ANOVA (Analysis of variance)

ANOVA (Analysis of variance) 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.
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  • Accessible - Available in many languages
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  • 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 Analysis of Variance

Analysis of variance (ANOVA) is a tool used to partition the observed variance in a particular variable into components attributable to different sources of variation.

Analysis of variance (ANOVA) uses the same conceptual framework as linear regression. The main difference comes from the nature of the explanatory variables: instead of quantitative, here they are qualitative. In ANOVA, explanatory variables are often called factors.

ANOVA model

If p is the number of factors, the ANOVA model is written as follows:

yi = β0 + ∑j=1...q βk(i,j),j + εi

where yi is the value observed for the dependent variable for observation i, k(i,j) is the index of the category of factor j for observation i and εi is the error of the model.

The hypotheses used in ANOVA are identical to those used in linear regression: the errors εi follow the same normal distribution N(0,s) and are independent. It is recommended to check retrospectively that the underlying hypotheses have been correctly verified. The normality of the residues can be checked by analyzing certain charts or by using a normality test. The independence of the residues can be checked by analyzing certain charts or by using the Durbin Watson test.

Options for ANOVA in XLSTAT

XLSTAT enables you to perform one and multiple way ANOVA (MANOVA). Interactions up to order 4 can be included in the model as well as nested and random effects.

XLSTAT can handle both balanced and unbalanced ANOVA.

Results for the analysis of variance in XLSTAT

The results given are a residuals analysis, parameters of the models, the model equation, the standardized coefficients, Type I SS, Type III SS, and predictions are displayed.

In addition several multiple comparison methods can optionally be performed: Bonferroni's and Dunn-Sidak corrected t test, Tukey's HSD test, Fisher's LSD test, Duncan's test, Newman-Keuls' (SNK) method and the REGWQ method. Also the Dunnett's test is available to allow users to perform multiple comparisons with control (MCC) and Multiple comparison with the best (MCB).

Charts for the analysis of variance in XLSTAT