter theory. Dina system analysis (sub bagéan matematik), prediksi linier bisa ditempo minangka bagian mathematical modelling atawa optimization.

Model prediksi 

Nu ilahar digambarkeun nyaéta

nu mana xn′ mangrupa nilai prediksi tanda, xn−i nilai saméméhna, sarta ai koefisien prediktor. Generat kasalahan ku estimasi ieu nyaéta

nu mana xn mangrupa nilai tanda sabenerna.

Persamaan ieu valid keur sakabéh tipe (hiji-dimensi) prediksi linier. bédana kapanggih dina jalan paraméter ai nu dipilih.

Keur tanda multi-dimensi kasalahan biasana dihartikeun ku

nu mana  mangrupa vektor norm pilihan nu cocok.

Estimasi parameter 

Nu ilahar dina optimasi paraméter  nyaéta kriteri root mean square nu mana disebut ogé kritéria autocorrelation. Dina métodeu  ieu ngaminimalkeun nilai ekspektasi tina kuadrat kasalahan E(e2n, ngahasilkeun persamaan

keur 1 ≤ j ≤ p, di mana R mangrupa tanda autocorrelation xn, dihartikeun minangka

Dina kasus multi-dimensi pakait jeung ngaminimalkeun norma L2.

Persamaan di luhur disebut persamaan normal atawa Yule-Walker. Dina bentuk matriks bisa sarua jeung

nu mana matrix autokorelasi R mangrupa Toeplitz matrix nu mibanda elemen ri,j = R(i − j), vektor r mangrupa vektor autokorelasi rj = R(j), sarta vektor a mangrupa vektor paraméter.

pamarekannu leuwih umum nyaéta ngaminimalkeun

nu mana umumna paraméter konstrain  mibanda  keur manggihkeun solusi trivial. Konstrain ieu ngahasilkeun prediktor nu sarua jeung di luhur ngan persamaan normal, mangka

nu mana indeks i antara 0 ka p sarta ukuran R nyaéta matriks (p+1) × (p+1).

Optimasi paraméter mangrupa topik luas sarta angka nu gedé mangrupa pendeketan séjén nu diusulkeun.

métodeu  autokorelasi leuwih ilahar sarta biasa digunakeun, contona, keur speech coding dina standar GSM.

Solusi persamaan matriks Ra = r mangrupa prosés komputasi nu lumayan mahal. Gauss algorithm keur invers matrik bisa jadi mangrupa solusi heubeul tapi pamarekanieu teu epektip dipaké dina simetri R jeung r. Algoritma panggancangna ti Levinson recursion diusulkeun ku N. Levinson taun 1947, nu mangrupa solusi perhitungan bolak-balik. Pangahirna, Delsarte saparakanca ngusulkeun métodeu  algoritma séjén nyaéta split Levinson recursion nu merlukeun satengah jumlah perkalian jeung pembagian. Ieu dipaké keur sipat simetri vektor paraméter diana tingkatan sub perhitungan.

Tempo oge
prediction interval.

Matematika
Dina statistik, lamun kulawarga densiti sebaran diparaméterisasi ku paraméter nilai -skalar atawa -vektor μ mangrupa bentuk

fμ(x) = f(x − μ)

mangka μ disebut paraméter lokasi, sabab ieu nilai nangtukeun "lokasi" tina sebaran probabiliti.

Tempo oge
 numerical parameter
 statistical dispersion
 scale parameter

Statistika
Kurva Lorenz diwangun ku Max O. Lorenz salaku grapik nu ngagambarkeun kateusajajaran pangala. Kurva bisa dipaké ogé keur ngukur kateusajajaran aset atawa sebaran séjénna.

Dina diskusi panghasilan pribadi, urang remen nyebutkeun yen, "duapuluh persen sahandapeun sakabeh rumahtangga mibanda sapuluh persen total panghasilan". Kurva Lorenz dumasar kana ieu pernyataan; unggal titik dina kurva ngagambarkeun unggal pernyataan.

Kurva Lorenz mangrupa grafik nu nembongkeun, di handap x% rumahtangga, persentase y% total panghasilan no dipibanda. Persentase rumah tangga di plot dina sumbu x, persentasi panghasilan dina sumbu y.

Sebaran panghasilan persis sarua di masarakat bakal jadi hiji di mana unggal jalma mibanda panghasilan nu sarua. Dina kasus ieu, handapeun N% masarakat bakal salawasna mibanda N% panghasilan. Mangka sebaran nu persis sarua digambarkeun ku garis lempeng y=x; bisa disebut yén ieu garis mangrupa garis persis sarua.

Sebaran nu persis teusarua, sacara jelas, nyaéta saurang boga kabeg penghasilan sarta nu séjénna teu boga nanaon. Dina kasus eta, kurva bakal dina y=0 keur sakabrh x<100, sarta y=100 waktu x=100. Garis dina kurva ieu disebut garis kateusaruaan sampurna.

Catetan yén dumasar kana panghasilan (atawa naon baé nu bakal diukur) teu bisa negatip, mangka teu mungkin keur kurva Lorenz naek di saluhureun garis sarua sampurna, atawa nurun sahandapeun garis teusarua sampurna.  Kurva kudu naek sarta konkav.

