An Overview of Aabel 3 Features

Summary

Aabel is a modern, powerful, and feature-rich Mac OS X Universal package, including:

Diverse statistical & exploratory data analysis methods
Easy to use data-reduction techniques for complex multivariate data
A unique pipeline design that allows real-time two-way interaction with data and makes multivariate & exploratory data analysis a breeze
Interactive data visualization, a rich variety of graph types, and over 240 styles of data representation
Thematic mapping and related importers & map projection utilities
Native worksheets providing numerous data management tools, a formula editor, and other utilities
Multidimensional data filtering comparable to a database search
Diverse data import and graphic file export support, a data manipulator, flexible customizing tools, Unicode support, publication quality graphics, and more

System Requirements

Mac OS 10.4.4.x or Leopard
Intel- or Power PC-based Mac
A color monitor with a minimum resolution of 1024 x 768

Aabel Unique Pipeline Architecture

Aabel employs a pipeline architecture that allows real-time, two-way interaction between graphic viewers and their source worksheets, and between plotted data displayed on the same or on different viewers. This unique design has many advantages. This design has many advantages:

You can perform graphing or statistical analysis from multiple Aabel worksheets, without a need to merge the data into a single worksheet.
You can have real-time interaction with data, e.g., change variables, change chart types, etc., all from within a single interface, and the results will be dynamically updated.
Saved graphic viewer files are not static graphic files. They are hot-linked to the data sources used to create the chart(s). If you make changes to source worksheets, the modifications will be dynamically updated on all charts using the data.
The pipeline architecture of Aabel has enabled the design of powerful and dynamic data exploration tools such as X-zooming, interactive data filtering based on data patterns, etc.

Data Exploration Tools

Data brushing can be used to highlight data interrelationships (see the image below). However, Aabel takes data exploration beyond data brushing.
A powerful tool called X-zoom (X for exclude) allows walking through hierarchies of numeric or categorical data rapidly, to discover patterns and information that are otherwise masked.
Data filtering: if you have mapped data patterns that you want to explore further, you can use the viewer filtering tools to extract subsets of data using multidimensional filter criteria.)

New: X-zooming now allows walking through hierarchies of data in both directions (i.e., step-wise excluding, and step-wise return to previous states).

For more information regarding the use of exploration tools, click here.

View QuickTime Movies of Aabel 3

Multidimensional Data Filtering Tools

Aabel provides easy to use tools for data filtering, comparable to a database search.
You can use multiple criteria that can span multiple variables for generating subsets of data.
Data filtering can be performed in worksheets, database metaphors, graphic viewer documents, and data manipulator.
The graphic viewer supports data filtering for generating subsets of data based on data patterns.
The data filtering results can be used interactively, or saved in auto-generated Aabel worksheets.

To view examples, click here.

Statistics and Exploratory Data Analysis

Aabel Stats Analyzer

The Stats Analyzer has a modern interface that is designed to provide flexibility and ease of use. It is an integral part of the graphic viewer that allows creating presentation and publication quality graphic outputs (tables and graphs).

Aabel Stats Analyzer is designed to allow different analyses without the need to create a different viewer for each method.
The graphs and tables generated by statistical methods and multivariate data analysis will be displayed on the viewer page(s).
The viewer filters, if activated, will be available to Stats Analyzer.
Many methods allow storing the results in auto-generated worksheets that can be used for follow-up analysis, etc.
A QuickTime movie of the ease of use of Stats analyzer is avaiable for either viewing or downloading. If interested click the image here.

Ease of Use of Stats Analyzer: 00.00.28

Statistical and Multivariate Data Analysis Methods

Testing for Normality

Probability plot and accompanying shapiro-wilk test
Kolmogorov-Smirnov test for testing normality of a single sample

New: Shapiro-Wilk test for normality

Testing for Homogeneity of Variance

New: Hartley's Fmax test
New: Bartlett's chi-Square test

Analysis of Variance (ANOVA)

One-way between-subjects ANOVA (for more information, click here)
Two-way between-subjects ANOVA (for more information, click here)
One-way within-subjects (repeated measures) (for more information, click here)

New: Two-way repeated measures ANOVA (within-subjects factorial) (for more information, click here)
New: Two-way mixed factorial ANOVA: mixed between-within design (for more information, click here)
New: Testing Strength of Association: Partial ω²
New: Locally best invariant test
New: Multi-sample sphericity test: Harris W
New: Extended data layout options for ANOVA designs

Multiple Comparison Tests Accompanying ANOVA

Tukey's HSD Test
Newman-Keuls (Neuman-Keuls) Test on Ordered Means
Tukey B Test for Contrast on Ordered Means
New: Dunnett Test
Tukey-Kramer Test
Scheffé Test
Bonferroni-Dunn Test

For more information regarding multiple comparisons accompanying ANCOVA, click here.

Analysis of Covariance (ANCOVA)

Single-factor between-subjects ANCOVA:

Analysis of covariance, analysis of variance for dependent, and analysis of variance of covariate.
New: Testing for homogeneity of regression
New: Tukey's HSD Test on Adjusted Means
New: Scheffé Test Adjusted Means

For more information regarding single-factor between-subjects ANCOVA, click here.

Chi-Square Tests

The Chi-Square Goodness-of-Fit Test
The Single-Sample Chi-Square Test for Population Variance

For more information, click here.

t-Tests

Single samples t-test
Paired samples t-test
Unpaired samples t-test
New: Extended data layout options for unpaired samples t-test

F-Test

Testing equality of variance
New: Extended data layout options for F-test

z-Tests

Paired samples z-test
Unpaired samples z-test
New: Extended data layout options for unpaired samples z-test

Correlations

Correlations and covariance matrices
Pearson product-moment correlation coefficient (Pearson's r)
New: Fisher's z transformation (z_r) (provided for both correlation matrix and Pearson's r)
Spearman's rank-order correlation coefficient (Spearman's ρ) (non-parametric)
Kendall's rank correlation coefficient (Kendall's τ) (non-parametric)

For more information, click here.

Internal Consistency Reliability

New: Cronbach's alpha
New: Kuder-Richardson rho (Formula 20)
New: Kuder-Richardson rho (Formula 21)

For more information, click here.

Non-Parametric Tests

Wilcoxon signed-ranks test
Wilcoxon matched pairs signed-ranks test
New: Correction for continuity for the normal approximation of the Wilcoxon signed-Rranks and Wilcoxon matched pairs signed-ranks
Mann-Whitney U test (Wilcoxon ranks sum test)
Kruskal-Wallis test
New: Extended data layout options for Mann-Whitney U and Kruskal-Wallis tests
Spearman's rank-order correlation coefficient
Kendall's rank correlation coefficient (Kendall's tau)
Friedman two-way analysis of variance by ranks
Kolmogorov-Smirnov goodness-of-fit test for a single sample

For more information, click here.

Contingency Table Analysis

Two-way contingency tables: a two-way frequency table used to summarize two categorical random variables
Two-way tables of cell descriptive statistics (mean, median, variance, standard variation, standard error, etc.)
Mosaic/Parquet matrix diagrams: a graphical method for visualizing n x m contingency tables

For more information, click here.

Kaplan-Meier Survival Analysis

Kaplan-Meier survival analysis using raw survival data
Kaplan-Meier survival analysis using summarized survival data
Output including survival curves, logrank significance test report, and life table

For more information, click here.

Receiver Operating Characteristic Curves (ROC)

ROC for a single test
ROC for two tests on paired samples
ROC for two tests on unpaired samples

For more information, see examples.

Regression Analysis and Curve Fitting

Regressions concerning two continuous variables

Linear (X on Y)
Linear (thru zero)
Major axis
Reduced major axis
Polynomial
Exponential
Logarithmic
Power
For more information and examples, click here.

Cubic Spline interpolation

A cubic spline is made from piece-wise third-order polynomials that pass through the control points provided.

User-Defined Non-Linear Regression

User-define regression provides a library of functions and an interactive interface.

For more information regarding regression methods in Aabel, click here.

Logistic Regression

Logistic regression in Aabel includes probability and logit (probability) and allows flexible customizing of the generated charts.
Probability charts with multiple dimension projections also generate a table of statistics.

For more information and examples, click here.

Multiple Regression and PLS (Partial Least Squares)

Multiple regression analysis

Multiple regression analysis provides an equation that relates a single dependent variable to multiple independent (predictor) variables.
Aabel provides predicted values and residuals, an ANOVA report for total regression, the regression summary table (providing regression parameters, the corresponding statistic, and the confidence limits), and an ANOVA report for testing the significance of individual predictor variables.

For more information, click here.

PLS (partial least squares regression)

The PLS method implemented in Aabel (i) uses principal component analysis (PCA) to derive the prediction functions from factors calculated from cross-product matrices involving both Y and X variables, and (ii) allows predicting one or more dependent variables from a set of independent (predictor variables).

PLS regression can be performed on a single data set (as for multiple regression), or using a training data set for predicting unknowns, new events, etc.
To use a calibration (training) data set, you can run a PLS regression on a representative data set and check the performance of the model before using it for predictive purposes.
The predictor coefficients and the predictions will be stored in two auto-generated worksheets.

Outlier Analysis

New: Mahalanobis Distance
New: Jackknifed Mahalanobis Distance

Log Center transformation is necessary for proportion or percentage data, i.e., for data where the row sums of the selected variables have a constant sum. The outlier analysis UI controls include the necessary pre-processing trasformation methods (such as log-centring), which can be chosen, if needed.

For more information, click here.

Principal Component Analysis (PCA)

PCA analysis allows optional pre-processing of the data prior to the main analysis.
PCA results can be stored in the source worksheet or in a new worksheet.
The scores and loadings can be graphically displayed using Aabel charts and tables.

For more information, click here.

Factor Analysis

Factor analysis allows optional pre-processing of the data prior to the main analysis.
Aabel provides R-mode and Q-mode factor analyses and the option for Kaiser varimax rotation.
The loadings, communality, and "unique" data will be placed in an auto-generated worksheet.

You can use Aabel graphing capabilities to display the loadings, the fraction of variance of the variables explained by the model (i.e., communality) and the fraction that is not (i.e., "unique").

For more information, click here.

Polynomial Trend Surface Analysis (Map Analysis)

Polynomial trend surface analysis of XYZ data
Polynomial trend surface analysis of matrix data
Matrix cellwise operations

The map analysis output includes new matrices and/or XYZ estimates of trend and residuals, as well as an ANOVA report for significance of regression of K^th order polynomial trend surface.

For more information, click here.

Cluster Analysis

New: K-Means Cluster Analysis

The method partition a data set of n objects into k clusters via an iterative process that continues until the sum of squares from points to the assigned cluster centers is minimized, i.e., until all cluster centers are at the mean of their voronoi sets.
Aabel uses the method of Hartigan and Wong (1979), performs several random starts, and attempts to converge to a global minimum of the squared error distortion.

For more information, click here.

Hierarchical cluster analysis

The weighted pair-group with arithmetic averaging

For more information, click here.

New: Dot Plots

Dot plots are an alternative to histograms of continuous data; in a dot plot, each data point (individual observation) is plotted on a continuous scale using a symbol (on the X-axis).
Option of applying object marker colors to dot symbols allows distinguishing groups of data.

For more information and examples, click here.

New: Parallel Dot Plot of Repeated Measures

This graph is designed to display dot plots of score (response values) form k >=2 repeated measures (dependent samples) on axes that are parallel to one another and equally spaced, with all axes having the same value range (see the right-hand side image).

Lines extending from their positions on one axis to the next connect the dependent data points.
The probability significance test (p value) provided with the plot is based on one-way repeated measures ANOVA.

Basic Heatmaps

Heatmap displaying a worksheet matrix

A basic heatmap diagram displays a worksheet matrix layout using a color scale, i.e., the color of each cell (within the color scale applied) is determined by its values.

Heatmaps with optional scaling of Z-values

Optional scaling of Z-values allows representing the color-coded Z scale proportional to the corresponding cell values.

To view examples of basic heatmaps, click here.

Frequency Distribution/ Histograms

Histograms

Histograms of continuous data: absolute, relative, cumulative
New: z-Score histogram
Histograms of categorical data: absolute, relative, cumulative
Pareto charts
Ogive
Spine plots

For more information, click here.

One-way frequency analysis of categorical data

This method generates a frequency table from a single categorical variable.

New: N-way frequency analysis of categorical data

This method allows generating n-way frequency output reports with 2D-data-slices representing levels of two or more grouping variables.

For more information, click here.

Statistical Quality Control Using Shewhart and Other Control Charts

Aabel provides Shewhart control charts for variables, Shewhart control charts for attributes, and other related charts:

Xbar (R) chart
Xbar (S) chart
R chart
S chart
Levey-Jennings chart
Individual measurements chart
Moving range chart
p chart
np chart
c chart
u chart

The Westgard multi-rules procedure and Western Electric Company (WECO) warning rules can be optionally applied to the appropriate quality control charts.

For more information, click here.

Probability Plot

Normal Probability
Uniform Probability

Normal probability plot that is provided as an option for testing normality, allows adding Shapiro-Wilk normality test to the plot output.

For more information, click here.

Box & Whisker and Box-Percentile Plots

One-way box & whisker plots (regular and notched)
Two-way box & whisker plots (regular and notched)
Different options for plotting the whisker and outliers

One-Way box-percentile plots
Two-Way box-percentile plots

New: Extended data layout options for generating box & whisker and box-percentile plots

For more information regarding box & whisker and box-percentile plots, click here.

Bar and Line Plots of Mean, Median, Max., Min.

These plots are used for comparing mean, medians, maximum, or minimum values of multiple variables, or of subgroups/categories of variables.

One-way bar plots
Two-way bar plots
One-way line plots
Two-way line plots
New: Extended data layout options for generating bar or line plots of mean, median, etc.)
To add error bars to mean bars/lines, the options include:
- Standard error of mean
- Standard deviation
- New: Confidence interval (including options of 90.0%, 95.0%, 97.5%, 99.0%)
For more information regarding bar plots, click here; for more information regarding line plots, click here.

New: Interaction plots

Stacks of mean lines, used to display the effect of one factor at each level of another factor
To add error bars to interaction plots, you can choose one of the following options:
- Standard error of mean
- Standard deviation
- Confidence interval (including options of 90.0%, 95.0%, 97.5%, 99.0%)
For more information, click here.

New: 3-Way Mean Plots

These plots compare the response values (scores, measurements) obtained from k >=2 samples/groups, each of which representing data from pqs levels of experimental conditions. The plot options include:

Three-way mean bar plot
Three-way mean dot plot
To add error bars to mean bars/dots, you can choose one of the following options:
- Standard error of mean
- Standard deviation
- Confidence interval (including options of 90.0%, 95.0%, 97.5%, 99.0%)
For more information, click here.

Diamond Mean Comparison Plots

One-way diamond mean comparison plot
Two-way diamond mean comparison plot
New: Extended data layout options for generating diamond plots)

For more information, click here.

Bland & Altman plot

In Aabel, the Bland & Altman method for comparing two methods of measurement or two paired variables provides:

A plot of differences vs. mean
A plot of differences as a % of averages vs. mean
A plot of ratios vs. mean
In addition to the plot, the results can optionally be displayed in a table or stored in a worksheet.
For more information and example graphs, click here.

Descriptive Statistics

One-way descriptive statistics that can include mean, median, standard deviation, standard error, maximum, minimum, variance, skewness, sum, count/sample size

Primary and Secondary Data Transformations

Standardizing, normalizing, etc.
log-center and mean-center transformations
Ranking variables individually or jointly

Thematic Maps and Map Projection Utilities

A thematic map displays the spatial distribution of an attribute relating to specific data themes (e.g., population density, rainfall, soil type, median age, number of housing units, pollutants concentration in air, etc.). Aabel provides import facilities, map projections utilities and graphing abilities to create thematic maps.

