- PSPP is a free statistical anaylsis software for Mac for analysis of sampled data. PSPP is similar to a free version of SPSS which we covered in our in-depth look at the best statistical software for Mac. However, PSPP is aimed more at statisticians, social scientists and students that need quick analysis of sampled data.
- Till I know STATISTICA version8 and above exclusively works on windows platform. You may use RStudio, Red R, PSPP, Rattle and Deducer for statistical and data mining task.
- TIBCO Statistica® Desktop allows users to execute ad-hoc analytics with scientific graphs and plots. In addition, use the code-free, drag-and-drop workspace to create analytic workflows. Users can also create code nodes in Spark, Python, C#, R, or Visual Basic.
- Statistica version 7 free download. Education software downloads - STATISTICA by StatSoft and many more programs are available for instant and free download.
Download JASP Entirely for free, no strings attached. Windows Windows 64bit Windows 32bit The pre-installed 64-bit or 32-bit version can be used if the msi fails. Please note that JASP0.14 is not available for Windows 7. MacOS Catalina Mojave Continue reading →.
What about cryptographic signing and error messages when you try to install free statistical software for Macs? See our “signing page.” ... and does this work on Mojave? Is it signed and 64-bit?
Dell Statistica Software
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Meet the free SPSS clones
I have taught statistics using JASP, Jamovi, and PSPP. Each has advantages and disadvantages, and there is nothing stopping you from using all three depending on what you are trying to do. Ironically, each one has a much faster user interface than SPSS—and all import and export SPSS .sav and syntax files.
JASP is a fork of (it was originally based on) Jamovi; both are still under active development, which have fairly similar user interfaces, and both saved a good deal of time and trouble by not reinventing the wheel—they are essentially user interfaces for another statistics program, the hard-to-learn-and-use R.
The programs have spreadsheet-like data editors, but it's best to prepare information for them somewhere else; they let you computer variables, but in a clunky and hard to use way. Importing variable labels and missing values from SPSS files sometimes fails (I've only seen the missing values problem on Windows), a major drawback to programs that will read SPSS files otherwise.
JASP and Jamovi share lightning-fast speed; a wide range of statistics, with extra plugins on Jamovi; and easy installation on Macs, Windows, and Linux. Their basic interface has an Office 365-style open/save/print/export tab; options on the left, output on the right layout; instant changes to the output if you change the input; and export of both data and output, as desired.
There’s a third SPSS clone, one which keeps most of the user interface from a relatively ancient version of SPSS: PSPP. At the moment there are some nasty bugs, but overall it might be easier for many people to use than JASP and Jamovi. It's easier to master if you're used to SPSS, but development has been very slow and JASP and Jamovi may be better options for that reason—unless you do a lot of computes and recodes and other data manipulation, or do a lot of t-tests. Then PSPP is the best choice.
JASP/Jamovi vs PSPP
|JASP and Jamovi||PSPP|
|t-tests||Shared variance only||Shared and unique variance|
|Output||Copies as tables||Copies as plain text|
|Windows||One triple-pane window||Three windows|
|Contextual help||Yes, nicely integrated||No|
|Can log commands to a file||Yes (can’t easily replay)||In theory/not working|
|Mac open/save/print boxes||Yes||No|
|Can use as SPV file viewer||Yes!|
JASP vs Jamovi vs PSPP: comparing free statistics software
|Regression||Stepwise, forward, backward||Enter (supports multi-step)||Enter (one step)|
|Missing values||Program-wide only||By variable||By variable|
The SPSS clones in more detail
PSPP: First clone of SPSS, with many bugs stomped out
Current Version: 1.41; Mac up to 1.4
Listing updated 10/30/2020
Last known software update: August 2020 (Mac version)
Note: Catalina version stable; unsigned software
PSPP is a free SPSS clone with a Mac version you can download from this site (it’s unsigned). It is also in MacPorts, but that's another level of effort. The pre-compiled Mac version is under 60 MB, while some other free software can take half a gigabyte; it loads almost instantly. SPSS is far slower in both calculations and launching. The user interface is nice and fast.
PSPP is aimed at social scientists, business people, and students, with a convenient, easy to learn interface. It is not quite as easy to install as it could be, unless you run Linux, which is its ideal environment (PSPPire).
The interface is similar to SPSS, though there are some oddities including having menus in the windows and not in the menubar; and using its own version of the open/save dialogue box. It includes common folders in the open/save box, including Desktop, Home, and disk root, but lacks custom folders (including OneDrive and Dropbox) you may have in your Finder sidebar. (Version 1.4 fixed problems with crashing on use of arrow keys in the open/save dialogue and autorecode. Mojave-specific bugs: “Recently used files” do not work, and the program still can't find .sav files unless you specify 'all files.' Oddly enough, these are not issues in Catalina.)