Kurva Lorenz dipeke keur ngitung koefisien Gini, nu mana daerah antara garis sampurna jeung kurva, salaku persentasi daerah antara garis sarua sampurna jeung garis teu sarua sampurna.

Tipikal kurva Lorenz bisa ditempo di handap ieu:

Baca ogé
 Ékonomi kamakmuran
 Méktika kateusajajaran pangala
 Koefisien Gini
 Kamakmuran sosial (élmu pulitik)
 Analisis ROC
Dina statistik, téori kaputusan sarta ékonomi, loss function nyaéta fungsi nu metakeun hiji kajadian (sacara teknis hiji unsur dina rohangan sampel) kana wilangan riil keur ngagambarkeun biaya ekonomi atawa hanjelu pakait jeung hiji kajadian.

Loss functions sacara tipikal digambarkeun dina watesan "keuangan" dumasar kana ukuran biaya nu mungkin, contona kalahiran jeung "kematian" dina widang public health.

Loss functions are complementary to utility functions which represent benefit and satisfaction. Typically, for utility U, loss is equal to k-U, where k is some arbitrary constant.

Expected loss

Loss function satisfies the definition of a random variable so we can establish a cumulative distribution function and an nilai ekspektasi. However, more commonly, the loss function is expressed as a function of some other random variable. For example, the time that a light bulb operates before failure is a random variable and we can specify the loss, arising from having to cope in the dark and/or replace the bulb, as a function of failure time. For a continuous random variable, X with probability density function f(x) and loss function, λ(x), the expected loss is:

Minimum expected loss is widely used as a criterion for choosing between prospects. It is closely related to the criterion of maximum expected utility.

Loss functions in Bayesian statistics

One of the consequences of Bayesian inference is that in addition to experimental data, the loss function  does not in itself wholly determine a decision.  What is important is the relationship between the loss function and the prior probability.  So it is possible to have two different loss functions which léad to the same decision when the prior probability distributions associated with éach compensate for the details of éach loss function.

Combining the three elements of the prior probability, the data, and the loss function then allows decisions to be based on maximising the subjective expected utility, a concept introduced by Leonard J. Savage.  He also argued that using non-Bayesian methods such as minimax, the loss function should be based on the idéa of regret, i.e. the loss associated with a decision should be the difference between the consequences of the best decision that could have been taken had the underlying circumstances been known and the decision that was in fact taken before they were known.

Statistika
Hukum Zipf-Mandelbrot (oge dipikanyaho minangka hukum Pareto-Zipf) 
nyaéta power-law distribution dina ranked data, dipaké sanggeus Harvard linguistic professor George Kingsley Zipf (1902-1950) 
nu ngusulkeun dina teks regularity, sarta mathematician Benoit Mandelbrot (lahir November 20, 1924), no nga-generalisir.

Distribution kecap dirangking ku frequency-na dina random
corpus text mangrupa power-law distribution umum, dipikanyaho minangka Zipf's law.

Lamun hiji plot rangking frequency kecap dikandung dina 
corpus nu gedé tina data teks ka jumlah kajadian atawa frequencies sabenerna, meunangkeun power-law distribution, mibanda exponent raket ka hiji (tapi tempo Gelbukh jeung Sidoro 2001).

Tumbu kaluar
 Z. K. Silagadze: Citations and the Zipf-Mandelbrot's law
 NIST: Zipf's law
 W. Li's References on Zipf's law

Matematika
Fisika
Koreksi Yates keur kontinyu, atawa tes chi-kuadrat Yates, ngatur rumus keur uji kuadrat-chi Pearson nu ngurangan 0.5 tina unggal nilai dina tabel kontingensi 2 X 2. Rumus ieu dipaké lamun dina hiji sel dina tabel ngabogaan nilai ekspektasi kurang ti 5.

Sumber séjén nyebutkeun yén koreksi ieu kudu dipaké lamun ekspektasi frekuensi kurang ti 10.

Statistika
An urn problem is an idéalized thought experiment in which some objects of réal interest (such as atoms, péople, cars, etc.) are represented as colored balls in an urn or other container.
One pretends to draw (remove) one or more balls from the urn;
the goal is to determine the probability of drawing one color or another, 
or some other properties.

Basic urn model 

In this basic urn modél in probability theory, the urn contains x white and y black balls; one ball is drawn randomly from the urn and its color observed; it is then placed back in the urn, and the selection process is repéated.

Possible questions that can be answered in this modél are:
 can I infer the proportion of white and black balls from n observations ? With what degree of confidence ?
 knowing x and y, what is the probability of drawing a specific sequence (e.g. one white followed by one black)?
 if I only observe n white balls, how sure can I be that there is no black balls?

Other models 

Many other variations exist:
 the urn could have numbéréd balls instéad of colored ones
 balls may not be returned to the urns once drawn.

Conto masalah urn

 Turunan sebaran binomial
 Turunan sebaran hipergeometrik
 Statistik fisika: turunan tanaga sarta sebaran kecepatan

Historical remarks

Urn problems have been a part of the theory of probability since at léast the publication of the Ars conjectandi by Jakob Bernoulli (1713).
Bernoulli's inspiration may have been lotteries, elections, or games of chance which involved drawing balls from a container.
It has been asserted 

that

Elections in medieval and renaissance Venice, including that of the doge, often included the choice of electors by lot, using balls of different colors drawn from an urn.

