Principal Component Analysis (PCA)

Principal Component Analysis (PCA) 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.


  • 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 Principal Component Analysis

Principle Component Analysis (PCA) is one of the most frequently used multivariate data analysis.

Principle Component Analysis can be considered as a projection method which projects observations from a p-dimensional space with p variables to a k-dimensional space (where k < p) so as to conserve the maximum amount of information (information is measured here through the total variance of the scatter plots) from the initial dimensions. If the information associated with the first 2 or 3 axes represents a sufficient percentage of the total variability of the scatter plot, the observations will be able to be represented on a 2- 3-dimensional chart, thus making interpretation much easier.

Use of Principal Component Analysis

There are several uses for Principle Component Analysis, including:

Principal Component Analysis input data

XLSTAT offers several possibilities for the matrix to be used in the Principle Component Analysis algotithm:

Rotation for Principal Component Analysis

Rotations can be applied on the factors. Several methods are available including Varimax, Quartimax, Equamax, Parsimax, Quartimin and Oblimin and Promax.

Results for Principal Component Analysis in XLSTAT

Correlation/Covariance matrix

This table shows the data to be used afterwards in the calculations. The type of correlation depends on the option chosen in the "General" tab in the dialog box. For correlations, significant correlations are displayed in bold.

Bartlett's sphericity test

The results of the Bartlett sphericity test are displayed. They are used to confirm or reject the hypothesis according to which the variables do not have significant correlation.


The eigenvalues and corresponding chart (scree plot) are displayed. The number of eigenvalues is equal to the number of non-null eigenvalues.

Factor loadings and correlations

XLSTAT displays the factor loadings in the new space, then the correlations between the initial variables and the components in the new space. The correlations are equal to the factor loadings in a normalized PCA (on the correlation matrix). If supplementary variables have been selected, the corresponding coordinates and correlations are displayed at the end of the table.


Contributions are an interpretation aid. The variables which had the highest influence in building the axes are those whose contributions are highest.

Squared cosines for the variables

As in other factor methods, squared cosine analysis is used to avoid interpretation errors due to projection effects. If the squared cosines associated with the axes used on a chart are low, the position of the observation or the variable in question should not be interpreted.

Factor scores

The factor scores in the new space are then displayed. If supplementary data have been selected, these are displayed at the end of the table.


The contribution table shows the contributions of the observations in building the principal components.

Squared cosines for the obsrevations

The squared cosines table displays the squared cosines between the observation vectors and the factor axes.

Results with rotations

Where a rotation has been requested, the results of the rotation are displayed with the rotation matrix first applied to the factor loadings. This is followed by the modified variability percentages associated with each of the axes involved in the rotation. The coordinates, contributions and cosines of the variables and observations after rotation are displayed in the following tables.

XLSTAT charts for Principal Component Analysis

Correlations charts

These charts show the correlations between the components and initial variables. You can also display the initial variables in the form of vectors.

Observations charts:

The obsrevations charts represent the observations in the new space.


The biplots represent the observations and variables simultaneously in the new space. Here as welle the initial variables can be plotted in the form of vectors. There are different types of biplots: