The kolmogorov smirnov test

67 %
33 %
Information about The kolmogorov smirnov test
Business & Mgmt

Published on February 27, 2014

Author: mitrasubhradeep


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.

Add a comment

Related presentations

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 ...
Read more

Kolmogorow-Smirnow-Test – Wikipedia

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

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

Kolmogorov-Smirnov-Test (Kolgoroff-Smirnoff-Test) -

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

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

Suchergebnis auf 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.
Read more

Kolmogorov-Smirnov-Test – PflegeWiki

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

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

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

Shapiro-Wilk-Test – Wikipedia

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