MathGrapher | The Mathematical Graphing Tool for Students, Scientists and Engineers


  • Functions
  • Data
  •       ==>
  • Curve Fitting
  • Iterations
  • ODEs
  • Matrices
  • L-systems
  • Game of life
  • Screenviews
  • Data
    You are here: Modules > Data
    Links in the text refer to the lower part of the page

    Data in 2D and 3D

    Edit and select Data from a grid and draw a 2D or 3D Graph. You may view 3D data in the 3D viewer and make Contour plots and Cross-sections through Contour plots. Some statistical properties of the data may be calculated. You may also draw a histogram or the (cumulative, normalized) distribution function of selected data.
    You may apply a Chi-square test or a Kolmogorov-Smirnov test to compare two distributions

    Data: Statistics

    Chi-square test - 1 and 2

    Chi-square test - 1 and 2

           The Chi-square test is used to test differences between binned distributions. The selected Y-values in grid 1 and grid 2 are compared.
    In the first test the Y-values in grid 1 are assumed to represent a theoretical distribution. Chi-squared is defined as


           where Ni is the number in the i-th bin and ni is the number expectred according to some known distribution. Both distributions should contain the same total number of events.
    The probablity (0<P<1) that the numbers Ni are drawn from the expected distribution is calculated. It is an incomplete Gamma function of Chi-squared. 
    In the second test two measured data sets (in grid 1 and grid 2) are compared. Chi-squared is then defined as


           where Ni and Mi are the numbers in the i-th bin of the distributions calculated in grid 1 and grid 2. The total numbers should be the same. The probablity P that the two distributions are drawn from the same underlying distribution is calculated. A small value of  P indicates that the two distributions are probably different.

    Kolmogorov-Smirnov test - 1 and 2

           The KS-test is used to test differences between unbinned distributions of a single continuous variable. The largest vertical difference D between the cumulative distributions is determined. This yields the probability that the two distributions are drawn from the same underlying distribution.
    The first test compares the data in grid 2 with a theoretical (normalized) distribution function defined in the Function panel.
    The second test compares (observed) data in grid 1 and grid 2.

      © MathGrapher 2006 | Freeware since 25 october 2013   Contact the Webmaster