#+TITLE: Rapport package team
#+AUTHOR: Kolmogorov-Smirnov-test
#+DATE: 2011-04-26 20:25 CET
** Description
This template will run a Kolmogorov-Smirnov-test
**** Introduction
[[http://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test][Kolmogorov-Smirnov
test]] is one of the most widely used
[[http://en.wikipedia.org/wiki/Non-parametric_statistics][nonparametric
tests]]. 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
[[http://en.wikipedia.org/wiki/Cumulative_distribution_function][Cumulative
Distribution Functions]] of the variables we compared:
[[plots/KolmogorovSmirnovTest-1-hires.png][[[plots/KolmogorovSmirnovTest-1.png]]]]
[[plots/KolmogorovSmirnovTest-2-hires.png][[[plots/KolmogorovSmirnovTest-2.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 |
#+CAPTION: 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
[[http://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test][Kolmogorov-Smirnov
test]] is one of the most widely used
[[http://en.wikipedia.org/wiki/Non-parametric_statistics][nonparametric
tests]]. 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
[[http://en.wikipedia.org/wiki/Cumulative_distribution_function][Cumulative
Distribution Functions]] of the variables we compared:
[[plots/KolmogorovSmirnovTest-3-hires.png][[[plots/KolmogorovSmirnovTest-3.png]]]]
[[plots/KolmogorovSmirnovTest-4-hires.png][[[plots/KolmogorovSmirnovTest-4.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 |
#+CAPTION: 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.
--------------
This report was generated with [[http://www.r-project.org/][R]] (3.0.1)
and [[http://rapport-package.info/][rapport]] (0.51) in /0.729/ sec on
x86\_64-unknown-linux-gnu platform.
[[images/logo.png]]