KOLMOGOROV-SMIRNOV TEST


The Kolmogorov-Smirnov is an ordinal test used with one- group samples. The experimenter uses it to find out whether a distribution of observations is significantly different from a theoretical distribution. The test compares the cumulative distribution of the observed scores and the cumulative distribution of the expected scores. The point where the two distributions show the largest divergence is then determined. Next, the experimenter refers to the sampling distribution to determine whether this divergence is the result of chance or a real difference. Do the scores in these two distributions come from the same population? To test this difference, one uses the critical value of D for the Kolmogorov-Smirnov test. The requirements for the Kolmogorov-Smirnov test are as follows :

  1. Ordinal data

  2. One group

  3. Simple random sample

The formula for the Kolmogorov-Smirnov test is:

where LD = large difference, N = number of individuals in the sample, O = number of individuals observed, E = number of individuals you would expect in the sample, OC = observed cumulative distribution, EC = expected cumulative distribution, and f = frequency of scores.

Special note:  

In the process of calculating this test, notice that the definitions of OC and EC are part of the cumulative distribution. Before you can use the Kolmogorov-Smirnov test, you must know how to create a cumulative distribution.




Six Sigma and Beyond. Statistics and Probability
Six Sigma and Beyond: Statistics and Probability, Volume III
ISBN: 1574443127
EAN: 2147483647
Year: 2003
Pages: 252

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