Multidimensional tests

Multidimensional tests 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 multidimensional tests

The multidimensional tests implemented in XLSTAT are used to compare samples described by several variables. Instead of comparing the average of two samples as with the Student t test, we compare here simultaneously for the same samples averages measured for several variables.

Compared to a procedure that would involve as many Student t-tests as there are variables, the method proposed here has the advantage of using the structure of covariance of the variables and of obtaining an overall conclusion. It may be that two samples are different for a variable with a Student t test, but that overall it is impossible to reject the hypothesis that they are similar.

Mahalanobis distance

The Mahalanobis distance, allows computing the distance between two points in a p-dimensional space, while taking into account the covariance structure across the p dimensions.

The square of the Mahalanobis distance writes:

dM² = (x1 - x2) ∑-1 (x1 - x2)

where xi is the vector x1 and ∑ is the covariance matrix.

The Mahalanobis distance can be used to compare two groups (or samples) because the Hotelling T² statistic defined by:

T² = [(n1*n2) ⁄ (n1 + n2)] dM

follows a Hotelling distribution, if the samples are normally distributed for all variables.

The F statistic that is used for the comparison test where the null hypothesis H0 is that the means of the two samples are equal, is defined by:

F = T² [n1+ n2 – (p-1)] ⁄ [(n1 + n2 – 2)*p]

This statistic follows a Fisher’s F distribution with p and n1+n2-p-1 degrees of freedom if the samples are normally distributed for all the variables.

If we want to compare more than two samples, the test based on the Mahalanobis distance can be used to identify possible sources of the difference observed at the global level. It is then recommended to use the Bonferroni correction for the alpha significance level.

Wilks’ lambda

Wilks' lambda is a statistical test used in multivariate analysis of variance to test whether there are differences between the means of the samples on a combination of dependent variables.

Testing the equality of the within-groups covariance matrices

Box test

The Box test is used to test the assumption of equality for intra-class covariance matrices. Two approximations are available, one based on the Chi² distribution, and the other on the Fisher distribution.

Kullback’s test

The Kullback’s test is used to test the assumption of equality for intra-class covariance matrices. The statistic calculated is approximately distributed according to a Chi² distribution.

Tutorials

Screenshots