Friedman test

Friedman test is part of:
  • Pro Core statistical software

  • System configuration

    • Windows:
      • Versions: 9x/Me/NT/2000/XP/Vista/Win 7/Win 8
      • Excel: 97 and later
      • Processor: 32 or 64 bits
      • Hard disk: 150 Mb
    • Mac OS X:
      • OS: OS X
      • Excel: X, 2004 and 2011
      • Hard disk: 150Mb.

Benefits

  • Easy and user-friendly
    Easy and user-friendly XLSTAT is flawlessly integrated with Microsoft Excel which is the most popular spreadsheet worldwide. This integration makes it one of the simplest available tools to work with as it utilizes the same philosophy as Microsoft Excel. The program is accessible in a dedicated XLSTAT tab. The analyses are grouped into functional menus. The dialog boxes are user-friendly and setting up an analysis is straightforward.
  • Data and results shared seamlessly
    Data and results shared seamlessly One of the greatest advantages of XLSTAT is the way you can share data and results seamlessly. As the results are stored in Microsoft Excel, anyone can access them. There is no need for the receiver to have an XLSTAT license or any additional viewer which makes your team-work easier and more affordable. In addition, results are easily integrable into other Microsoft Office software such as PowerPoint, so that you can create striking presentation in minutes.
  • Modular
    Modular XLSTAT is a modular product. XLSTAT-Pro is a core statistical module of XLSTAT which includes all the mainstream functionalities in statistics and multivariate analysis. More advanced features contained in add-on modules can be added for specific applications. This way you can adapt the software to your needs making the software more cost-efficient.
  • Didactic
    Didactic The results of XLSTAT are organized by analysis and are easy to navigate. Moreover useful information is provided along with the results to assist you in your interpretation.
  • Affordable
    Affordable XLSTAT is a complete and modular analytical solution that can suit any analytical business needs. It is very reasonably priced so that the return of your investment is almost immediate. Any XLSTAT license comes with top level support and assistance.
  • Accessible - Available in many languages
    Accessible - Available in many languages We have ensured XLSTAT is accessible to everyone by making the program available in many languages, including Chinese, English, French, German, Italian, Japanese, Polish, Portuguese and Spanish.
  • Automatable and customizable
    Automatable and customizable Most of the statistical functions available in XLSTAT can be called directly from the Visual Basic window of Microsoft Excel. They can be modified and integrated to more code to fit to the specificity of your domain. Adding tables and plots as well as modifying existing outputs becomes easy. Furthermore, XLSTAT includes some special tools on the dialog boxes to generate automatically the VBA code in order to reproduce your analysis using the VBA editor or to simply load pre-set settings. This effortless automation of routine analysis will be a huge time saver on your part.

Principles of the Friedman test

The Friedman test is a non-parametric alternative to the ANOVA with two factors where the assumption of normality is not acceptable. It is used to test if k paired samples (k>2) of size n, come from the same population or from populations having identical properties as regards the position parameter. As the context is often that of the ANOVA with two factors, we sometimes speak of the Friedman test with k treatments and n blocks.

Use the Friedman's test when you have k paired samples corresponding to k treatments concerning the same blocks, in order to illustrate a difference between the treatments.

Friedman test definition

If Mi is the position parameter for sample i, the null H0 and alternative Ha hypotheses for the Friedman test are as follows:

Let n be the size of k paired samples. The Q statistic from the Friedman test is given by:

Q = 12/(nk(n+1)) Σi=1..k [Ri²-3n(k+1)]

where Ri is the sum of the ranks for sample i.

Where there are ties, the average ranks are used for the corresponding observations.

The p-value associated with a given value of Q can be approximated by a Chi² distribution with (k-1) degrees of freedom. This approximation is reliable when kn is greater than 30, the quality also depending on the number of ties. The p-values associated with Q have been tabulated for (k = 3, n = 15) and (k = 4, n = 8) (Lehmann 1975, Hollander and Wolfe 1999).

When the p-value is such that the H0 hypothesis has to be rejected, then at least one sample (or group) is different from another. To identify which samples are responsible for rejecting H0, multiple comparison procedures can be used.

Multiple comparison for the Friedman test

For the Friedman test, one multiple comparison method is available, the Nemenyi method (1963). This method is similar to the one of Dunn, but takes into account the fact that the data are paired.

Tutorials