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All rights reserved. The non-commercial (academic) use of this software is free of charge. The only thing that is asked in return is to cite this software when results are used in publications.

Here you find a collection of Free Descriptive Statistics Software modules (Calculators). The modules have been grouped in Univariate, Bivariate, Trivariate, and Multivariate categories. All modules can be used with any dataset that contains ungrouped observations.

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Univariate Descriptive Statistics - Ungrouped Data
Plot & describe dataseriesgenerates a simple plot of the dataseries and allows one to enter a description (useful for future reference when the computation is submitted to the archive)
Central Tendencyarithmetic mean, geometric mean, harmonic mean, median, midrange, midmean, robustness of central tendency (winsorized and trimmed mean), etc...
Variabilityrange, variance, standard deviation, variation, MSE, absolute deviation, interquartile difference, coefficient of quartile variation, Gini's mean difference, Leik's D, dispersion, diversity, qualitative variation, mean square deviation, etc...
Concentrationentropy, exponential index, Herfindahl, variation coefficient, Gini coefficient, Lorenz curve, etc...
Momentsgeneral, non centered & centered moments, trimmed moments
Skewness/KurtosisFisher 3rd centered moment, Fisher beta 1 & gamma 1, Pearson, Yule's skewness (according to 8 different quartile definitions), Beta, Gamma, small sample skewness, Fisher 4th centered moment, Fisher beta 2 & gamma 2, small sample kurtosis, etc...
Percentilesnormal probability plot, weighted average, empirical distribution, closest observation, TrueBasic(TM), Excel(TM), etc...
Histogramcomputes the histogram (and frequency table) for a univariate data series
Kernel Density Estimationcomputes and plots the density trace of a data series for different Kernels: Gaussian, Epanechnikov, Rectangular, Triangular, Biweight, Cosine, and Optcosine
Harrell-Davis Quantilescomputes the Harrell-Davis Quantiles and associated standard errors.
Stem-and-leafComputes the Stem-and-leaf plot of a dataseries
Univariate EDAcomputes a series of graphical tools for the purpose of Explorative Data Analysis
Bootstrap Plot - Central Tendencycomputes the Bootstrap Plot for three measures of Central Tendency
Blocked Bootstrap Plot - Central Tendencycomputes the Blocked Bootstrap Plot for three measures of Central Tendency (for stationary time series)
Mean Plotcomputes the Mean Plot for a (time) series
Standard Deviation Plotcomputes the Standard Deviation Plot for a (time) series
(Partial) Autocorrelation Functioncomputes the autocorrelation and partial autocorrelation function for any univariate time series
Variance Reduction Matrixcomputes the Variance Reduction Matrix that can be used to determine which combination of seasonal and non-seasonal differencing.
Standard Deviation-Mean Plotcomputes the Standard Deviation-Mean Plot and the Range Mean Plot
Spectral Analysiscomputes the raw periodogram and the cumulative periodogram of a univariate time series (with the 95% Kolmogorov-Smirnov confidence intervals)
Mean versus Mediancomputes the arithmetic mean and the median of a univariate dataset. It displays the Kernel Density Plot and the Harrell-Davis quantiles with an indication of the arithmetic mean and the median.
Univariate Summary Statisticscomputes descriptive, summarizing statistics for any univariate data series.

Bivariate Descriptive Statistics - Ungrouped Data
Plot & describe dataseriesplots a bivariate data series
CorrelationPearson correlation, covariance, determination coefficient, scatter plot, etc...
Spearman Rank Correlationcomputes the Spearman Rank Correlation between two data series with the R language
Simple Regressiongeneral linear model, mean and variances, covariance, correlation, least squares estimation, parameters, response, significance, determination coefficient, ANOVA, residuals, autocorrelation, model selection, model performance, etc...
Bivariate Densitycomputes Bivariate Kernel Density Estimates
Kendall Rank Correlationcomputes the Kendall tau Rank Correlation between two data series
Box-Cox Linearity Plotcomputes the Box-Cox Linearity Plot
Linear Regression Graphical Model Validationcomputes the Simple Linear Regression model (Y = a + b X) and various diagnostic tools from the perspective of Explorative Data Analysis
Back to Back Histogramcomputes the Back to Back Histogram (sometimes called Bihistogram) for a bivariate dataset
QQ Plotscomputes various QQ Plots and Histograms for a bivariate dataset
Cross Correlation Functioncomputes the Cross Correlation Function for any univariate time series
Somers Dxy Rank Correlationcomputes the Somers Dxy Rank Correlation
Bagplotcomputes the Bagplot for a bivariate data set
Bivariate EDAcomputes a series of graphical tools for the purpose of Explorative Data Analysis

Trivariate Descriptive Statistics - Ungrouped Data
Partial CorrelationPearson Product Moment Partial Correlation.
Trivariate Scatterplotscomputes 3-dimensional scatterplots, combinations of 2-by-2 scatterplots, histograms, bivariate density plots

Multivariate Descriptive Statistics - Ungrouped Data
Kendall tau Correlation Matrixcomputes the (multivariate) correlation plot based on Kendall tau rank correlations
Notched Boxplotscomputes notched boxplots for every variable of the multivariate dataset
Star Plotcomputes the Star Plot for a multivariate dataset
Agglomerative Nesting (Hierarchical Clustering)computes the agglomerative hierarchical clustering of a multivariate dataset (Kaufman and Rousseeuw)
Hierarchical Clusteringcomputes the hierarchical clustering of a multivariate dataset based on dissimilarities.
Survey Scorescomputes various numerical scores for a matrix containing results of a survey with questions that are measured on a Likert scale.
Cronbach Alphacomputes Cronbach Alpha and related statistics for items that belong to a construct.

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To cite Wessa.net in publications use:
Wessa, P. (2024), Free Statistics Software, Office for Research Development and Education,
version 1.2.1, URL https://www.wessa.net/

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