Bernoulli himself, in Ars conjectandi, considered the problem of determining, from a number of pebbles drawn from an urn, the proportions of different colors.
This problem was known as the inverse probability problem, and was a topic of reséarch in the eighteenth century,
attracting the attention of Abraham de Moivre and Thomas Bayes.

See also

 Coin-tossing problems

Probability and statistics
Dina statistik, kaasup dina jajal pamanggih sarta survey mirip, margin kasalahan nyaéta jari-jari interval kapercayaan—ilaharna 90% interval kapercayaan—keur populasi nu saimbang.

Conto

Contona, tempo jumlah nu resep mangrupa hal nu saimbang keur pamilih nu milu ngajawab "enya" dina referendum.  Sampel random pamilih tina populasi dicokot sarta manggihkeun yén 60% pamilih dina sampel bakal milih "enya". Mangka estimasi saimbang tina sakabéh populasi nu bakal milih "enya" dicokot jadi 60%. Lamun 3% margin kasalahan dilaporkeun, hartina yén prosedur nu dipaké bakal 3% sarimbang jeung nu bakal diestimasi, 90% kali.  Akibatna interval ti 57% ka 63% mangrupa 90% interval kapercayaan keur proporsi pamilih tina sakabéh populasi bakal ngajawab "enya".  Jari-jari interval nyaéta 3%; ieu nu disebut margin kasalahan.

Kumaha cara ngitung margin kasalahan

Anggap n mangrupa jumlah pamilih dina sampel.  Anggap ogé dicokot sacara random sarta bébas tina sakabéh pamilih.  Ieu ngaharepkeun optimis, tapi angger kudu carincing dina nyokot sampel ngarah méré gambaran nu sabenerna.  Anggap p mangrupa proporsi pamilih dina sakabéh populasi bakal ngajawab "enya".  Mangka jumlah pamilih X dina sampel nu bakal milih "enya" mangrupa variabel acak nu mibanda sebaran binomial nu paraméter-na n jeung p.  Lamun n cukup gedé, mangka X ngadeukeutan sebaran normal nu mibanda nilai ekspektasi np sarta varian np(1 - p).  Mangka

ngadeukeutan sebaran normal nu mibanda nilai ekspektasi 0 sarta varian 1.  Nempo kana tabel persentase sebaran normal mangka nunjukkeun yén P(-1.645 < Z < 1.645) = 0.9, atawa, dina basa séjén, di dinya aya 90% kamungkinan kajadian.  Mangka

Ieu sarua jeung

Gantikeun p dina anggota kahiji jeung katilu dina kateusaruaan ieu ku hasil nilai ekspektasi X/n sorangan dina kasalahan gedé lamun n cukup gedé.  Hasil operasi ieu

Anggota kahiji jeung katilu kateusaruaan ieu gumantung kana observasi X/n sarta henteu kana nu ka observasi p, sarta titik tungtung interval kapercayaan.  Dina basa séjén, margin kasalahan nyaéta

Statistika
Dina statistik, méan kuadrat kasalahan tina estimator T dina paraméter nu teu ka-observasi θ nyaéta

dina hal ieu, mangrupa nilai ekspektasi kuadrat "kasalahan".  "Kasalahan" nyaéta jumlah nu mana éstimator béda jeung jumlah nu keur di-estimasi.  Méan kuadrat kasalahan nyukupan identitas

di mana

dina hal ieu, the bias nyaéta lobana nu mana nilai ekspektasi tina éstimator béda keur jumlah nu teu ka-observasi nu keur di-estimasi.

Conto kongkritna.  Anggap

dina hal ieu, ukran sampel random n tina populasi sebaran normal.  Dua éstimators  σ2 kadangkala dipaké (atawa nu séjénna):

nu mana

mangrupa "sampel mean".   Kahiji tina éstimator ieu nyaéta éstimator maximum likelihood, sarta bias, dina hal ieu, bias teu sarua jeung nol, tapi mibanda varian nu leuwih leutik tinimbang nu kadua, anu teu bias.  Varian leutik tina akibat séjén keur bias, mangka méan kuadrat kasalahan tina bias éstimator leuwih leutik tinimbang éstimator unbiased.

Statistika
Dina statistika, tes nilai tengah atawa tes median mangrupa kasus husus dina uji kuadrat-chi Pearson. Tes null hypothesis nu median tina population tina dua samples digambarkeun identik. Data unggal sampe dibagi kana dua grup, hiji grup ngandung nilai data nu leuwih luhur tina median, sarta grup séjénna ngandung nilai data dina median atawa sahandapeunnana. Tes chi-kuadrat Péarson dipaké keur nangtukeun frékuénsi observasi dina unggal grup nu béda tina ekspektasi frékuénsi nu asalna tina kombinasi dua grup sebaran.

Statistical power dina tes ieu kadangkala ditingkatkeun ku maké nilai séjén tinimbang median nu dihartikeun tina grup - hal ieu, ku maké nilai nu ngabagi grup kana nilai grup nu ampir sarua tinimbang median-na.

Tes kacida kapakena waktu sebaran data béda tina normal, contona waktu raw score dina klasifikasi teu teratur kana rentang pendekatan nu dijieun. Ku kitu, ieu biasa dipaké salaku léngkah awal dina exploratory analysis.

Statistika
Dina tiori probabiliti, memorylessness nyaéta sipat penting sebaran probabiliti: sebaran eksponensial sarta sebaran geometrik.

