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===Overview of the Kolmogorov-Smirnoff Test=== | ===Overview of the Kolmogorov-Smirnoff Test=== | ||
| − | The Kolmogorov-Smirnoff test (KS-test) compares how distinct two datasets are. The KS-test | + | The Kolmogorov-Smirnoff test (KS-test) compares how distinct two datasets are. The KS-test makes no assumptions about the distribution of data, and therefore is a [http://en.wikipedia.org/wiki/Non-parametric_statistics non-parametric, or distribution-free, test]. Other [http://en.wikipedia.org/wiki/Parametric_statistics parametric tests], e.g., Student's t-test, Normal Z-test, etc., may be more [[AP_Statistics_Curriculum_2007_Hypothesis_Basics#Type_I_Error.2C_Type_II_Error_and_Power | sensitive]] if the ''data meet the requirements'' of the test. [http://en.wikipedia.org/wiki/Kolmogorov-Smirnov_test More information about the Kolmogorov-Smirnoff Test is available here]. |
| − | ===Examples== | + | ===Examples=== |
| − | This example is based on a dataset from the '''R package''' under the library '''MASS'''. The dataset's name is '''oats'''. The quantitative variable '''Y''' (yields of oats field) is grouped by three varieties (the categorical variable here), '''Victory''', '''Golden.rain''' and '''Marvelous'''. | + | ====Oats Example==== |
| + | Go to the [http://www.socr.ucla.edu/htmls/ana/KolmogorovSmirnoff_Analysis.html SOCR Kolmogorov-Smirnoff Test Applet]. This [http://www.springerlink.com/content/up3783363417vq75/fulltext.pdf example is based on a dataset] from the '''R package''' under the library '''MASS'''. The dataset's name is '''oats'''. The quantitative variable '''Y''' (yields of oats field) is grouped by three varieties (the categorical variable here), '''Victory''', '''Golden.rain''' and '''Marvelous'''. | ||
| − | + | : The treatment structure in this experiment was a 3 × 4 full factorial, with 3 oat varieties and 4 nitrogen concentrations. The agricultural plots for this experiment were grouped into 6 blocks, each with 3 plots. Each plot was subdivided into 4 subplots. The varieties were randomly assigned to the plots within each block. The nitrogen concentrations were randomly assigned to the subplots within each plot. Physically, there are three levels of grouping of the experimental units: block, plot, and subplot. Because the treatments are randomly assigned at each level of grouping, we may be tempted to associate random effects with each level. | |
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| + | <center>[[Image:SOCR_AnalysisActivities_KS_Dinov_102208_Fig1a.png|300px]]</center> | ||
* As you start the [http://www.socr.ucla.edu/htmls/SOCR_Analyses.html SOCR Analyses Applet], click on '''Kolmogorov-Smirnoff Test''' from the combo box in the left panel. Next, click on '''Example 4''' and then the '''Data''' tab on the top of the right panel. You will see something like below. The data have been divided into 6 columns by groups. | * As you start the [http://www.socr.ucla.edu/htmls/SOCR_Analyses.html SOCR Analyses Applet], click on '''Kolmogorov-Smirnoff Test''' from the combo box in the left panel. Next, click on '''Example 4''' and then the '''Data''' tab on the top of the right panel. You will see something like below. The data have been divided into 6 columns by groups. | ||
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: '''Note''': if you happen to click on the "Clear" button in the middle of the procedure, all the data will be cleared out. Simply start over from step 1. | : '''Note''': if you happen to click on the "Clear" button in the middle of the procedure, all the data will be cleared out. Simply start over from step 1. | ||
| + | ====Example 2: Control-Treatment test==== | ||
| + | [http://www.physics.csbsju.edu/stats/KS-test.html This examples also illustrates a control vs. treatment examples that compares the (independent) T-test and the corresponding analysis using the Kolmogorov-Smirnoff Test]. | ||
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| + | ====Model fitting==== | ||
| + | The SOCR [[SOCR_EduMaterials_ModelerActivities_MixtureModel_1#Model_Fitting |mixture-modeler provides an example of using the Kolmogorov-Smirnoff Test to assess quality of fitting a Gaussian mixture distribution model to user-specified data]]. | ||
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Latest revision as of 13:52, 29 January 2010
Contents
SOCR Analysis Activities - SOCR Analyses Example on Kolmogorov-Smirnoff Test
Overview of the Kolmogorov-Smirnoff Test
The Kolmogorov-Smirnoff test (KS-test) compares how distinct two datasets are. The KS-test makes no assumptions about the distribution of data, and therefore is a non-parametric, or distribution-free, test. Other parametric tests, e.g., Student's t-test, Normal Z-test, etc., may be more sensitive if the data meet the requirements of the test. More information about the Kolmogorov-Smirnoff Test is available here.
Examples
Oats Example
Go to the SOCR Kolmogorov-Smirnoff Test Applet. This example is based on a dataset from the R package under the library MASS. The dataset's name is oats. The quantitative variable Y (yields of oats field) is grouped by three varieties (the categorical variable here), Victory, Golden.rain and Marvelous.
- The treatment structure in this experiment was a 3 × 4 full factorial, with 3 oat varieties and 4 nitrogen concentrations. The agricultural plots for this experiment were grouped into 6 blocks, each with 3 plots. Each plot was subdivided into 4 subplots. The varieties were randomly assigned to the plots within each block. The nitrogen concentrations were randomly assigned to the subplots within each plot. Physically, there are three levels of grouping of the experimental units: block, plot, and subplot. Because the treatments are randomly assigned at each level of grouping, we may be tempted to associate random effects with each level.
- As you start the SOCR Analyses Applet, click on Kolmogorov-Smirnoff Test from the combo box in the left panel. Next, click on Example 4 and then the Data tab on the top of the right panel. You will see something like below. The data have been divided into 6 columns by groups.
- Click on the Mapping tab to map the groups you would like to include in the analysis. Select two groups.
- Now you will click on Compute to let the program produce the results. Click on Result to view the results.
- Click on Graph to view plots.
- Note: if you happen to click on the "Clear" button in the middle of the procedure, all the data will be cleared out. Simply start over from step 1.
Example 2: Control-Treatment test
Model fitting
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