Dina [[statistik]], tes '''Kolmogorov-Smirnov''' dipake keur ngabedakeun dua [[probability distribution|distributions]] empiris atawa ngabedakeun sebaran empiris beda jeung sebaran tiori.
TheCumulative empiricaldistribution cumulative distributionempiris forkeur ''n'' observationsobservasi ''y<sub>i</sub>'' isdiartikeun defined asku ''E''(''x'') = <font size=+1>Σ</font> <sub>''i''</sub> (''y<sub>i</sub> < x''). TheTes twostatistik onedua-sidedsisi Kolmogorov-Smirnov test statistics statistics are givendirumuskeun byku
:<math>D_n^{+}=\max(E(x)-F(x))</math>
Baris ka-7:
:<math>D_n^{-}=\max(F(x)-E(x))</math>
wherenumana ''F''(''x'') isnyaeta thesebaran hypothesizedhipotesa distributionatawa orsebaran anotherempiris empirical distributionsejenna. The probabilityProbability distributions ofdua thesestatistik two statisticsieu, given thatnunjukkeun theyen null hypothesis ofsebaran equalitysarua ofnyaeta distributions is truebener, does not depend on whathenteu thegumantung hypothesizedkana distributionhipotesa issebaran, assalila long as it is continuouskontinyu. [[Donald Knuth|Knuth]] givesnunjukkeun asacara detailedjentre descriptionkumaha ofcara howanalisa tosignifikan analyzetina thepasangan significancestatistik ofieu. this pair of statistics. Loba Manymasarakat peoplenu usemake max(''D<sub>n</sub><sup>+</sup>, D<sub>n</sub><sup>-</sup>'') instead, but the distribution oftapi thissebaran statisticdina isieu morestatistik difficultleuwih tohese dealkeur withdirengsekeun.
NoteHiji thatcatetan whendina thekaayaan underlyingvariabel independentbebas variable is cyclic''berulang'', assaperti withpoe daydina ofsataun theatawa yearpoe ordina day of the weeksaminggu, then [[Kuiper's test]] isleuwih morehade appropriatedipake. Numerical Recipes is angarupakeun goodsumber sourcenu ofhade informationkeur oninformasi thisieu.
NoteCatetan furthermoresaterusna, that thetes Kolmogorov-Smirnov testleuwih issensitip moredina sensitivetitik atnu pointsdeukeut near thekana median ofsebaran thetinimbang distributiondina than on its tailstungtungna. The [[Anderson-Darling test]] issalah a testsahiji thattes providesnu equalnunjukkeun sensitivitykasaruaan atsensitip thedi tailstungtung.
