Statistics.Test.KolmogorovSmirnov

Kolmogov-Smirnov tests are non-parametric tests for assesing whether given sample could be described by distribution or whether two samples have the same distribution. It's only applicable to continous distributions.

Kolmogorov-Smirnov test

kolmogorovSmirnovTest

Arguments

:: Distribution d

=> d

Distribution

-> Double

p-value

-> Sample

Data sample

-> TestResult

Check that sample could be described by distribution. Significant means distribution is not compatible with data for given p-value.

This test uses Marsaglia-Tsang-Wang exact alogorithm for calculation of p-value.

kolmogorovSmirnovTestCdf

Arguments

:: (Double -> Double)

CDF of distribution

-> Double

p-value

-> Sample

Data sample

-> TestResult

Variant of kolmogorovSmirnovTest which uses CFD in form of function.

kolmogorovSmirnovTest2

Arguments

:: Double

p-value

-> Sample

Sample 1

-> Sample

Sample 2

-> TestResult

Two sample Kolmogorov-Smirnov test. It tests whether two data samples could be described by the same distribution without making any assumptions about it.

This test uses approxmate formula for computing p-value.

Evaluate statistics

kolmogorovSmirnovCdfD

Arguments

:: (Double -> Double)

CDF function

-> Sample

Sample

-> Double

Calculate Kolmogorov's statistic D for given cumulative distribution function (CDF) and data sample. If sample is empty returns 0.

kolmogorovSmirnovD

Arguments

:: Distribution d

=> d

Distribution

-> Sample

Sample

-> Double

Calculate Kolmogorov's statistic D for given cumulative distribution function (CDF) and data sample. If sample is empty returns 0.

kolmogorovSmirnov2D

Arguments

:: Sample

First sample

-> Sample

Second sample

-> Double

Calculate Kolmogorov's statistic D for two data samples. If either of samples is empty returns 0.

Probablities

kolmogorovSmirnovProbability

Arguments

:: Int

Size of the sample

-> Double

D value

-> Double

Calculate cumulative probability function for Kolmogorov's distribution with n parameters or probability of getting value smaller than d with n-elements sample.

It uses algorithm by Marsgalia et. al. and provide at least 7-digit accuracy.

Data types

data TestType

Test type. Exact meaning depends on a specific test. But generally it's tested whether some statistics is too big (small) for OneTailed or whether it too big or too small for TwoTailed

Constructors

OneTailed

TwoTailed

Instances

Eq TestType

Ord TestType

Show TestType

Typeable TestType

data TestResult

Result of hypothesis testing

Constructors

Significant

Null hypothesis should be rejected

NotSignificant

Data is compatible with hypothesis

Instances

Eq TestResult

Ord TestResult

Show TestResult

Typeable TestResult

References

• G. Marsaglia, W. W. Tsang, J. Wang (2003) Evaluating Kolmogorov's distribution, Journal of Statistical Software, American Statistical Association, vol. 8(i18).