Importers

Importers are provided to enable users to import and arrange polygon data and create thematic maps that are suitable for their purpose, instead of being provided with maps without ability to choose or modify them. Aabel provides importers for:

ArcView shape files and associated dBase files
Formats provided by the USGS Coastline Extractor: Arc/Info Ungenerate, Mapgen, Matlab, Splus

Thematic map diagrams

Polygon thematic maps (that can display descriptive statistics or original values of associated data by color-coding)
Polygon point frequency thematic maps
Thematic grouping (a feature that allows combining a base map with a chart such as a bubble diagram to create thematic maps using point symbols, or with a scatter pie to display contribution of parts to a whole in different X-Y coordinates)

Map projection utilities (coordinate transformations)

Map projection utilities (coordinate transformations) are an integrated part of Aabel worksheets, and include 19 projection systems.

For more information and example thematic maps, click here.

Data Visualization and Graph Types

Features of Graphic Viewer

The graphic viewer is the Aabel interface for data visualization & charting and for displaying the graphical results of statistical analysis.

The graphic viewer can work simultaneously with multiple data sources, and has a real-time, two way interaction with data.
The graphic viewer toolbar provides tools for interacting with data, zooming, moving and resizing graphics, creating tables and single or multi-line text, drawings, and numerous customizing features.
Saved graphic viewer files do not store static blocks of data; they store references to the source documents containing the data.
The viewer palettes include data browsers and controls that allow interaction with data, dynamic data visualization and charting, arranging and ordering graphic sub-layers.
You can create color themes that are stored as part of the global parameters and can be accessed from any viewer.

Specialized Scientific Graphing

Structural Diagrams: Stereographic, Rose, and Lineament

The corresponding data for stereographic charts are stored in worksheets with selected variables as:
- Trend
- Dip/Plunge
- Azimuth

Stereographic diagrams (displaying stereographic projections of directional data):

Stereographic scatter
Stereographic contour

Rose diagrams (circular histograms):

Full circle rose with area of the petals proportional to the frequency (symmetric or asymmetric>
Full circle rose with length of the petals proportional to the frequency (symmetric or asymmetric
Half circle rose

Structural lineament diagrams:

Full circle lineament (symmetric or asymmetric>
Half circle Full circle lineament

To view examples, click here.

Geospider Plots Diagram (Multi-Element Spidergram)

Geospider diagram, also known as a multi-element spidergram, is used to compare the element composition of a rock, normalized against known reference rocks.
Aabel is distributed with a plot definitions library that includes 34 spidergram reference plot definitions for representing geochemical data.

To view examples, click here.

Sequence Alignment Diagrams

This diagram is designed to plot genomic sequence alignment by mapping query sequences to target sequences.
Four plot types are provides.
Stepwise X-zooming allows exploring the sequence alignment data.

To view examples, click here.

Combination Column Graphs (CCG Diagrams)

This diagram is designed to permit a combination of single and/or multiple variable column graphs that reflect variation against sorted values (in an increasing order) of a common Y-axis. It is hence ideal for plotting variations against depth, time, or similar variables.
Each column graph can be created from a single variable or from multiple variables.
The CCG graphs can combine bars, text, area or stacked area, and single or multiple line plots.

To view examples, click here.

General-Purpose 2-D, Ternary, Matrix, Contour, and Polar Graphs

In addition to diagrams designed for specialized scientific graphing (listed above), and to graph categories that have been outlined earlier on this page (in the context of statistical methods), Aabel provides a diverse range of general-purpose graph types and graphing capabilities (see the following information).

Matrix Scatter Diagram and Related Plots

Full matrix with X=Y cells displaying histograms, variable names or other options
Half matrix
Multi-profile diagram
Styles:
- Connecting data points by X, by Y, or by pipeline order
- Connecting data points by bgroup by X, by Y, or, by pipeline order
- Connecting data points to origo
- Displaying convex hulls of groups
- New: Connecting data points to group centroids
- New: Connecting data points to group medians
- New: Connecting the group centroids
- New: Connecting the group medians

To view examples, click here.

Voronoi Diagram (Thiessen or Dirichlet Polygons)

The Voronoi diagram subdivides the X-Y space of the chart into polygons surrounding each data point. These polygons represent the most compact division of space possible.
The plot types include:
- Plain Voronoi
- Polygons color coded by calculated area
- Polygons color coded by values of a third variable
- Polygons color coded by area-normalized values of Z
To view examples, click here.

Waterfall Charts

New: Waterfall line series
New: Waterfall area series
New: Waterfall pseudo-surface

Waterfall charts are ideal for comparing variations between multiple data sets that are obtained under similar conditions.

To view examples, click here.

The waterfall pseudo-surface chart shown here, displays the Mauna Lao CO² monthly mean for 1985-2007.

2-D Contour Charts

X-Y-Z contour (contouring by triangulation)
Contouring by gridding; for creating a continuous surface from an unevenly-spaced data set, Aabel gridder uses:
- The n-nearest neighbors method, with or without a quadrant or octant constraint on the search pattern
- New: The option of generating the real world coordinate values for labeling the columns and rows of the gridded data (this feature allows displaying the real world coordinate values along the X- and Y-axis of matrix plots such as gridded vector graphs or heatmaps)
Contour matrix chart (map view of regularly spaced data)
Ternary contour (a 2-D projection of a ternary diagram using four variables, contouring by triangulation)

To view examples, click here.

For information regarding 3-D contour plots, refer to General Purpose 3-D Charts.

Bubble Charts

Bubble charts displaying values of a 3rd variable using size of the bubble marker (the bubble markers can be round or square)
Bubble charts displaying values of a 3rd variable using a color scale
Bubble charts displaying values of a 3rd variable using size of the bubble marker, and of a4th variable using a color scale

To view examples, click here.

