Descriptive Statistics - Free Statistics and Forecasting Software (Calculators) v.1.1.22-r6

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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 dataseries	generates 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 Tendency	arithmetic mean, geometric mean, harmonic mean, median, midrange, midmean, robustness of central tendency (winsorized and trimmed mean), etc...

Variability	range, 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...

Concentration	entropy, exponential index, Herfindahl, variation coefficient, Gini coefficient, Lorenz curve, etc...

Moments	general, non centered & centered moments, trimmed moments

Skewness/Kurtosis	Fisher 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...

Quartiles	weighted average, empirical distribution, closest observation, TrueBasic(TM), Excel(TM), etc...

Percentiles	normal probability plot, weighted average, empirical distribution, closest observation, TrueBasic(TM), Excel(TM), etc...

Histogram	computes the histogram (and frequency table) for a univariate data series

Kernel Density Estimation	computes and plots the density trace of a data series for different Kernels: Gaussian, Epanechnikov, Rectangular, Triangular, Biweight, Cosine, and Optcosine

Harrell-Davis Quantiles	computes the Harrell-Davis Quantiles and associated standard errors.

Stem-and-leaf	Computes the Stem-and-leaf plot of a dataseries

Univariate EDA	computes a series of graphical tools for the purpose of Explorative Data Analysis

Bootstrap Plot - Central Tendency	computes the Bootstrap Plot for three measures of Central Tendency

Blocked Bootstrap Plot - Central Tendency	computes the Blocked Bootstrap Plot for three measures of Central Tendency (for stationary time series)

Mean Plot	computes the Mean Plot for a (time) series

Standard Deviation Plot	computes the Standard Deviation Plot for a (time) series

(Partial) Autocorrelation Function	computes the autocorrelation and partial autocorrelation function for any univariate time series

Variance Reduction Matrix	computes the Variance Reduction Matrix that can be used to determine which combination of seasonal and non-seasonal differencing.

Standard Deviation-Mean Plot	computes the Standard Deviation-Mean Plot and the Range Mean Plot

Spectral Analysis	computes the raw periodogram and the cumulative periodogram of a univariate time series (with the 95% Kolmogorov-Smirnov confidence intervals)

Mean versus Median	computes 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 Statistics	computes descriptive, summarizing statistics for any univariate data series.


Bivariate Descriptive Statistics - Ungrouped Data

Plot & describe dataseries	plots a bivariate data series

Correlation	Pearson correlation, covariance, determination coefficient, scatter plot, etc...

Rank Correlation	Spearman Rank Order Correlation (corrected and non-corrected).

Simple Regression	general linear model, mean and variances, covariance, correlation, least squares estimation, parameters, response, significance, determination coefficient, ANOVA, residuals, autocorrelation, model selection, model performance, etc...

Bivariate Density	computes Bivariate Kernel Density Estimates

Kendall Rank Correlation	computes the Kendall tau Rank Correlation between two data series

Box-Cox Linearity Plot	computes the Box-Cox Linearity Plot

Linear Regression Graphical Model Validation	computes the Simple Linear Regression model (Y = a + b X) and various diagnostic tools from the perspective of Explorative Data Analysis

Back to Back Histogram	computes the Back to Back Histogram (sometimes called Bihistogram) for a bivariate dataset

Cross Correlation Function	computes the Cross Correlation Function for any univariate time series

Somers Dxy Rank Correlation	computes the Somers Dxy Rank Correlation


Trivariate Descriptive Statistics - Ungrouped Data

Partial Correlation	Pearson Product Moment Partial Correlation.

Trivariate Scatterplots	computes 3-dimensional scatterplots, combinations of 2-by-2 scatterplots, histograms, bivariate density plots


Multivariate Descriptive Statistics - Ungrouped Data

Kendall tau Correlation Matrix	computes the (multivariate) correlation plot based on Kendall tau rank correlations

Notched Boxplots	computes notched boxplots for every variable of the multivariate dataset

Star Plot	computes the Star Plot for a multivariate dataset

Agglomerative Nesting (Hierarchical Clustering)	computes the agglomerative hierarchical clustering of a multivariate dataset (Kaufman and Rousseeuw)

Hierarchical Clustering	computes the hierarchical clustering of a multivariate dataset based on dissimilarities.

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