% Rapport package team
% Kolmogorov-Smirnov-test
% 2011-04-26 20:25 CET
## Description
This template will run a Kolmogorov-Smirnov-test
#### Introduction
[Kolmogorov-Smirnov test](http://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test) is one of the most widely used [nonparametric tests](http://en.wikipedia.org/wiki/Non-parametric_statistics). With the help of that in this case we use to check if two continuous variables had the same distribution. We do not test that here, but there is a possibility to use that in the way to check if a sample/variable followed an expected distribution.
#### Distributions
Before we use the K-S test to look at the possible statistical differences, it could be useful to see visually the distributions we want to observe. Below lie the [Cumulative Distribution Functions](http://en.wikipedia.org/wiki/Cumulative_distribution_function) of the variables we compared:
[![](plots/KolmogorovSmirnovTest-1.png)](plots/KolmogorovSmirnovTest-1-hires.png)
[![](plots/KolmogorovSmirnovTest-2.png)](plots/KolmogorovSmirnovTest-2-hires.png)
#### Test results
Now we will test if the Internet usage for educational purposes (hours per day) and the Age had statistically the same distribution.
---------------------------------------------------
Test statistic P value Alternative hypothesis
---------------- --------- ------------------------
1 _0_ * * * two-sided
---------------------------------------------------
Table: Two-sample Kolmogorov-Smirnov test on Internet usage for educational purposes (hours per day) and Age
The requirements of the Kolmogorov-Smirnov Test test was not met, the approximation may be incorrect.
So the variables do not follow the same distribution, according to the Kolmogorov-Smirnov test statistic.
## Description
This template will run a Kolmogorov-Smirnov-test
#### Introduction
[Kolmogorov-Smirnov test](http://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test) is one of the most widely used [nonparametric tests](http://en.wikipedia.org/wiki/Non-parametric_statistics). With the help of that in this case we use to check if two continuous variables had the same distribution. We do not test that here, but there is a possibility to use that in the way to check if a sample/variable followed an expected distribution.
#### Distributions
Before we use the K-S test to look at the possible statistical differences, it could be useful to see visually the distributions we want to observe. Below lie the [Cumulative Distribution Functions](http://en.wikipedia.org/wiki/Cumulative_distribution_function) of the variables we compared:
[![](plots/KolmogorovSmirnovTest-3.png)](plots/KolmogorovSmirnovTest-3-hires.png)
[![](plots/KolmogorovSmirnovTest-4.png)](plots/KolmogorovSmirnovTest-4-hires.png)
#### Test results
Now we will test if the cyl and the carb had statistically the same distribution.
-----------------------------------------------------------
Test statistic P value Alternative hypothesis
---------------- ----------------- ------------------------
0.625 _7.453e-06_ * * * two-sided
-----------------------------------------------------------
Table: Two-sample Kolmogorov-Smirnov test on cyl and carb
The requirements of the Kolmogorov-Smirnov Test test was not met, the approximation may be incorrect.
So the variables do not follow the same distribution, according to the Kolmogorov-Smirnov test statistic.
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This report was generated with [R](http://www.r-project.org/) (3.0.1) and [rapport](http://rapport-package.info/) (0.51) in _0.729_ sec on x86_64-unknown-linux-gnu platform.
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