Ternary Charts

Ternary scatter: a 2-D projection of a ternary plot, displaying the relative proportions (as percentages) of three variables on three axes
Ternary contour: a 2-D projection of a ternary diagram that displays values of a 4th dimension using a color scale
New: Ability to draw the plot clockwise or counterclockwise
The option of displaying error regions (calculating all possible combinations and using convex hull to delineate the resulting hexagonal error region)

To view examples, click here.

Spider Charts

Spider charts, also known as radar charts, plot variations in multiple data series that represent the same factors.

Stacked area spider with equal scaling
Line spider chart
Line spider with equal scaling (i.e., values of spokes are equally scaled relative to the one with the largest value)
Line spider for percentage data
Line spider that transforms data to 100%
Filled spider chart
Filled spider with equal scaling (the area covered by different categories (data objects) are filled by color)

To view examples, click here.

Polar Charts

Polar charts can be used to display non-directional data series (e.g., wind speed) against variation in angles. Aabel provides:

Polar line series
New: Polar stacked area
New: Polar stacked petal
New: Polar scatter series

To view examples examples, click here.

X-Y Binary Scatter and Related Charts

A binary scatter chart displays the data as a set of points on an X, Y set of coordinates. You can generate subsets of data from selected data points, and the selections can be regular or irregular.

Binary scatter graph types:

Binary scatter displaying values of a 3^rd variable as value labels at the X-Y data point coordinates
Connecting data points by X, by Y, or by pipeline order
Connecting data points by group by X, by Y, or, by pipeline order
Connecting data points to origo
Displaying convex hulls of groups
New: Connecting data points to group centroids
New: Connecting data points to group medians
New: Connecting the group centroids
New: Connecting the group medians

To view examples, click here.

X-Y and Double X-Y Scatter Series Charts

Scatter series charts display scatter data points from one or more data series, plotted against a value axis, a category axis, or date & time. In a horizontal style plot, data from each worksheet row have the same X coordinate and unique Y coordinates. In a vertical style plot, data from each worksheet row have the same Y coordinate and unique X coordinates.

X-Y horizontal scatter series
X-Y vertical scatter series:
Scatter series across X categories
Scatter series across Y categories
Double Y horizontal scatter Series
Double X scatter series
Double X-Y scatter series

Line Charts (Line Series)

X-Y line series (sort along X): X and Y value-axes
X-Y line series (sort along Y): X and Y value-axes
Line series across X categories: Y value-axis, X is category-axis
Line series across Y categories: X value-axis, Y category-axis
Double Y line series (sort along X): Y1, Y2, and X value-axes
Double X line series (sort along Y): X1, X2, and Y value-axes
Double Y line series across X categories: Y1 and Y2 value-axes, X category-axis
Double X line series across Y categories: X1 and X2 value-axes, Y category-axis
Double X-Y line Series (sort along X1, X2): Y1, Y2, X1, X2 all value-axes
Double X-Y line Series (sort along Y1, Y2): Y1, Y2, X1, X2 all value-axes

To view examples, click here.

New: Using a color gradient range to differentiate the series (instead of defining color attributes for each series individually)
New: Breaking the series lines for missing data points

2-D Column and Bar Charts

Column and charts
Stacked column and stacked bar charts
Clustered column and clustered bar charts
X-Y (value-axes) column and bar charts

To view examples, click here.

2-D Area Charts

Single-variable area charts
Stacked (multiple variables) area charts
X-Y (value-axes) area charts

To view examples, click here.

Combination Charts (Column-Line, Bar-Line, Area-Line)

Double Y combination column-line
Double Y combination bar-line
Double Y combination area-line
Double X combination area-line
Wedged hexagonal prism
Quartz-Shaped Prism (Quartz)

To view examples, click here.

Multiple Value Axes Stacked Column, Bar and Area Diagrams

These diagrams are used to graph stacks of column, bar, or area charts having independent value-axes, but sharing a common category-axis. These plots are hence useful for comparing the changes in values of multiple variables across a given category axis and relative to each other.

Multiple-Y column (each Y-axis is an independent value axis, and the X is the diagram's common category axis)
Multiple-Y area
Multiple-X bar (each X-axis is an independent value-axis, and the Y is the diagram's common category-axis)
Multiple-X area

Automatic data processing of the value axes includes:

Calculating fraction for each data object (worksheet row)
Calculating fraction for each variable (worksheet column)
Standardizing each data object (worksheet row)
Standardizing each variable (worksheet column)

To view examples, click here.

Pie Charts and X-Y Scatter Pie

2-D pie chart
3-D pie chart
Different options are available for scaling the individual pies when plotting more than one pie in a given chart pane: radius (r) proportional to sum (linear or logarithmic), r² proportional to sum (linear or logarithmic), or r³ proportional to sum (linear or logarithmic).
X-Y scatter pie charts display pies on an X-Y chart, i.e., each whole pie represents a worksheet row, each pie slice is a variable, and the center of each pie has a unique X-Y coordinate.

To view examples, click here.

High-Low, High-Low-Close, Open-High-Low-Close, and Range Charts

High-low-close (H-L-C) charts
Open-high-low-close (O-H-L-C) charts
Range charts (using ordered or unordered data series)
X-Y (value-axes) high-low charts (the high and low values of one or more data series are plotted against a continuous variable)
X-Y (value-axes) range charts (the high, midpoint, and low values of one or more data series are plotted against a continuous variable)

To view examples, click here.

Vector Charts

Matrix vector angle (with geographical and geometrical options)
Matrix vector radius-angle (with geographical and geometrical options)
X-Y vector (with geographical and geometrical options)

To view examples, click here.

