# The kolmogorov smirnov test

67 %
33 %
Information about The kolmogorov smirnov test

Published on February 27, 2014

Source: slideshare.net

The Kolmogorov-Smirnov Test XIMB

The Kolmogorov-Smirnov Test (K-S Test) is used to test the goodnessof-fit of a theoretical frequency distribution, i.e., whether there is a significant difference between an observed frequency distribution and a given theoretical (expected) frequency distribution. •Similar to what the Chi-Square test does, but the K-S test has several advantages: More powerful test. Easier to compute and use, as no grouping of data is required. The test statistic is independent of the expected frequency distribution. It only depends on the sample size n. THE HYPOTHESES: H0: The observed frequency distribution is consistent with the theoretical frequency distribution (Good fit). H1: The observed frequency distribution is not consistent with the theoretical frequency distribution (Bad fit). α = Level of significance of the test. •Here we use the cumulative probability distribution (CDF) of observed and theoretical frequencies.

The K-S Test Statistic: Here, Fe = the expected relative cumulative frequencies(CDF). Fo = the observed relative cumulative frequencies(CDF). •If the gap between Fe and Fo is large then Ho should be rejected. •The value of the test statistic is obtained from the observed data listed in the tabular form. •A K-S test is a one tailed test. •The critical values of Dn have been tabulated and can be found from the K-S table for corresponding levels of significance and sample size n. •The calculated value of Dn is compared with the critical value of Dn. If the calculated value > critical value, then reject H0.

Example: Pg # 834, Prob. # SC14-7. Soln.: H0: The distn. is normal with µ= 6.80, σ= 1.24. H1: Above not true. Value of the variable fo Cumulat ive fo Fo (obs. CDF) Fe (exp. CDF) |Fe – Fo| ≤ 4.009 13 13 0.0173 0.0122 0.0051 4.010-5.869 158 171 0.2280 0.2266 0.0014 5.870-7.729 437 608 0.8017 0.7734 0.0373 7.730-9.589 122 730 0.9733 0.9878 0.0145 >9.590 20 750 1.0000 1.0000 0.0000 We obtain Fe values from the normal table, z= (X- µ)/ σ. The calculated value of Dn is the maximum value in the | Fe - Fo | column. Thus, 0.0373. For 0.15 level of significance, Dcritical = 1.14/√n = 1.14/√750 = 0.0416. Dn < Dcritical , so accept H0 and conclude that it is a good fit.

 User name: Comment:

## Related presentations

#### Cheapest canvas prints shopcanvasprintcom

April 2, 2014

Canvas Prints at Affordable Prices make you smile.Visit http://www.shopcanvasprint...

#### Paseo en bici por la historia del comercio gijones

April 1, 2014

30 Días en Bici en Gijón organiza un recorrido por los comercios históricos de la ...

#### Meta anlysis of 5 spanish ropo studies minerva ove...

April 1, 2014

Con el fin de conocer mejor el rol que juega internet en el proceso de compra en E...

#### Informa Whitepaper - The Rise of Australia's LNG I...

April 1, 2014

With three established projects across the country and seven more in the pipeline,...

#### Decoding Retail StartUp : Comprehensive Roll-Out S...

April 1, 2014

Retailing is not a rocket science, neither it's walk-in-the-park. In this presenta...

#### What is research??

April 2, 2014

Explanatory definitions of research in depth...

## Related pages

### Kolmogorov–Smirnov test - Wikipedia, the free encyclopedia

The Kolmogorov–Smirnov test may also be used to test whether two underlying one-dimensional probability distributions differ. In this case, the ...

### Kolmogorow-Smirnow-Test – Wikipedia

Der Kolmogorow-Smirnow-Test (KS-Test) (nach Andrei Nikolajewitsch Kolmogorow und Nikolai Wassiljewitsch Smirnow) ist ein statistischer Test auf ...

### quantitative - Nachweis der Normalverteilung: Kolmogorov ...

3.1.3.3.2 Nachweis der Normalverteilung: Kolmogorov-Smirnov-Test. Der Kolmogorov-Smirnov-Test kann auch bei kleineren Stichproben eingesetzt werden, um zu ...

### Kolmogorov-Smirnov-Test (Kolgoroff-Smirnoff-Test) - faes.de

Kolmogorov-Smirnov-Test (Kolgoroff-Smirnoff-Test) Zur Durchführung des Chiquadrat-Tests zur Prüfung auf Normalverteilung müssen die ...

### quantitative - Kolmogorov-Smirnov-Test mit SPSS

3.1.3.3.2.1 Kolmogorov-Smirnov-Test mit SPSS. A. Sie wählen in SPSS den Menüpunkt ANALYSIEREN. B. Aus den heruntergeklappten Alternativen wählen Sie ...

### Suchergebnis auf Amazon.de für: Kolmogorov-Smirnov test ...

Auszug Seite 190: ... Mit dem Kolmogorov-Smirnov-Test und dem Shapiro-Wilk-Test kann geprüft ... Zufällige Seite in in diesem Buch.

### Kolmogorov-Smirnov-Test – PflegeWiki

Der Kolmogorov-Smirnov-Test untersucht, ob zwei Stichproben (Datenreihen) aus derselben Verteilung stammen. Üblicherweise wird er auch angewendet, um zu ...

### 1.3.5.16. Kolmogorov-Smirnov Goodness-of-Fit Test

Test for Distributional Adequacy The Kolmogorov-Smirnov test (Chakravart, Laha, and Roy, 1967) is used to decide if a sample comes from a population with a ...

### Kolmogorov-Smirnov-Anpassungstest | Marktforschungs-Wiki ...

Die Prüfung auf das Vorliegen einer Normalverteilung erfolgt idealerweise mit einem Anpassungstest, wie beispielsweise dem Kolmogorov-Smirnov-Anpassungstest.

### Shapiro-Wilk-Test – Wikipedia

Der Shapiro-Wilk-Test ist ein statistischer Signifikanztest, der die Hypothese überprüft, dass die zugrunde liegende Grundgesamtheit einer Stichprobe ...