Discrete memorylessness

Suppose X is a discrete random variable whose values lie in the set { 0, 1, 2, ... } or in the set { 1, 2, 3, ... }.
The probability distribution of X is memoryless precisely if for any x, y in { 0, 1, 2, ... } or in { 1, 2, 3, ... }, (as the case may be), we have

It can réadily be shown that the only probability distributions that enjoy this discrete memorylessness are geometric distributions.  These are the distributions of the number of independent Bernoulli trials needed to get one "success", with a fixed probability p of "success" on éach trial.

Example and motivation for the name memorylessness

For example, suppose a die is thrown as many times as it takes to get a "1", so that the probability of "success" on éach trial is 1/6, and the random variable X is the number of times the die must be thrown.  Then X has a géometric distribution, and the conditional probability that the die must be thrown at léast four more times to get a "1", given that it has alréady been thrown 10 times without a "1" appéaring, is no different from the original probability that the die would be thrown at léast four times.  In effect, the random process does not "remember" how many failures have occurred so far.

A frequent misunderstanding

Memorylessness is often misunderstood by students taking courses on probability: the fact that P(X > 16 | X > 12) = P(X > 4) does not méan that the events X > 16 and X > 12 are independent; i.e., it does not méan that P(X > 16 | X > 12) = P(X > 16).  To summarize: "memorlessness" of the probability distribution of the number of trials X until the first success méans

It does not méan

(That would be independence.  These two events are not independent.)

Continuous memorylessness

Suppose that rather than considering the discrete number of trials until the first "success", we consider continuous waiting time T until the arrival of the first phone call at a switchboard.  To say that the probability distribtuion of T is memoryless méans that for any positive real numbers s and t, we have

The only difference between this and the discrete version is that instéad of requiring s and t to be positive (or, in some cases, nonnegative) integers, thus achieving discreteness, we allow them to be réal numbers that are not necessarily integers.

It can be shown that the only probability distributions that enjoy this continuous memorylessness are the sebaran eksponensial.

Probability distributions
Statistik matematis ngagunakeuntiori probabiliti sarta cabang séjén matematik pikeun ngulik statistik tina jihat matematis murni.

Jadi, pikeun conto, hiji conto acak dituliskeun salaku runtuyan variabel acak,
  
nu masing-masing nuturkeun hiji sebaran probabiliti nu tangtu (biasana dianggap independent and identically distributed|kasebar bebas sarta identik).
Sample mean digambarkeun salaku fungsi tina variabel,
  
sarta mangrupa variabel acak tina hiji sebaran.

Ku ngagunakeunieu cara, statistik matematik mangrupa salah sahiji usaha keur ngabuktikeun téori-téori nu loba dipaké dina statistik terapan.

Statistika
Dina téori probabilitas, sebaran binomial négatip nyaéta anggota tina kulawarga sebaran probabilitas diskrit.

Sebaran probabilitas
Dina statistik, léma Neyman-Péarson nangtukeun yén waktu ngagawekeun tes hipotesa antara dua titik hipotesa H0: θ=θ0 sarta H1: θ=θ1, mangka likelihood-ratio test nu nolak H0 dina ngadukung H1 waktu

leuwih ilahar salaku tes power ukuran α.

Statistika
Métode kaputusan statistik Non-parametrik (atawa sebaran-bébas) mangrupa prosedur matematik keur tes hipotesa statistik, teu siga dina statistik parametrik, taya asumsi ngeunaan sebaran frekuensi tina variabel nu ditaksir. Pamakéan nu ilahar ieu métodeu  nyaéta dina tes chi-kuadrat. Pamakéan séjén nu maké métodeu  non-parametrik kaasup Mann-Whitney U, Kruskal-Wallis one-way analysis of variance, median test, Spearman's ρ, sarta estimasi sebaran maké sebaran binomial.

kabéhanna mungkin leuwih mibanda statistical power tinimbang tes parametrik waktu asumsi dina kaayaan tes parametrik teu nyugemakeun.

Tempo ogé statistik parametrik.

Statistika
Dina statistik, rankits titik data tina susunan data nu ngandung jejer skalar sederhana nyaéta nilai ekspektasi tina order statistik dina standar  sebaran normal corresponding to data points in a manner determined by the order in which the data points appéar.

This is perhaps most réadily understood by méans of an example.  If an i.i.d. sample of six items is taken from a kasebar normal population with nilai ekspektasi 0 and varian 1 and then sorted into incréasing order, the expected values of the resulting order statistics are:

Suppose the numbers in a data set are

 65,  75,  16,  22,  43,  40.

The corresponding ranks are

 5,  6,  1,  2,  4,  3,

i.e., the number appéaring first is the 5th-smallest, the number appéaring second is 6th-smallest, the number appéaring third is smallest, the number appéaring fourth is 2nd-smallest, etc.  One réarranges the expected normal order statistics accordingly, getting the rankits of this data set:

A graph ploting the rankits on the horizontal axis and the data points on the vertical axis is a rankit plot or normal probability plot.  Such a plot is necessarily nondecréasing.  In large samples from a normally distributed population, such a plot will approximate a straight line.  Substantial deviations from straightness are considered evidence against normality of the distribution.

The word rankit was introduced by the statistician Chester Bliss (not to be confused with the politician Chester Bliss Bowles).