General Purpose 3-D Charts

Rotation of 3-D charts in Aabel is partly hardware accelerated using OpenGL graphic system, for speed and interactivity.

3-D Contours and 3-D Mesh Plots

New: 3-D contour surface of regularly spaced data

New: 3-D mesh (wire frame) plots

3-D X-Y-Z Contour Points (3-D projection of irregularly spaced data, contouring by triangulation)

To view examples, click here.

3-D Scatter and 3-D Spinning Scatter
3-D Scatter

Displaying the data points at intersections of X, Y, and Z values in a 3-D grid

Providing the option of displaying values of a 4^th dimension using a color scale

To view examples, click here.

3-D Spinning Scatter

Suitable for exploratory pattern recognition in multivariate data

Providing the option of displaying values of a 4^th dimension using a color scale

3-D Column, Pyramid, Band, and Area Charts

For generating vector graphics, the options are:

Different types of prism/column, pyramid (Quartz)
Pyramid (Quartz)
Area (Quartz)
Band (Quartz)

To view examples, click here.

For generating bitmap graphics, the options include:

Column and Z-colored column (OpenGL)
Pyramid and Z-colored pyramid (OpenGL)

New: Pseudo-3D Surface

This is a waterfall chart type in which the series are represented as a pseudo-surface. An example of a waterfall Pseudo-3D Surface was shown earlier on this page.

To view an example, click here.

Applying Error Bars

Adding error bars to charts allows a graphical display of the statistical probability of errors, the experimental and analytical errors, etc.

The Error Bars Defined for Individual Variables

Binary scatter plots
Matrix Scatter diagram
Scatter series
Line series
Column and bar charts (including stacked and clustered columns and bars)
Area and stacked area charts

Error bars can be symmetrical or asymmetrical, and can be based on standard error, standard deviation, fixed values, or values of a variable (e.g., calculated errors, etc.)

For error bar examples, click here.

Ternary Error Regions:

The error bars defined for individual variables can not be applied independently to a ternary chart.
Aabel calculates 33 possible combinations for each ternary data point and uses the convex hull to delineate the resulting hexagonal error region.

For more information regarding ternary error regions, click here.

Curve Fitting

Curve Fitting The curve fitting features were outlined earlier, in the context of regression analysis.

For more information regarding curve fitting with pre-defined functions, click here.
For more information regarding user-defined, non-linear curve fitting, click here.

Graphic Export Formats

Format for exporting graphics

PDF
Bit images (raster files), including:
- BMP
- JPEG
- TIFF
- PNG
- Bitmap PICT
- Photoshop
- SGI
- TGA

For information regarding export resolution and to view example, click here.

Formats for copying graphics/ drag & drop

Features of Aabel Worksheets

Worksheets are Aabel's data storage mechanism, and provide numerous data management functions and utilities. They also act as dynamic data sources for data analysis and visualization.

Supported Data Import Formats

Excel format: 95, 97-2004 workbook (.xls)
Delimited text data (tab, comma, semicolon, space, etc.)
Fortran formatted data
Delimited numeric matrix data
Binary numeric matrix formats (8 bit, 16 bit, 32 bit, and 64 bit data)
dBase (II, III, IV) formats
Arc/Info Ungenerate
Mapgen
Matlab
Splus
ArcView shape files
To view the UI for delimited and shape file importers, click here.

Supported Variable Types

Numbers (any legal numerical representation with no explicit sample space)
Cartographic coordinates:
- Longitude, Latitude
- Easting, Northing
Directional/orientational data:

Trend
Dip/Plunge
Azimuth

Date and Time (30 built-in date & time formats, and tools for custom-defining a format)
Text (with Unicode support)

Numbers of Rows & Columns

Aabel does not impose limits on the number of rows and columns in worksheets. The limitation is mainly related to the speed penalty imposed by currently available hardware technology and the CPU resources and physical memory available to the application. Other factors that can impose speed penalty are (i) large amounts of complex unicode textual data, and (ii) use of complex symbols, or unicode symbols for graphing large data sets.

Quality Control of Numeric Data

Aabel's quality control tools allow:

Displaying report summary statistics for each variable with a single click
Checking the number of missing values of a variable (discontinuous data, etc.)
Detecting out-of-range values (impossible values, punching errors, etc.) and highlighting them in the corresponding worksheet rows
Dealing with out-of-range values using different options

Pre-defined Units of Weights and Measures

Data stored in different worksheets or databases do not always have the same units of measurement. This may result in inconsistencies during data analysis and processing from multiple data sources. Aabel provides the optional feature of tagging the variables with their appropriate units.
A wide range of pre-defined units of weights and measures are included. Once you set or change your preferred units in the global preferences, during data analysis, charting, or data processing, Aabel checks the tagged variables for unit inconsistencies and transforms the data to your preferred unit without modifying the source data.

The Worksheet Map Projection Utilities

Aabel worksheet projection utilities allow:

Transforming data that has been imported with no explicit sample space to cartographic coordinates and store the data as longitude-latitude, or to define data using a different projection system
Transforming data from one projection system into another system
For more information regarding this feature, click here.

The Worksheet Notebook

The worksheet notebook has four functions:

It displays a list of all variables present in the worksheet
If a worksheet has been generated from the results of data filtering, the user-defined filter criteria will be stored in the worksheet notebook
If the worksheet has been generated from cross-tabulating and pivoting, the information regarding the original worksheet file, primary and secondary split variables, etc., will be stored in the worksheet notebook
It provides a text area for storing notes, e.g., data source references, etc.

