To Plot or Not to Plot: Statistical Data Analysis And Mathematical Modeling Software

Date: December 7, 1998Statistical Software TableThe science of biometry, or biological statistics, and the art of graphic display have made major advances with the advent of the desktop computer. These advances include quick, multivariant statistical analyses of large data sets and real-time re-analyses with different parameters; the ability to test a mathematical model with raw data; and a multitude of two- and three-dimensional graphical display methods. A wide array of statistics applications are available today from the very basic (for example, Cricket Graph from Computer Associates) to the very complex (such as SAS from SAS Institute). There is also an excellent collection of mathematical modeling applications, most of which include a broad array of numerical and statistical functions. Among the leaders in this pack are Maple V (Waterloo Maple Software), Mathematica (Wolfram Research), and MATLAB (The MathWorks). Almost all statistics and mathematics applications offer a solid suite of graphics visualization options.Statistics plays a major part in almost all medical studies from epidemiology to clinical research. In most clinical trials and behavioral studies, an assessment of statistical considerations usually dictates beforehand the type and amount of data that needs to be collected and provides the technical or procedural framework for an experiment. Without such an assessment, a researcher could collect the wrong data for the explicit question being asked or not collect enough proper data and thus resign the results to 80 percent accuracy, when a few more data points may have assured 98 percent accuracy. Some statistics software packages (such as, STATGRAPHICS from Manugistics, SAS from SAS Institute, and SPSS by SPSS), provide the capability to perform this type of assessment.The most common type of statistics seen in the scientific literature is descriptive statistics, which includes means, medians, standard deviations, variances, coefficients of variation, and the like. These are usually used to describe a result and, to a limited extent, determine the reliability of data upon which a conclusion is based. Statistics are also used to make inferences--that is, to analyze a set of data with the intent of inferring behavior and predicting patterns of data in another related phenomenon. This type of analysis encompasses probability, discrete/continuous probability distributions, estimation, hypothesis testing, and regression and correlation methods.With the exception of mathematical modeling applications, most statistical programs differ in the selection of inference statistics routines and visualization modes. For example, a basic program usually contains a full suite of descriptive statistics routines, a fair collection of inference routines (regression, ANOVA, nonparametric tests), and a basic set of plot types (XY line graph, 2-D and 3-D histogram, pie chart). A full-featured statistics application, on the other hand, can contain as many as 200 statistical routines, a number of mathematical routines, and a seemingly endless selection of plot types. Both classes of software are excellent; however, prospective users are cautioned to make their selections wisely, for the applications could hinder the analyses if one has to struggle with the "options" every time. A researcher who really needs only descriptive statistics should select the application that provides these routines and contains a collection of plotting types, without the added inference statistics routines. Two examples of a "basic" package are CCA-Cricket Graph III (Computer Associates) and CoStat (CoHort Software), whose features can be enhanced with its sister programs, CoPlot (plotting functions) and CoVis (animated scientific graphs).Researchers who need a full suite of descriptive and inference statistics routines, including graphic visualization, should consider a higher end product. Advanced graphing capabilities commonly found in a high-end statistics package include (in addition to those found in a basic application) box, polar, contour, 3-D (scatter, surface, bar), perspective and orthographic projections, as well as spline and line plots (linear, exponential, logarithmic) with an extensive selection of chart customizing and editing features. A broad array of curve-fitting routines (nonlinear, Gaussian, Lorentzian, Boltman, etc.) is also mandatory. Most of the applications listed in Table 1 (Statistics, Mathematics and Presentation Software Suppliers) fall within this category to varying degrees based on the total number of statistical routines and graphics options. Those that include basic inference statistics (in addition to descriptive routines), provide an enhanced collection of graph types and editing functions and are relatively easy to use include DeltaGraph (SPSS), EasyPlot (Spiral), InStat (GraphPad), KaleidaGraph (Synergy), PRISM (Graphpad), SigmaStat (SPSS), StatView (SAS), and Winks (TexasSoft). Some of the most popular high-end, full-featured statistics packages include, Mathematica (Wolfram Research), SAS (SAS Institute), SPSS (SPSS), and Statistica (StatSoft). These latter packages will likely provide the user with every function needed, and if not, the user can build custom routines provided by built-in programming tools.A relatively new mathematical treatment of data is mathematical modeling which in some cases, is a by-product or extension of statistical analyses. Mathematical modeling has opened up new avenues for bioscience exploration, especially in cases where a researcher has a limited data set to work with, wants to apply an experimental observation onto another behavior, or wishes to further test statistical results. This method of complex data analysis has been made possible for lay researchers by the data-collection capabilities and processing speeds of modern desktop computers. Models are usually designed around experimental and observational studies. Based on these studies, a result or behavior is defined in mathematical terms. These equations are translated into a mathematical model that simulates a specific behavior given a specific input (data value).Using a mathematical model, a researcher can test a large set of input parameters in a theoretical setting to find those that may have a real effect in an experimental test and in so doing reduce the number of "bench" tests that need to be performed. The researcher also may purposely input an aberrant data point to see what effect it has on the model to gain a glimpse at what might be occurring in the biological world. For example, for a model that mimics heart electrical activity, a researcher may test the effect of electrical spikes (in amplitude and frequency) on heart rhythm--something no human subject would willingly be exposed to!Mathematical modeling is a very powerful experimental tool, but it is not without its pitfalls. Caution should always play a part in any mathematical analysis because the failure of "modeled" data to fit an experimental observation could be due to any number of factors: poor experimental design, improper data collection, or simply a poor model. It can be difficult to know which result is the reality, and it is only a highly observant and statistically knowledgeable researcher who will see and understand the difference. Most mathematical models are constantly undergoing modifications by their authors as they gain more information and a better understanding of the biological phenomena the model is supposed to simulate.Examples of statistics or mathematics applications that provide mathematical modeling functionality include Maple V (Waterloo Maple Software), Mathematica (Wolfram Research), MATLAB (The MathWorks), SAS (The SAS Institute), and SPSS (SPSS). By design, all modeling applications come with a full graphics suite to enable visualization of the mathematical model in both 2-D and 3-D.An annotated list of applications on the market today is presented in the table Statistics, Mathematics, and Presentation Software Suppliers. Additional listings may be found on the World Wide Web. A few comments on some of the most widely used applications are provided in the product snippets below. Keep in mind that not all applications are the same. It is highly recommended that potential buyers contact the software distributors for additional information. Many distributors offer demonstration versions of their software, which can be invaluable resources in assessing whether a particular application is right for your data analysis needs.Despite how much help these computer programs may provide to researchers, one should keep in mind that these are only tools. To make effective and proper use of them demands a general understanding of how they work, their assets, and their limitations which in this case, means a basic command of statistical theory. For those wishing to review or expand their knowledge, a fair selection of books can be found at your library, or you may consult the web-accessible resources listed in Table 2. A few of the books I consult on occasion are Biostatistical Analysis (J. H. Zar, Englewood Cliffs, Prentice-Hall, 1984, 2nd Ed.), Encyclopedia of Biostatistics (P. Armitage and T. Colton, New York, John Wiley & Sons, 1998) Fundamentals of Biostatistics (B. Rosner, Duxbury Press, 1986, 2d ed.), Intuitive Biostatistics (H. Motulsky, New York, Oxford UK, Oxford University Press, 1995), and Primer of Biostatistics (S. A. Glantz, New York, McGraw-Hill, 1997, 4th ed).An Advanced Graphics Software's SlideWrite graph with curve fits, error bars, and independent left and right Y axesSlideWrite Plus from Advanced Graphics Software combines fundamental graphing and chart making with excellent presentation capabilities. The graphing features include curve-fitting (linear, log, exponential, spline, and polynomial [first to sixth order]); basic statistical analyses of data (sum, mean, maximum, minimum, standard deviation, polynomial coefficients); a variety of graph types (bar, line, scatter, area, mixed, high-low, pie), including 3-D effects for bar, area, and line graphs; and several different bar styles (normal, overlapping, histogram). The word chart, as well as the draw module utilities provide "What You See Is What You Get" editing, so charts may be manipulated on-screen. This