PSPP imports SPSS data files, long variable names, and variable and value labels. Common options are included in some dialogue boxes without the need to dig deeper. Development seemed to accelerate in the last few years, though it's not moving as quickly as JASP and Jamovi are.
While you can copy from the output window, you have to copy from the left-hand contents, not from the main pane. The output window yields plain-text, delimited by spaces and pipes, just as SPSS 4 did. That’s not ideal for importing to spreadsheets or word processors, unless you’re really, really good at using BBEdit. There’s also no way to clear anything from the output window; and you have to use control keys instead of command keys.
The capabilities are impressive, including graphing, data transformation, crosstabs, tables, various t-tests, ANOVA, regressions, factor analysis, ROC curves, and nonparametric tests. It’s a fine way to avoid spending thousands of dollars on the big cheese. A great deal of work has gone into the analyses themselves, and the routines the program does run are well fleshed out.
The user interface can be awkward, but it’s fast both in the user interface and in the calculations; while on SPSS it takes a long time for windows to form and disappear.
Oh, and one more thing: you can get rid of the slow, buggy 740 megabyte SPSS “SmartViewer.” PSPP will happily open SPV files with the original formatting. It's amazing.
JASP: the first really good effort at making R more accessible
Current Version: 0.13.1
Listing updated: July 2020; program updated in 2020
Not signed by Apple (you may see a warning)
JASP was created as “a low fat alternative to SPSS, a delicious alternative to R,” and comes out of the University of Amsterdam (its 650MB weight is below SPSS’ gigabyte-plus).
JASP uses the native open/save dialogue box, albeit with a weird Microsoft Office-style setup requiring more than one click; and JASP is easy to install. It would be very nice if it was signed.
The software looks and feels like SPSS to a degree; it feels almost as native a SPSS. Calculations and screen drawing are far, far, far faster than in “real SPSS” — when you select the tests, they might actually be pumped out before your finger is fully off the mouse. Stepwise regression is supported (unlike Jamovi). However, when you do t-tests, if equal variances are not present, it only prints out a warning, rather than using the alternative method of calculating t.
We loaded our test file instantly — and ran descriptives instantly. Survey researchers will be happy to know they can assign value labels — and unhappy to know they must be done variable by variable, without syntax. The labels are retroactively applied to whatever is in the output window, very rapidly. Unfortunately, too, variable labels are not supported (though value labels are)—nor is there a clear way to compute new variables. Presumably one has to export the data, make the changes, and bring it back again. You can't mark missing values variable-by-variable; missing values are applied to the entire dataset, which is a bit nuts.
Oddly, t-tests in both JASP and Jamovi are done only with the assumption of shared variance, and a warning to tell you if that assumption is violated.
JASP is still being developed fairly quickly; but the lack of variable labels is a major drawback from PSPP. The clever user interface, allowing users to go back and change things in a past run simply by clicking on it in the output pane, is pretty cool, though (and shared with Jamovi); and the speed is terrific, if not quite at Stata levels. Pretty much everything is instant, while on SPSS it takes a long time for windows to form and disappear.
JASP’s advantage over Jamovi is that it supports forward, backward, and stepwise regression, while Jamovi only supports 'Enter.' The reason is ideology, so we don’t expect that to change. There is a great deal of documentation at the site Jasp for Nonprofits which sadly has not been updated since 2016, and the newish (2019) book Learning Statistics with JASP. There is also a new Machine Learning module with 13 “analyses that can be used for supervised and unsupervised learning.”
Dive more deeply into JASP (full MacStats review).
Jamovi: deceptively powerful
Current Version: 1.25
Listing updated: 7/2020; program updated 2020
Cryptographically signed by Apple
Jamovi: A free, open source package, built on top of an R foundation (Thanks, Dr. Kim-Oliver Tietze). Don’t let that put you off: Jamovi uses a simple spreadsheet interface with full graphics, and while it allows you to use syntax, you can also use menus. You can edit via spreadsheet; and your data, analyses, and options are saved in a single file, so others can reproduce your work. A large number of analyses are easy to find, or you can use R syntax.
The results are attractive (see above), with menus that will be familiar to any SPSS users — and with many options. Copying and pasting output is cleverly done; right-click on a section of output, and you can paste it into Word as a nicely formatted table. Paste into BBEdit, and it will be plain-text, formatted with spaces. Plots can also be copied and pasted, but seem to be limited to screen resolution; there are three built in plot themes, including an SPSS-clone one.