To view the UI, click here.

The Worksheet Data Management Tools

Cross-interpolation
Sorting with a single as well as with multiple keys
Transposing
Merging multiple textual data columns into one column
Merging numeric or textual data without concatenating
Reordering rows and columns
New: Providing a palette for rapid scanning through data columns in a worksheet with large number of variables or for bringing a specific data column into the field of view
Recoding text, or numeric values to categories
Pivoting and summarizing multidimensional data (cross tabulation)
Splitting and pivoting saw data
Splitting and recoding a categorical variable to binary dummy variables
Stacking columns
Grouping data objects based on values of a categorical variable: mapping categorical data to markers
New: Grouping data objects based on values of a numeric variable: mapping numeric values to marker color properties
Mapping object markers to categorical data
Mapping marker codes to marker
Multidimensional data filtering tools for generating subsets of data

The Worksheet Formula Editor

The formula editor provides 46 pre-defined mathematical and statistical functions, and includes standard as well as boolean/conditional operators.
In Aabel, variables are identified by names, and not by the position of worksheet columns. However, to facilitate sequential calculations, the formula editor provides functions that operate on variables by indices instead of names.
New: The current version allows addressing worksheet row indices, i.e., Aabel worksheet operations are column based; the new feature enables addressing the worksheet cells explicitly.
In addition to functions provided for column-wise calculations, the formula editor provides a number of functions for row-wise calculations.
Assign and calculate commands are provided for applying the same formula to multiple columns.

The Worksheet Symbol and Color Palettes

Symbol and color palettes are used for defining markers that represent individual data objects, data groups, or the source worksheet(s) on the plotted graphs. For significance of worksheet markers in data representation, view an example.
A color palette is provided for coloring the values of selected cells.

Data Manipulator

While the worksheet formula editor is provided for data processing within a given the worksheet, the data manipulator has the following abilities:

It can simultaneously process data from multiple worksheets and database metaphors
It allows building custom formulas
It permits multi-dimensional data filtering to enable data processing based on user-defined criteria

To view the manipulator UI, click here.

Aabel Database Metaphor

An Aabel database metaphor is a data management container for holding any combination of Aabel worksheets and folders containing worksheets. A saved database metaphor document does not store a static block of data, but stores references to the source worksheets.

It acts as a dynamic data source for data analysis, data processing, and data visualization and charting
The current features are designed for:
- Being used as a more powerful alternative to templates
- Easy exclusion/inclusions of groups of objects in exploratory plots
- Performing multi-dimensional data filtering of datasets sourced from multiple worksheets
For functions, practical use, and limitations of database metaphor, click here.

Aabel Viewer Text and Table Editors

Aabel table and text editors support Unicode.

The Table Editor

The table editor is provided for editing the auto-generated tables that are part of the statistical methods output, and for creating tables

The Text Frame (Text Box) Editor

The text frame editor allows adding multiple-line notes or comments to graphs

The Text Line Editor

The text line editor allows adding titles or rotated text line to graphs

For more information regarding Aabel table and text editors, click here.

Unicode Support

Aabel supports Unicode for storing data in worksheets, for graphing data, and for creating tables, text lines and text frames.
Ranking of categorical data is based on the US English writing system to ensure consistency in statistical outputs independent of the machine language settings.

Viewer Color Themes

Aabel viewer color themes provide an interactive means of creating or changing color themes required for different purposes.
By default, Aabel graphic viewers use a white background with black drawings of chart axis, ticks and grids, axis labels and titles. Color themes can be created and stored, allowing you to define a background color for the viewer; colors for chart axes, ticks, and grids; colors for labels and titles, regression lines, confidence belt outlines and fills, outlines and fills of bars, etc.
The background of a color theme can be an imported image or a selected color.
Each color theme you create is stored as part of the global parameters that can be accessed from any viewer (new or existing).

An example of use of a color theme with background being an imported image, is shown below.

Graphic Sublayers Manager

Each chart pane or other graphic object you create is placed in a transparent sublayer of the current viewer page and its specifications are displayed in the graphic sublayers palette. The sublayers palette allows:

Creating multiple live charts (hot-linked to data) from the same pipeline or different pipelines on a single viewer page
Overlaying X-Y charts, or creating a thematic group
Selecting objects (useful for selecting objects positioned behind other objects on the viewer page)
Changing the stacking order of sublayers and hence the objects they contain
Hiding sublayer, locking the objects they contain, deleting objects, etc.
Modifying the chart pane size by defining exact dimensions
Modifying the transparency of fills, lines, and markers of 2-D graphs
Applying X-zoom to exclude data from a given chart without affecting other charts using the same data source(s)
Hiding/showing chart legends and 2-D chart axes

Color Management and Interactive Color Palette Editor

The color palettes and color gradient palettes in Aabel are initially represented using default colors. However, you can freely change the items of a palette or create new color gradients from simple, complex, or pure colors, with a few clicks of the mouse: the color editor in Aabel is interactive and easy to use.
Color palettes are present in worksheets, the graphic viewer, database metaphors, and all chart customizing dialogs. They allow choosing or modifying colors of markers, lines, fills, contours, color-coded tables, text, etc.
When using a color scale to represent data, the data range will map to the color space of the gradient palette. You can customize the color gradient palette or create and save new palettes for different plotting purposes.

For more information, click here.