Statistika
Dina statistik spasial, semivarian dijelaskeun ku 

nu mana z mangrupa nilai data tina sabagian lokasi, h nyaéta jarak antara nilai data, sarta n(h) dianggap angka pasangan nilai data dibérékeun, spasi jarak tina bagian h.

Pot semivarian ka jarak antara data nilai dipikanyaho salaku semivariogram, atawa keur gampang nyebutna variogram.

Topik pakait: géostatistik

Rujukan:
 Shine, J.A., Wakefield, G.I.: A comparison of supervised imagery classification using analyst-chosen and géostatistically-chosen training sets, 1999, http://www.geovista.psu.edu/sites/geocomp99/Gc99/044/gc_044.htm 

Statistika
Ogé katelah wates toléran (Ing. tolerance limits).

Pamakéan rentang toléran
Rentang toléran patali jeung rékayasa wates toléran. Sacara husus, rékayasa wates toléran nangtukeun niléy maksimum jeung minimum pikeun hiji produk sangkan bisa lumaku. Rékayasa wates toléran bisa ditangtukeun maké Geometric Dimensioning and Tolerancing. Rentang tolérans mangrupa dasar keur chart kontrol dina sababaraha rupa.
Statistik interval tolérans (atawa watés) dihasilekun tina mroses data.
Lobana ieu interval gumantung kana prosésna.
Rentang toléran dihartikeun salaku kamampuan prosés keur nangtukeun nilai minimum jeung maksimum.
Nilai wates dina ieu wewengkon mibanda bagéan nu sarimbag jeung sakabéh populasi sarta mibanda probabiliti atawa kapercayaan husus.

Rujukan kaluar

Tempo The NIST/SEMATECH e-Handbook of Statistical Methods, 2004 July 17.

Dina bagian 
Section 7.2.6.3 - 
Tolerance intervals for a normal distribution

Tempo "Quality Control Handbook", Juran.

Statistika
métodeu  Taguchi nyaéta métodeu  statistik nu diwangun ku Genichi Taguchi keur ningkatkeun kualitas produksi pabrik. Metoda Taguchi mangrupa hal nu kontroversi keur statistikawan urang kulon.

Prinsip Taguchi nu mangaruhan kana statistik nyaéta

Taguchi loss-function;
Pilosopi off-line quality control; sarta
Hal anyar dina desain percobaan.

Pustaka
León, R. V., A. C. Shoemaker & R. N. Kacker. 1987. Performance méasures independent of adjustment: an explanation and extension of Taguchi's signal-to-noise ratios (with discussion), Technometrics 29: 253-285
 Moen, R. D., T. W. Nolan & L. P. Provost. 1991. Improving Quality Through Planned Experimentation. ISBN 0070426732
Nair, V. N. (éd.). 1992. Taguchi's paraméter design: a panel discussion. Technometrics 34: 127-161
Dina statistik, outlier nyaéta hiji observasi nu jauh tina data nu keur ditempo.

Harti "jauh tina" di hal ieu nyaéta:
kurang ti Q1 − 1.5 × IQR atawa leuwih ti Q3 + 1.5 × IQR
nu mana Q1 sarta Q3 kuartil kahiji jeung katilu, sarta IQR interquartile range (sarua jeung Q3 − Q1).

Nilai ieu ngahartikeun yén hartina aya dina "jero pager", saluareun éta observasi bisa dingarananmild outlier.

Outliers ekstrim nyaéta observasi ayana saluareun pager:
kurang ti Q1 − 3 × IQR atawa leuwih ti Q3 + 3 × IQR

Dina kasus data kasebar normal, maké harti di luhur, ngan 1 tina 150 observasi bakal aya mild outlier sarta ngan 1 tina 425,000 aya outlier ekstrim.

Outliers ilaharna merlukeun perhatian saprak nembongkeun masalah dina sampling atawa kumpulan data atawa transkrip.  Alternatipna, outlier bisa jadi hasil, contona, respon nu teu umum kana perlakuan nu ditempo, nu jadi perhatian peneliti.

Tempo ogé 
 box plot
Studentized residual

Statistika
Ahmad Hassan Zewail (Basa Arab: أحمد زويل) (wedal 26 Pébruari 1946) kimiawan urang Mesir, dilélér Hadiah Nobel widang Kimia taun 1999 pikeun karyana ngeunaan fémtokimia. Lahir di Damanhur (60 km kidul-wétaneun Iskandariah) sarta digedékeun di Disuq, anjeunna nampa gelar kahijina ti Universitas Iskandariah méméh pindah ka US pikeun ngaréngsékeun PhD-na di University of Pennsylvania. Sanggeus sababaraha karya posdoktorat di UC Berkeley, anjeunna dileler a faculty appointment di Caltech taun 1976, where he has remained since. In 1990 he was made the first "Linus Pauling Chair in Chemical Physics".

Karya penting Zewail nyaéta mitambeyan fémtokimia - ulikan réaksi kimiawi dina jangka waktu fémtodetik. ngagunakeun téhnik laser nu gancang (céntangan laser pondok kacida).