A syntax mode shows the generated R syntax for each menu command, helping you to learn R syntax or make scripts to reproduce the same actions over and over, ... except for importing data. Data can be imported in numerous ways, including formatted SPSS files and, according to the programmers, SAS and Stata files. When we imported an SPSS file, value labels came through, but it does not support variable labels at all. Likewise, it did not export variable labels consistently. Export from Jamovi to SPSS resulted in errors on some data files as the number of characters in some fields was not correctly marked.
Jamovi is fairly fast, but (like PSPP) doesn’t fully use the Mac interface; pretty much everything is instant, while on SPSS it takes a long time for windows to form and disappear.
Jamovi’s menus are kept within its own window instead of at the top of the screen, and the open/save dialogue box is very different, though it does show shortcuts for the documents, downloads, desktop, and home folders (it also has the odd new Microsoft approach to open/save/print, creating a whole new window/interface for it). You can, however, drag and drop data files onto it — saving time.
One downside: for ideological reasons, you only get Enter for linear regression. Now, though, it allows you to do multiple blocks, so you can still do sensible multiple regressions. Also, as with JASP, it will do t-tests only one way, assuming equal variances, giving you a footnote to tell you if the assumption has been violated.
Newer versions of Jamovi support having different missing values for each variable, an advantage over JASP.
Developer Jonathon Love pointed us to the Jamovi library of extra procedures, which is expanding fairly rapidly. A long, well-illustrated Jamovi blog post also goes over the fine graphics capabilities within Jamovi, which PSPP can only dream of.
The program is almost 700 megabytes in size, due largely to the integrated software — R, Electron, Mantle, Python, and ReactiveCoca. Accuracy is pretty much assured by the R underpinnings.
Dive more deeply into Jamovi (full MacStats review).
Free and promising general statistics software (other than the SPSS clones)
Past 4 (PAleontological STatistics): an absurdly wide-ranging, easy to use package
Current Version: 4.03
Listing updated: 8/2020 (program updated July 2020)
64-bit and Catalina capable
Not signed by Apple (you may see a warning)
“Past is free software for scientific data analysis, with functions for data manipulation, plotting, univariate and multivariate statistics, ecological analysis, time series and spatial analysis, morphometrics and stratigraphy.” That said, Dennis Helsel wrote, “While its name shows its origin (Paleontology), it is a full-fledged stat package which includes multivariate and permutation tests, with a nice interface.” There is good support for geographical and map-based statistics.
When Dennis says “full-fledged,” he isn’t kidding — the range of this software is stunning. Yet, the download is a mere 10 MB — far, far, far less than many others. What’s more, every new version brings a wide range of new features.
Our test file imported in less than a second, but be warned that import formats are limited and exclude SPSS files; some rather esoteric formats are accepted, though, and you can copy and paste from Excel (with caution). Summary statistics came in a fraction of a second on a laptop. Our survey file never caused more than a slight pause. In the past, very large files choked the software, but we haven't tested version 4 yet.
PDF manual. Dive more deeply into PAST (full MacStats review).
Other free general statistics software
Statistica Macbook Download
Current Version: 8.7
Listing updated: 4-1-19
Size: 3.5 GB (yes, GB)
SageMath is not specifically for statistics; it’s general math software, but it has the ability to do numerous statistical processes including graphing/plotting. It can be used for just about any type of math, and can be used either with the command line or or from a web browser. You can install it onto a server if you want, and create embedded graphics, typset-style math expressions, and more; it also includes sharing. The program was designed for both education and research. It is not a typical Mac program; it has a command line element and is accessed from browsers.
SageMath was built atop existing packages including NumPy, SciPy, matplotlib, Sympy, Maxima, GAP, FLINT, and R.
Configurations Available: Intel processors (10.6+)
Current Version: 5.06.5
Unsigned and not 64-bit
Listing updated: August 2020 (software last updated June 2012)
MacAnova is a free, noncommercial, interactive statistical analysis program developed by Gary Oehlert and Christopher Bingham of the University of Minnesota School of Statistics. Their web site notes:
MacAnova has many capabilities but its strengths are analysis of variance and related models, matrix algebra, time series analysis (time and frequency domain), and (to a lesser extent) uni- and multi-variate exploratory statistics. MacAnova has a functional/command oriented interface. The Macintosh and Windows versions also have several window/menu/mouse type features. Although the language and syntax are S-like, MacAnova is not S or R.