application also provides for the incorporation of images into graphs and charts. Images may be extracted from an internal library (over 400 predesigned images), imported from a scanned image or other drawing application, or created on-screen using a selection of drawing tools. The inclusion of drawing capability makes this entire application very useful for generating eye-catching, easily interpretable graphs, tables, and charts.Dataxiom's Ness SoftwareThe StatMost statistical analysis and graphics package is developed by the DataMost Corporation and distributed by Dataxiom Software, Inc. This application is available for all Windows platforms. It offers an impressive collection of data management (data handling, recoding, ranking, normalizing, sorting, trimming), analytical tools (descriptive statistics functions, and nonparametric, correlation, ANOVA, regression, time series analyses), and graphics display modes (standard 2-D and 3-D plot types). This program also includes a suite of drawing and text editing tools, so charts, graphics, and plots may be enhanced by the addition of images. All functions are governed by pull-down menus, which facilitate ease of use. StatMost should meet the needs of the researchers looking for a simple, easy-to-use statistics and graphics presentation application. Not commonly found in the general statistics package, StatMost also includes a wide array of numerical analysis including numerical solutions to differential equations and nonlinear algebraic equations. GraphPad Software is designed for scientists, not statisticiansGraphPad Software markets InStat, StatMate, and PRISM. InStat (Windows and Mac) is marketed as an "instant biostatistics" package, and it measures up to the bill. Available for both Windows and Mac platforms, it provides a full suite of routine statistical tests, including group comparisons (t-tests, nonparametric tests, one-way ANOVA), analyses of contingency tables (Chi-square, Fisher's exact test), correlation, linear regression, and multiple regression. InStat guides the user to pick an appropriate test and interpret the results. Compared to larger statistics programs, InStat provides limited graphics and data management.For more comprehensive graphics display, GraphPad PRISM (Windows and Mac) is recommended. PRISM is a very useful display tool, specifically designed for scientific data analysis and graphing. It is particularly suited for biologists, as it can graph error bars from replicate measurements and fits curves to models commonly used in biology. Graphical display of results is easily performed by simply selecting from a pull-down menu of choices (bar graphs, scatter plots, line plots, etc.). How the results are displayed and what is displayed can be easily modified with a page-layout editor. This is an excellent program for the biological researcher looking for a simple-to-use, statistics package combined with nonlinear regression and publication quality graphics.GraphPad StatMate (Windows) is a companion application for InStat and PRISM, providing a collection of statistical calculators to aid in the design of experiments. It can compute sample size and power when comparing two means or two proportions, but it is not appropriate for more complicated experimental designs.Manguistics's STATGRAPHICS Plus offers many 3-D plots, like this contoured response surface plot.STATGRAPHICS Plus from Manugistics is a full-featured statistics package integrated with a comprehensive graphics presentation set for Windows platforms. It provides routines that support descriptive statistics, ANOVA and regression analysis, and multivariant and nonparametric methods, forecasting, time series analyses,and so forth. It also contains a fair sampling of mathematical functions (numerical differentiation, root finding, eigenvectors, Fourier transform). Analyzed data can be displayed in any of a number of graphics formats (X-Y-Z) line and scatterplots, barcharts, piecharts). STATGRAPHICS Plus version 4 is available in three configurations: the Standard Edition, Quality and Design, and Professional. The "Experimental Design" module is very attractive in the biological arena because it can help the experimenter design an experiment, determine what factors may affect the experiment, and identify and factor in potential problems in the experimental process. Mathsoft offers a range of over 80 2-D and 3-D graph types.MathSoft develops the S-PLUS and AXUM data analysis and graphics display packages for Windows platforms. S-PLUS (Windows, Unix, and Linux) is another comprehensive statistics and mathematics analysis application. It provides basic statistical functions (description statistics routines), as well as linear, polynomial, and logistic regression; nonlinear regression; and minimization; nonparametric regresssion; ANOVA; smoothing and interpolation; and multivariate; and cluster analysis. Coupled with these analytical tools is a very advanced graphics and visualization capability, including a broad array of 2-D and 3-D plots, scatter plots, and time series plots. S-PLUS is expandable and customizable. Using the S-PLUS object-oriented programming language, users can develop new routines