2.13.1.9 kstest
Brief Information
One sample Kolmogorov-Smirnov test for normality
Command Line Usage
kstest irng:=col(2)
X-Function Execution Options
Please refer to the page for additional option switches when accessing the x-function from script
Variables
Display Name
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Variable Name
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I/O and Type
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Default Value
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Description
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Input
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irng
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Input
Range
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<active>
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Specify the input data range
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Statistics
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stat
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Output
double
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<unassigned>
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Specify the mean of the normal distribution. If value is <auto>, Origin will calculate it automatically
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Variance
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df
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Output
double
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<unassigned>
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Specify the variance of the normal distribution. If value is <auto>, Origin will calculate it automatically
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Statistics
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prob
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Output
double
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<unassigned>
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The computed test statistics, D.
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Description
This function provides Kolmogorov-Smirnov test to compare the maximum distance between sample cumulative distribution function with the theoretical cumulative distribution function to determine whether the sample comes from a population of the theoretical distribution specified by user. Currently, Origin tests the normality only.
Examples
1. Highlight and right-click a column, select Fill Column With: Normal Random Numbers to fill some data on the column.
2. Type kstest on the command window. The probability of null hypothesis can be seen from kstest.prob.
Algorithm
For a given sample data , let and ) represent the sample cumulative distribution function and the theoretical (null) cumulative distribution function respectively at the point where is the ith smallest sample observation, the K-S test provides a test of the null hypotheses : The data are a random sample of observations from the theoretical distribution specified by user. Currently, Origin tests the normality only.
To measure the difference between and , K-S test compute the maximum absolute difference between the two cumulative distribution functions:
And then D will be used to compute the probability of null hypothesis.
Origin calls a NAG function, nag_1_sample_ks_test (g08cbc), to compute the statistics. Please refer to related NAG document, for more details on the algorithm.
References
William H. Press, etc. 2002. Numerical Recipes in C++. Cambridge University Press.
Related X-Functions
kstest2, swtest, lillietest
Keywords:variance
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