Customizing Tools for Data Representation

Aabel Symbols and Unicode Glyphs

Colored symbols (markers) are used to represent data in many chart types. Markers representing data can be pre-defined or inherited from the source worksheet(s). The uniqueness of markers is defined by their symbols, color, and size. Aabel provides two types of symbol palettes:

Aabel symbols: A palette with 175 marker symbols, each of which can be scaled from 50 to 200% of the initial size (100%) in 20 steps.
Unicode glyphs/symbols: A palette that holds 176 Unicode characters/symbols/glyphs is available for data representation. Each item in this palette can be replaced by a Unicode character/glyph from the System character palette, and can be scaled from 50 to 200% of the initial size (100%) in 20 steps.

To view examples, click here.

Customizing Chart Axis Attributes

Numerous chart-axis customizing tools are provided for different chart categories. Features include (but are not limited to):

Choice of linear or logarithmic scale, forward or reverse (when applicable)
Editing abilities to choose title proxy names
Applying subscript, superscript, or Greek glyphs to axis titles
Control of the axis line thickness, color, length and type of major and minor grids
Control of the axis range and steps (when applicable)
Numeric label display format settings (fixed or scientific format, decimal places, use of leading zero, use of a prefix or suffix, etc.)
Control of axis text properties and the position of labels (e.g., font properties, color, etc.)
Controls for customizing axis attributes of plot types that do not share the common axis properties of 2-D and 3-D charts (e.g., spider, rose, stereographic, polar, mosaic, dendrograms)

For more information and examples, click here.

Displaying Object and Value Labels on Charts

You can optionally display object or value labels on many Aabel charts.
Value labels can display a 3rd dimension on an X-Y chart, a 4th dimension on a ternary, bubble, contour point, or 3-D scatter chart, and a 5th dimension on a bubble, ternary contour, or 4-D scatter chart.
The labels can be customized with frames and backdrop colors, or different font properties.

To view examples, click here.

Customizing Chart Legends and Legend Entries

Legends provide explanation for data represented by graphical information.

Legend entries representing data groups or data series

The legend keys (markers, lines, color or pattern fill)
The legend text items (names of the data groups or series associated with the legend keys)

Legend entries editor allows modifying:

Symbol, color, and size of markers representing data objects or data series
Thickness, type, and color of lines representing data series
Regression lines, confidence belt, and major axis ellipse fill and line attributes
Fill attributes representing data series.

Legend entries representing data ranges

Color scale legends are used in 2-D and 3-D contours, 3-D mesh, bubble charts, waterfall pseudo-surface, and thematic maps.
The editor for this legend type allows adding frame to the legend, changing font attributes of the legend title, defining the legend labels font, and display format attributes, binning the color range, etc.

Legend font and background properties

The legend font size and style can be changed using the Text menu or shortcuts.
Chart legends have a transparent background by default. You can optionally add a colored background to any legend type.

For more information regarding options for customizing legends and legend entries, click here.

High Quality Quartz Patterns for Black & White Publications

Many 2-D graph types use fill attributes to identify different data series or data groups (e.g., color or pattern properties of columns, bars, areas, etc.). Due to high cost of color publications, many users prefer to use B & W patterns (when possible) for publication purposes.

Aabel provides numerous Quartz patterns, which are vector/stencil drawings, designed for use with high quality Quartz graphic system and PDF.
Despite that the design of these patterns has been for assisting the users in generating high quality 2-D graphics for B & W publications, they can be used in combination with any color.
To view an example of use of patterns in B & W, and to see the diversity of patterns provided, click here.

Managing Transparency

The transparency tab in the Graphics Sublayers Manager provides separate controls for modifying transparency of fills, lines, and markers of 2-D graphs.

Drawing Lines and Geometric Shapes

Drawing tools include:

Line tools for drawing a straight line, or polygons/polylines
Shape tools for drawing a rectangle, rounded rectangle, circle or ellipse.

For these lines and geometrical shapes, you can change the color of line or fill, apply patterns to fill, and change transparency of the fill.

Viewer Pages

In a graphic viewer you can create many pages, each of which can hold a single or multiple chart(s), graphical displays of statistical analysis, tables, etc.
If the output results from statistical analysis include more graphics and tables that can be displayed on a single viewer page, Aabel will automatically create new pages and display the results on multiple pages.
You can export viewer pages as PDF in a single document.
You can give a live presentation by moving from page to page via clicking the corresponding radio button.

User-Defined Templates

Templates can be created for each chart category and can include properties that do not have any data-dependency.
Examples of attributes that can be saved as templates are chart axis lines (thickness and color), axis label and title fonts (font type, size, color), markers, lines, fill attributes used for representing data series (if you are not using variable hot-linked properties).
A saved template can be loaded into any viewer. The properties defined for any chart in the template will override the corresponding document attributes for the given chart(s).

Aabel Stats SDK

Aabel Stats Plug-in SDK allows users to write their own statistical methods/use Open Source code while using the services and technology that Aabel provides through the API.

New: SDK 2 to be used with Aabel 3.

For more information, click here.

Tutorial Style User Guide Documentation

The Aabel user guide is PDF-based and is designed to provide:

An on-screen manual with high-resolution graphics, flexible navigation controls, and complete hot linked cross-referencing throughout the user guide that includes over 600 illustrations
High quality print output
Step-by-step instructions for using the features and capabilities that the application offers

Aabel is distributed with over 50 data files (proprietary of Gigawiz as well as textbook/published example data), which are used in the application user guide; they also show the data layouts and variable types supported for using different statistical and multivariate data analysis methods.