2.13.1.9 kstest

1 Brief Information
2 Command Line Usage
3 X-Function Execution Options
4 Variables
5 Description
6 Examples
7 Algorithm
8 References
9 Related X-Functions

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	Variable Name	I/O and Type	Default Value	Description
Input	irng	Input Range	<active>	Specify the input data range
Statistics	stat	Output double	<unassigned>	Specify the mean of the normal distribution. If value is <auto>, Origin will calculate it automatically
Variance	df	Output double	<unassigned>	Specify the variance of the normal distribution. If value is <auto>, Origin will calculate it automatically
Statistics	prob	Output double	<unassigned>	The computed test statistics, D.

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 $x_1,x_2,... ,x_n$ , let $S_n(x_{(i)})$ and $F_0(x_{(i)})$ ) represent the sample cumulative distribution function and the theoretical (null) cumulative distribution function respectively at the point $x_{(i)}$ where $x_{(i)}$ is the ith smallest sample observation, the K-S test provides a test of the null hypotheses $H_0$ : 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 $S_n(x_{(i)}$ and $F_0(x_{(i)})$ , 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.