or modify existing S-PLUS functions, customizing the data analysis and display environment to their own needs. AXUM (PC), acquired from Trimetrix, is a very comprehensive graphics display application, incorporating a number of analytical routines (descriptive statistics functions, ANOVA, correlations, frequency analyses, and simple, multiple, and polynomial regression and nonlinear least squares regression analysis). Graphics display encompasses a seemingly endless variety of 2-D graph types, 2-D/3-D graphs, 3-D bar, surface graphs and line graphs, from linear to log, exponential, polynomial, and nonlinear curve fitting. The graphics capability is enhanced by over 100 built-in programming functions and operators used to customize analyses and graphics display.Poly Software International's PsiPlot supports variant coordinate systems.PSI-Plot, first introduced in 1992 by Poly Software, is perhaps one of the most cost-beneficial applications on the market today. It contains a good collection of descriptive statistical functions, ANOVA, t-test, f-test, nonparametric tests, and so on. In addition, it also contains graphical attributes (3-D-polar mapping with customized editing) found in many higher priced products. ProStat is a new product recently released by Poly Software that focuses on statistical analyses and includes a full range of basic and advanced multivariate statistical methods. It has a fair sampling of the plotting and editing routines found in PSI-Plot. Together, these two applications can make a winning combination in most research laboratories.SAS's GRAPH produced this graphic based on output from bivariate kernal density.The SAS (Statistical Analysis System) package is the showcase product for SAS Institute. The system is an integrated suite of independent programs (modules) for data entry, retrieval, and management; report writing and graphics; statistical and mathematical analysis; forecasting; and applications development. The current release of SAS software (Version 7) supports Windows 95, Windows 98, Windows NT, OS/2, Digital UNIX, HPUX, AIX, Sun Solaris, MVS, CMS, VMS/Alpha, and VMS VAX platforms. It is a comprehensive system and thus also has a very steep learning curve. Once the learning hurdle is overcome, there is very little numerical data that the researcher will not be able to analyze using SAS.SAS Institute also recently introduced the JMP statistical discovery software, a comprehensive, self-contained (nonmodule) application for statistical visualization and exploratory data analysis. This package contains most of the statistical functions found in the SAS base module. It also includes a function for "design of experiments," which provides routines to estimate various experimental effects (based on one or more factors on a dependent variable), providing researchers with theoretical insight so they may better design their experiments.StatView is another popular statistical analysis package for the Macintosh (and now also available for Windows machines), developed by Abacus Concepts and now supported by SAS Institute. It provides basic statistical functions descriptive statistics for continuous and nominal variables, frequency distributions, variance tests, and a fair set of drawing and presentation tools. It is perhaps one of the easiest programs to use.SPSS, the developer of the renowned SPSS statistical package, has acquired several competitive and complementary products over the past few years, including SYSTAT, SigmaPlot, DeltaGraph, and SigmaStat. Although these products share many common functions, each offers unique capabilities. SigmaPlot is marketed as a scientific graphing program. Resident routines include an excellent collection of statistical and mathematical functions, but what makes this application stand out is its graphical display of data and calculated results. The variety of preformatted plot types offered and the ability to customize these plots provides for a seemingly unlimited selection of graphical display opportunities. It is available for Windows and older versions (7.x but not 8.0) of MacOS. DeltaGraph is chiefly, as its name indicates, graphing applications. It contains over 40 mathematical and statistical functions, and results may be visualized using any one of over 200 customizable chart styles. DeltaGraph is available for both Macintosh and PC computers.With SigmaPlot from SPSS, Excel spreadsheets can be merged with SigmaPlot's menus.SigmaStat ranks among the top intuitive statistical packages for scientific data analysis. Its graphical display options may be mediocre compared to other graphics- intensive programs (for example, its sister product SigmaPlot), but its statistical and mathematical functions are extensive. It is a relatively easy-to-learn program, and the combination of its simple GUI interface and operation on basic desktop systems makes this a highly recommended application for research scientists with large data sets, requiring complex analyses. The SPSS statistics package is the showcase product line for SPSS. The education version of SPSS is geared toward students but could just as well be used in a research setting. The full SPSS package is very