MacAnova is Intel native, and there is source code available. The program started up very quickly on a Intel Mini and had a fairly good menu system, which output visible code that we could copy and manipulate, or save and run later. It is almost similar to SPSS 4 in that regard, though better integrated into the system and lacking a separate output window. MacANOVA includes linear model and GLM routines.
Unless you really need something unique in it, though, look elsewhere, since the last update was in 2012.
Current Version: 2.8 (updated May 2019; prior version was dated May 2017)
Listing updated: August 2019
64-bit, signed, works well in Mojave
Michael McLaughlin’s Regress+ is a free package that includes regression, stochastic modeling, bootstrapping and robust goodness of fit measures. The software and a tutorial are available at the Regress+ web site. Older versions are still available for older operation systems, while version 2.5 is available for OS X and 9.2.
The program is accompanied by full documentation in PDF form which doubles as a statistics reference guide.
Regress+ 2.7, née Regress+ 3.0, was a complete rewrite; it added data modeling (equations and distributions), extensive documentation, and publication quality graphics. Regress+ 2.8 was a substantial upgrade.
This program appears to cover every aspect of regression you can think of. It's graphically oriented but has strong statistics. The code is “more than 100 times faster than before [2.7].”
Version 1.46; Listing updated August 2019; Code updated 11/2017
Windows, Linux versions at version 1.52 as of 7/2019
Not signed; 64-bit
SOFA Statistics (Statistics Open For All) emphasizes ease of use, discoverability, and clean reporting. It can connect directly to database sources, or use data brought in from spreadsheets. The usual statistical processes are available, including one-way ANOVA, t-tests, signed ranks, chi-square, and R; nested tables can be produced with row and column percentages, totals, standard deviations, means, medians, and sums.
SOFA Statistics is written in Python, using a wxPython widget toolkit. Statistics come via the Scipy stats module. Analysis and reporting can be automated using Python scripts, either exported from SOFA or written by hand.
Configurations: Requires Java; should work on Intel and PPC Macs
Current Version: 4.9
Listing updated: 8/2019
Software updated: 1/30/2019
Statistics101 is giftware to help teach probability and statistics the easy way—by simulation. “Gain deeper understanding of traditional statistics concepts and methods. Increase your awareness of the role of variability in probability and statistics. Learn and apply simple to very sophisticated statistical techniques without tables or complicated formulas.” Interprets and executes the simple “Resampling Stats” programming language. The original Resampling Stats language and computer program were developed by Dr. Julian Simon and Peter Bruce to teach statistics.
A somewhat steeper learning curve or tougher install
Python software / Listing updated: 10/19/2018 / Software updated 2014
Last news on the web site is from 2014
Salstat dates back to the early 2000s and runs on Python; installing the free version on the Mac may require quite a bit of library-and-Python downloading, but a paid version makes everything easy. There is a reward to the work of installation, though, in a free program which makes highly presentable graphics, is relatively easy to use, provides a great deal of descriptive statistics with parametric and nonparametric tests, shows its own source code, does crosstabs, and “charts, imports CSV, HTML, XML, Excel, LibreOffice and SAS file formats, and can even scrape tables of data from web pages.” The source code listing claims a last-update date of 2014.
A post in April 2018 claimed the company was creating a new version of Salstat.
R (CRAN) / “R for Mac OS X” / R.App and R GUI
Current Version: 3.6; under active development
Signed, 64-bit, requires XQuartz
Listing updated 8/2019
This is an exceedingly flexible program, with a large number of libraries and built in routines, and the ability to run many S or S-Plus programs. R loads and runs quickly but has a steep learning curve.
R programs and algorithms are distributed by the Comprehensive R Archive Network (CRAN). A simple and somewhat frustrating graphic user interface is included for Mac users; R Commander can be installed using the built-in package installer, which can also install file import features (which aren't installed by default). R Commander is an X11 program, which means it uses an alien interface and has odd open/save dialogues, but if you get past that it offers menu driven commands not dissimilar from, say, SPSS, just a lot more awkward to use, and without an output or data window.
There are now numerous front ends for R, several of which are mentioned earlier on this page.
R has a massive range of tests, PDF and PostScript output, a function to expand zip archives, and numerous other unexpected features. For much more information about R, including advantages, drawbacks, resources, and tips, see our incredibly outdated R statistics software for the Mac page.
Current Version: 1.1x
Listing updated: 4/2018; program updated 3/2018
Signed by Apple
R Studio is commercial open-source software, designed for creating and managing R applications rather than, say, doing exploratory research or testing the odd hypothesis. With frills, it can get expensive, but without frills, it’s free. The Mac version seems to be developed at the same time as Linux and Windows versions. It’s a bit of a porker (500MB plus R itself at around 130MB) and requires a separate R download; R itself is updated regularly and has a signed Mac package.
