MVN: a web-tool for assessing multivariate normality (ver. 1.6)

Select a detection method

This methodology has following steps: 1. Compute robust Mahalanobis distances (MD(xi)) 2. Compute the 97.5%-Quantile Q of the Chi-Square distribution 3. Declare MD(xi) > Q as possible outlier

This methodology has following steps: 1. Compute robust Mahalanobis distances (MD(xi)) 2. Compute the 97.5% Adjsuted Quantile (AQ) of the Chi-Square distribution 3. Declare MD(xi) > AQ as possible outlier

Detailed information about this method can be found in Filzmoser et al

See also mvoutlier package from R

Input data

Load example data:

n: number of observations

p: number of variables

Upload a delimited text file:

You can upload your data as separated by comma, tab, semicolon or space.

Note: First row must be header.

Paste or enter your data below:

You can paste or manually enter your data as separated by comma, tab or semicolon.

Note: First row must be header.

Choose a univariate normality test

Choose a univariate plot
Note: Box-plots are based on standardized values (centered and scaled).

Choose a MVN test
Values: g1p: Mardia's multivariate skewness statistic chi.skew: Chi-square value of the skewness statistic p.value.skew: p-value of the skewness statistic g2p: Mardia's multivariate kurtosis statistic z.kurtosis: z value of thekurtosis statistic p.value.kurt: p-value of the kurtosis statistic chi.small.skew: Chi-square value of the small sample skewness statistic p.value.small: p-value of small sample skewness statistic
Values: HZ: the value of Henze-Zirkler statistic at significance level 0.05 p-value: significance value for the HZ test
Values: H: the value of Royston's H statistic at significance level 0.05 p-value: an approximate p-value for the test with respect to equivalent degrees of freedom (edf)

Choose a MVN plot

Assessing the assumption of multivariate normality is required by many parametric multivariate statistical methods, such as MANOVA, linear discriminant analysis, principal component analysis, canonical correlation, etc. It is important to assess multivariate normality in order to proceed with such statistical methods. There are many analytical methods proposed for checking multivariate normality. However, deciding which method to use is a challenging process, since each method may give different results under certain conditions. Hence, we may say that there is no best method, which is valid under any condition, for normality checking. In addition to numerical results, it is very useful to use graphical methods to decide on multivariate normality. Combining the numerical results from several methods with graphical approaches can be useful and provide more reliable decisions.

Here, we present a web-tool application to assess multivariate normality. This application uses the MVN package from R. This tool contains the three most widely used multivariate normality tests, including Mardia’s, Henze-Zirkler’s and Royston’s, and graphical approaches, including chi-square Q-Q, perspective and contour plots (Multivariate analysis tab). It also includes two multivariate outlier detection methods, which are based on robust Mahalanobis distances (Outlier detection tab). Moreover, this web-tool performs the univariate normality of marginal distributions through both tests and plots (Univariate analysis tab). More detailed information about the tests, graphical approaches and their implementations through this web-tool and MVN package can be found in the paper of the package. All source codes are in GitHub.

If you use this tool for your research please cite: Korkmaz S, Goksuluk D, Zararsiz G. MVN: An R Package for Assessing Multivariate Normality. The R Journal. 2014 6(2):151-162.

Usage of the web-tool

In order to use this application,

(i) load your data set using Data upload tab. If data set has a group variable, users can define whether this variable is in the first or last column then the analysis will be performed in each sub-group,

(ii) check univariate normality through univariate normality tests and plots in the Univariate analysis tab. Users also can get descriptive statistics using this tab,

(iii) check multivariate outliers in the Outlier detection tab,

(iv) check multivariate normality through MVN tests and plots in the Multivariate analysis tab.

Users can download univariate results (both descriptive statistics and univariate normality tests, as txt) and univariate plots (as pdf) from Univariate analysis tab, outlier set (as txt), data set without outliers (as txt) and chi-square QQ plot (as pdf) from Outlier detection tab, also MVN test results (as txt) and plots (as pdf or png) can be downloaded by using Multivariate analysis tab.

Please note that box-plots are based on standardized values (centered and scaled), and perspective and contour plots are only available for bivariate normal distributions.

If there are missing values in the data, a listwise deletion will be applied and a complete-case analysis will be performed.




Selcuk Korkmaz

Hacettepe University Faculty of Medicine Department of Biostatistics

Dincer Goksuluk

Hacettepe University Faculty of Medicine Department of Biostatistics

Gokmen Zararsiz

Hacettepe University Faculty of Medicine Department of Biostatistics

Izzet Parug Duru

Marmara University Faculty of Arts and Sciences Department of Physics

Vahap Eldem

Istanbul University Faculty of Science Department of Biology


Version 1.6 (June 9, 2015)

(1) Advanced options have been added for both perspective and contour plots.

Version 1.5 (June 2, 2015)

(1) Advanced options have been added for the multivariate outlier detection.

(2) Bug fixes.

Version 1.4 (January 20, 2015)

(1) MVN paper published at The R Journal. The complete reference information is at the Citation tab

(2) Minor improvements and fixes.

Version 1.3 (November 20, 2014)

Univariate descriptive statistics, tests and plots have been added.

September 12, 2014

MVN web-tool presented at 16th National Biostatistics Congress in Antalya.

Version 1.2 (June 8, 2014)

(1) Sub-group analysis has been added.

Version 1.1 (May 13, 2014)

(1) Three different outlier detection methods, including Mahalanobis distance, adjusted quantile and PCOut, are available now.

(2) New data set without outliers can be downloaded.

Version 1.0 (March 10, 2014)

(1) Web-tool version of the MVN package has been released.

Other Tools

easyROC: a web-tool for ROC curve analysis

MLViS: machine learning-based virtual screening tool

DDNAA: Decision support system for differential diagnosis of nontraumatic acute abdomen

Please feel free to send us bugs and feature requests.