robust, providing a plethora of mathematical and statistical functions and graphics display options. Its sister product, in both mathematical and graphical functions, is SYSTAT, geared for producing publication-quality graphs. Either one provides biological users with all they could ever wish for in a statistics application.StatSoft offers a varity of ways to visualized data including 2-D and 3-D contour surface plots.StatSoft develops and distributes STATISTICA and Quick STATISTICA. The former is the company's flagship product--a comprehensive, integrated statistical data analysis, graphics, database management, and custom application development system for Windows systems. The seamless integration of the statistical tools with graphical display routines provides true interactive data analysis. An exceptional set of drawing, image import, text editing, and page layout tools completes this package. The opportunities to revisit data and results by using different statistical functions or easily changing parameters provides opportunities to uncover hidden patterns in the data. Quick STATISTICA is a streamlined version of STATISTICA, incorporating all the data management functions and statistical and presentation graphics capabilities of the parent program. It does not contain advanced statistical routines (for example, multivariate techniques, survival-failure time techniques, time series/forecasting, or structural equation modeling). Statistica and Quick Statistica are available for Windows and MacOS computer systems.Synergy Software's KaleidaGraph made this scatter plot of pressure data with a polynomial curve fit.KaleidaGraph from Synergy Software is a simple, versatile data analysis and graphing application. It is menu driven, providing users with easy access to a host of descriptive statistical functions. Curve-fitting routines include smooth, weighted, cubic spline, interpolate, and least squares regression, plus the ability to enter your own curve-fit equation. Results can be displayed in 16 2-D plot types. Additional plot tools allow users to customize the look of standard result plots. This is a very good program for students of statistics and graphical display.MathWork's MATLAB supports multidimensional datadisplay as shown in this visualization of a 3-D fast fourier transformMATLAB, developed by the MathWorks, is a versatile and comprehensive data analysis application. It couples a broad suite of numerical methods and statistical routines with advanced graphics and visualization capabilities. As with other applications in its class, it also provides programming tools to customize routines. Mathematical models can be developed and tested (simulations) and compared against real data sets. This application also contains a comprehensive set of signal processing and time-series analysis tools, so data may be imported directly into the program, facilitating immediate data analysis. MATLAB is distributed for a number of stand-alone and multi-user platforms, including PC, Sun, HP9000, IBM RS/6000, DEC (RISC, VAX, OSF/1, OpenVMS), SGI, and Convex.Waterloo Maple Software's MapleVWaterloo Maple Software's Maple V application provides over 2,500 mathematical functions for data analysis, including mathematical modeling. In addition, this package includes a robust set of graphics and document presentation tools. The mathematical tools for numeric and symbolic computation, coupled with animation for modeling processes and time-variant information, provide for comprehensive mathematical analyses and mathematical model generation and testing. This application also has built-in programming capability, so new functions may be created or in-house functions customized. The broad variety and numerous mathematical, graphic, and presentation options can make using to learn this package a daunting task, but once mastered, there is very little data analysis that cannot be achieved with this application. In addition, it runs on all the major operating systems available today.Mathematica from Wolfram offers a combination of analysis, graphing, and publishing capabilities.Mathematica from Wolfram Research is another member of the elite club of full-featured applications that bundle complex numerical, symbolic, and graphical computations and mathematical modeling with a broad array of visualization tools. New computational functions may be developed and resident routines enhanced using the built-in symbolic programming language. Mathematica is available for basic desktop platforms, and multi-user systems. Although this application is rather complex and the learning curve steep, numerous books, journals, and electronic discussion groups are available to assist end users. The computational benefits of this application far outweigh its liabilities. In fact, some data analysis applications (for example, multivariant computational modeling) can only be achieved using a small pool of two to three products, one of which is Mathematica.Statistical Software TableThe author can be reached at csmith@the-scientist.com.

To Plot or Not to Plot: Statistical Data Analysis And Mathematical Modeling Software

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