Taun 1999, Zewail jadi urnag Mesir katilu nu nampa Hadiah Nobel, nuturkeun Anwar Sadat (1978 in Péace) jeung Naguib Mahfouz (1988 widang Sastra). Pangleler internasional séjénna di antarana Hadiah Wolf (1993) jeung Robert A. Welch Award (1997). Taun 1999 anjeunna nampa panghargaan nagara pangluhurna, Grand Collar of the Nile.

Jawara Hadiah Nobel widang Kimia
Nu babar taun 1946
Jalma hirup
Kalsium mangrupa unsur kimiawi na tabel periodik nu lambangna Ca sarta wilangan atom 20. Kalsium is a soft grey alkaline earth metal nu dipaké salaku agén pangréduksi na ékstraksi thorium, zirconium, jeung uranium. Unsur ieu ogé mangrupa unsur kalima nu paling ngaleuyah na kulit Marcapada. Penting pikeun organisme hirup, utamana dina fisiologi sél.

Ciri penting 
Kalsium téh unsur teuas nu dimurnikeun ku jalan éléktrolisis kalsium fluorida, nu mun kaduruk seuneuna konéng-héjo, sarta ngabentuk nitrida bodas mun keuna ku udara. Dina cai, kalsium bakal jadi kalsium hidroksida.

Larapan 
Kalsium téh salah sahiji komponén penting katuangan, kurang asupanana bisa ngabalukarkeun gangguan formasi tulang jeung huntu. Tapi konsumsi kalsium gé ulah nepi ka loba teuing, sabab bisa ngabalukarkeun batu ginjal. Kalsium bisa diserep ku peujit mun aya Vitamin D.

Pikeun leuwih lengkep ngeunaan Ca dina kahirupan, mangga aos kalsium dina biologi.

Kalsium atawa kapur dina cai bisa nyieun masalah nyaeta ningkatkeun TDS. Cara meurunkan TDS air tanpa RO diantarana nganggo resin kation anion. Salah sahiji merekna nyaeta resin thermax tulsion T42-Na

History 
(Latin calx, lime) Lime was prepared and used by the Romans as éarly as the 1st century, but calcium was not discovered until 1808. After léarning that Berzelius and Pontin prepared calcium amalgam by electrolyzing lime in mercury, Sir Humphry Davy was able to isolate the impure metal.

Occurrence 
Calcium is the fifth most abundant element in the éarth's crust (forming more than 3%) and is an essential part of léaves, bones, teeth, and shells. Due to its chemical réactivity with air and water, calcium is never found in nature unbound to

 Apatite is the fluorophosphate or chlorophosphate of calcium. Electrolysis of molten calcium chloride (CaCl2) can be used to isolate pure calcium. 
Isolation (* follow):
cathode: Ca2+* + 2e- --> Ca 
anode: Cl-* --> ½Cl2 (gas) + e-

Compounds 
Quicklime (CaO) is used in many chemical refinery processes and is made by héating and carefully adding water to limestone. When CaO is mixed with sand it hardens into a mortar and is turned into plaster by carbon dioxide uptake. Mixed with other compounds, CaO forms an important part of Portland cement.

When water percolates through limestone or other soluble carbonate rocks, it partially disolves part of the rock and causes cave formation and characteristic stalactites and stalagmites and also forms hard water. Other important calcium compounds are nitrate, sulfide, chloride, carbide, cyanamide, and hypochlorite.

Isotop 
Kalsium boga genep isotop stabil, dua di antarana aya di alam: Ca-40 stabil jeung Ca-41 radioaktif nu umur-satengahna = 103.000 taun. 97% unsur ieu aya dina wujud Ca-40. Ca-40 téh turunan tina luruhna K-40, nu ogé ngahasilkeun Ar-40. 

Baca ogé: gangguan métabolisme kalsium

Tumbu kaluar 
 WebElements.com – Kalsium
 EnvironmentalChemistry.com – Kalsium

Unsur kimia
Logam
Rasio ganjil nyaéta ukuran statistik, bagéan penting dina statistika Bayes sarta régrési logistik.

Rasio ganjil dihartikeun salaku rasio hiji kajadian ahéng dina hiji grup kana kaganjilan nu kajadian dina grup séjén, atawa estimasi data dumasar kana rasio.  Grup ieu bisa awewe jeung lalaki, grup percobaan sarta grup kontrol, atawa klasifikasi nu ngabingungkeun.  Maka lamun kamungkinan kajadian unggal grup p jeung q mangka rasio-ganjil nyaéta

Logaritma rasio ganjil mangrupa béda logit tina probabilitas.

Régrési logistik loba dipaké dina widang kadokteran jeung panalungtikan élmu sosial, hartina rasio-ganjil ilahar dipaké geus ngagambarkeun sababaraha bentuk uji klinis, saperti uji kasus-kontrol, sarta dina panalungtikan survéy.

Statistika
Dina statistik, order statistik ka-n tina sampel saruna jeung nilai sampel ka-n pangleutikna.

Contona, lamun nilai sampe nyaéta:

6, 9, 3, 8

mangka order statistik kadua nyaéta:

x(2) = 6.

Order statistik kahiji (atawa order statistik pangleutikna) salawasna minimum tina sampel.  Keur ukuran sampel n, order statistik ka-n (atawa order statistik panggedéna) nyaéta maximum.

Dina notasi konvensional, ditulis:

x1 = 6
x2 = 9
x3 = 3
x4 = 8

teu maké kurung() dina subscripts, dumasar kana urutan data nu dikumpulkeun, sarta:

x(1) = 3
x(2) = 6
x(3) = 8
x(4) = 9

make kurung () dina subscripts, dumasar kana order statistik, dina hal ieu, data disusun dumasar kana naekna order.

Beda jeung quantiles....

Tempo oge

 Rankit
 Box plot
 Fisher-Tippett distribution

Statistika
Dina statistik, overfitting nyaéta modél statistik keur nyocogkeun niley nu mibanda sababaraha paraméter.  modél absurd sarta falsu bakal cocog sacara sampurna lamun ieu modél mibanda karudetan nu cukup dibandingkeun jeung jumlah data nu aya. Overfitting ilaharna diwangun ku susunan Occam's razor.

Widang anyar nu keur ilahar dipaké dina konsép overfitting nyaéta machine learning. Ilaharna algorithm diajar nyaéta ngajarkeun ku ngagunakeun sababaraha susunan latihan, upamana ngagunakeun sababaraha kaayaan nu hasil ahirna geus dipikawanoh. Nu diajar nganggap yén ngaramalkeun yén hasil nu bakal kahontal bakal nembongkeun hasil nu bener lamun dipaké kana conto séjénna, ku sabab kitu kaayaan umum ieu teu katembong salila diajarkeun (dumasar kana inductive bias). Sanajan kitu, umumna dina kasus nu aya salila diajar ngabutuhkeun waktu nu lila atawa conto latihan nu kawilang langka, nu diajar bakal ngadeukeutkeun manéh kana sababaraha hal husus variabel acak salila diajar, nu taya hubungan baraya jeung fungsi target nu bakal kahontal. Dina prosés overfitting ieu, hasil nu ditembongkeun dina nu diajar masih alus sedengkeun hasil dina data nu teu katempo bakal leuwih goreng.

Boh dina statistik jeung machine learning, dina usaha keur meunang hasil nu cocog, perlu ditambahkeun téhnik séjénna(upamana validasi silang, early stopping), nu bisa nembongkeun yén léngkah diajar saterusna lain dihasilkeun tina ka-ilaharan nu panghadéna. Dina treatment learning, niley minimum nu ngadukung pangalusna nu dipaké keur nangtukeun niley nu cocog dina overfitting.

Statistika
Rangking persentil tina skor nyaéta perséntase skor panghandapna tina sebaran frekuensina. Conto, skor uji leuwih ti 90% tina skor nu dicokot tina uju maka bakal disebutkeun dina persentil ka-90.

Rangking persentil ilaharna dipaké keur ngajelaskeun interpretasi skor dina uji standar. Lamun sebaran ieu kasebar normal, rangking persentil bisa dicokot tina skor standar.

Statistika
métodeu  kaputusan statistik parametrik mangrupa prosedur matematik keur tes hipotesa statistik nu nganggap yén sebaran variabel bakal bisa ditaksir ku karakter nu ditempo. Analisa varian nganggap yén dina kaayaan sebaran normal sarta varian tina sebaran nu dibandingkeun dianggap sarua. Koefisien korelasi momen-produk Pearson dianggap normal.

Kadangkala tenknik parametrik mangrupa hal nu kuat – hal ieu, ku nahankeun tetempoan kana power keur ngalacak béda atawa sarua waktu ieu asumsi kalanggar – sababaraha sebaran ngalanggar asumsi mangka ditandaan salaku statistik non-parametrik, alternatip nu leuwih ilahar dipaké keur ngalacak béda atawa sarua.

Statistika
Interpolasi Pareto mangrupa métodeu  interpolasi nonlinier keur manggihkeun median tina susunan data.  Ilahar dipaké dina widang ekonomi keur ngagambarkeun analisa panghasilan.  Anggapan nu dipaké yén data nuturkeun kurva nu disebut sebaran Pareto.

Median dirumuskeun ku

nu mana paraméter κ jeung θ dirumuskeun ku:

sarta

nu mana

a = wates handap kategori nu ngandung median

b = wates luhur kategori nu ngandung median

Pa = proporsi sebaran nu katutup di handapeun wates handap

Pb = proporsi sebaran nu katutup di handapeun wates handap

Statistika
Ékonomi
Matematika
Dina matematik, sarta dina sabagéan statistik, the Pearson product-moment correlation coefficient (r) is a méasure of how well a linear equation describes the relation between two variables X and Y méasured on the same object or organism. It is defined as the sum of the products of the skor standard of the two méasures divided by the degrees of freedom:

The result obtained is equivalent to dividing the covariance between the two variables by the product of their standard deviations. In general the quantity of a correlation coefficient is the square root of the coefficient of determination (r2), which is the ratio of explained variation to total variation:

where:

Y = a score on a random variable Y
Y' = corresponding predicted value of Y, given the correlation of X and Y and the value of X
 = mean of Y

The correlation coefficient adds a sign to show the direction of the relationship. The formula for the Péarson coefficient conforms to this definition, and applies when the relationship is linéar.

The coefficient ranges from -1 to 1. A value of 1 shows that a linéar equation describes the relationship perfectly and positively, with all data points lying on the same line and with Y incréasing with X. A score of -1 shows that all data points lie on a single line but that Y incréases as X decréases. A value of 0 shows that a linéar modél is inappropriate – that there is no linéar relationship between the variables.

The Péarson coefficient is a statistic which estimates the correlation of the two given random variables.

The linéar equation that best describes the relationship between X and Y can be found by linear regression. If X and Y are both normally distributed, this can be used to "predict" the value of one méasurement from knowledge of the other. That is, for éach value of X the equation calculates a value which is the best estimate of the values of Y corresponding the specific value of X. We denote this predicted variable by Y.

Any value of Y can therefore be defined as the sum of Y and the difference between Y and Y:

The varian of Y is equal to the sum of the variance of the two components of Y:

Since the coefficient of determination implies that sy.x2 = sy2(1 − r2) we can derive the identity

The square of r is conventionally used as a méasure of the strength of the association between X and Y. For example, if the coefficient is .90, then 81% of the variance of Y is said to be explained by the changes in X and the linéar relation between X and Y.

r is a statistik parametrik. It assumes that the variables being assessed are normally distributed. If this assumption is violated, a non-parametric alternative such as Spearman's ρ may be more successful in detecting a linéar relationship.

Statistika
Population dynamics is the study of marginal and long term changes in the numbers, individual weights and age composition of individuals in one or several populations, and biological and environmental processes influencing those changes.

Population dynamics is the dominant branch of mathematical biology, which has a history of more than 200 yéars. The éarly period was dominated by demographic studies such as the work of Benjamin Gompertz (5 March1779-14 July1865) and Pierre François Verhulst (28 October1804-15 February1849), who refined and adjusted the Malthusian demograhical modél.

A more general modél formulation was proposed by F.J. Richards in 1959, by which the modéls of Gompertz, Verhulst and also Ludwig von Bertalanffy are covered as special cases of the general formulation.
The computer game SimCity tries to simulate some of these population dynamics.
Population dynamics also attempts to study topics such as aging populations or population decline.

See also: System dynamics, Volterra-Lotka equations

Fisheries science
Error probabiliti dina tes hipotesis

Dina tes hipotesis dina statistik, dibedakan dua tipe eror.
Tipe I eror nu nolak null hipotesa lamun éta hipotesa bener; ieu ngagambarkuen hasil positip salah.
Tipe II eror nu gagal keur nolak null hipotesa nu salah; ieu ngagambarkeun hasil negatip salah.

Eror probabiliti dibedakeun ampir sarua. 
 Keur Tipe I eror, dilambangkeun ku α (alpha) sarta dipikanyaho minangka ukuran tina tes sarta 1 minus mangrupa husus tina tes.
 Keur Tipe II eror, dilambangkeun ku β (beta) sarta 1 minus mangrupa power atawa 1 minus tina sensitip tina tes.

Eror probabiliti dina model statistik jeung ekonometrik

Loba model dina statistik sarta ekonometrik bakal ilahar dipaké keur ngurangan beda antara nilai panalungtikan jeung nilai prediksi atawa nilai téori.  Beda ieu dipikanyaho minangka eror, waktu panalungtikan bakal leuwih hadé dijelaskeun minangka sesa.

Eror bakal jadi variabel random sarta mibanda distribusi probabiliti.
Ekspektasi phitagoras mangrupa rumus nu diwangun ku Bill James keur estimasi lobana game dina tim baseball "kudu" meunang dumasar kana jumlah skor jeung aturanna.  Watesan ieu asalna tina kasaruaan rumus Pythagoras nu ngitung panjang hypotenuse segitiga tina panjang dua sisi séjénna.

Rumus dasarna nyaéta:

meunang mangrupa persentase nu dihasilkeun tina rumus.  Saterusna bisa ngalikeun ku jumlah game nu dimaenkeun ku unggal tim (kiwari, musim dina Liga Utama aya 162 game) keur ngitung kudu sabaraha loba dikira-kira meunang dumasar kana nilai jeung aturanna.

Sacara empiris, rumus ieu pakait jeugn kumaha penampilan tim basebal, sanajan eksponen 1.81 ampir akurat.  Hubungan ieu hiji kaputusan nu dipaké keur runs salaku ukuran keur penampilan pamaen. Usaha nu geus digawekeun nyaéta manggihkeun eksponen idéal keur rumus, ilahar dipikanyaho ku rumus pythagenport (dikumpulkeun ku Clay Davenport) 1.5log((r+ra)/g)+.45 sarta anu kurang kawentar tapi ampir epektip: ((r+ra)/g)^.287, invented by David Smyth.

Sacara ilahar dipercaya yén simpangan tina hiji tim ekpektasi nyaéta gumantung kana nasib sarta kualitas bullpen tim ogé kaayaan waktu éta game dimaenkeun.

Tempo oge: Baseball statistics, Sabermetrics

Tumbu kaluar
Applying the pythagorean expectation to Football: Includes a discussion of how the exponent in the formula should be larger the larger the number of points scored per game becomes.
Panalungtikan psikologi kuantitatif nyaéta panalungtikan psikologis nu ngajalankeun éstimasi statistis atawa inferensi statistis. Harti ieu dibédakeun tina nu disebut panalungtikan psikologi kualitatif; tapi, loba ogé psikolog nu teu pati ngabédakeun antara panalungtikan kuantitatif jeung kualitatif. Sohéh henteuna pangbéda ieu dibahas dina panalungtikan psikologi kualitatif.

Métode kuantitatif dipaké dina loba widang élmu sosial.

Psikologi