When you first load R Studio, it tells you to go back and install R. Once you've done that and restarted, it finds R easily enough, and presents you with an integrated development environment (IDE). If you try to do something, such as importing SPSS data, that isn’t possible without further downloads, it automatically connects to the Internet and installs whatever you need. The user interface is Mac-standard in most ways — you get a menu at the top of the screen (as well as menus in the window itself), and the open/save dialogues are thankfully quite normal.
Though you can manage your R installation from R Studio, it’s a tool for dealing directly with syntax, and for managing projects; it’s not a beginner’s tool (as, say, Jamovi can be). R Studio never claims to be anything but an IDE, with many options and good operating-system integration.
Current Version: 1.0
Listing updated: 2/2019 (program updated 2/2019)
Signed, 64-bit; good for El Capitan through Mojave
Currently just 4.6 MB, no license; intended to become open source at a later date
From the writer of Regress+ comes a free, powerful program to analyze any kind of data. MacMCMC is part of a two-part set—the other part being a free ebook. Data can be imported from plain text (UTF-8). There are 27 built-in distributions, including 16 continuous, 8 discrete, and three homogeneous mixtures — Normal, Bivariate Normal, and Poisson; users can also define their own distributions. There are 15 built-in functions. Reports include MAP, mean, median, mode, and Gelman-Rubin; credible intervals; trace; plots of marginals; and trace comparison for selected chains. The program has other features, described on its web site, along with a sample input, data, model, and output.
Advantages of MacMCMC, in addition to its price, include being a complete standalone Mac program (hence its small size and fast operation); 100% Bayesian inference; parallel processing; and access to low-level options. Users can check for updates from a dropdown menu. The basic method of using the program is to set up the model via a simple text format, easily figured out from the examples or the ebook; load data (in ASCII format); run Compile, run Setup, change any parameters desired, and then run. That yields a plain-text report and a graph which can be adjusted as needed.
Current Version: 3.194 / requires OS 10.7-10.13
Older versions: 680x0; PowerPC; OS X (Universal Binary); Windows and DOS
Listing updated: 8/2019 (program updated Feb, 2019)
Signed, 64-bit; no mention of Mojave
G*Power was developed by Axel Buchner to provide power analyses for the most common statistical tests in behavioral research: t-tests, F-tests (including ANOVA, regression, etc.), and Chi-squared tests. G*Power computes power values for sample sizes, effect sizes, and alpha levels; sample sizes for given effect sizes, alpha levels, and power values; and alpha and beta values for given sample sizes, effect sizes, and beta/alpha ratios. It is a remarkably small program, just over 2 MB in size. Updates (for both Mac and Windows) are slow, with nothing but bug-fixes since March 10, 2014. Version 3.1 itself dates back to 2009, though there were numerous improvements from 2009 to 2014.
gretl can do general statistical routines and many specialized ones; it is in our “special purpose and general math programs” page.
GMT (“The Generic Mapping Tools”)
Current version: 5.45
Program updated: Jan 4, 2019
Listing updated: 9-2-2019
Command-line tools that run on Unix-like systems, including Mac OS X. See https://github.com/GenericMappingTools/gmt for details. Many of the main developers, including Paul Wessel, use Mac OS X. From their site, GMT is...
... about 80 command-line tools for manipulating geographic and Cartesian data sets (including filtering, trend fitting, gridding, projecting, etc.) and producing PostScript illustrations ranging from simple x–y plots via contour maps to artificially illuminated surfaces and 3D perspective views; the GMT supplements add another 40 more specialized and discipline-specific tools. GMT supports over 30 map projections and transformations and requires support data such as GSHHG coastlines, rivers, and political boundaries and optionally DCW country polygons. GMT is developed and maintained by Paul Wessel, Walter H. F. Smith, Remko Scharroo, Joaquim Luis and Florian Wobbe, with help from a global set of volunteers, and is supported by the National Science Foundation. It is released under the GNU Lesser General Public License version 3 or any later version.
Graphviz and Instaviz
Configurations: PPC (older versions), 10.5+ (current)
Current Version: 2.20.3
Software updated prior to 7-7-13
Listing updated 9-2-2019
Statistica Download Mac Software
Graphviz is the AT&T open source drawing package. The Mac OS X version and the overall project have their own web sites. The OS X version uses the Aqua user interface. Prepare for a steep learning curve but it may be worth it if you have graphs you do frequently; not what I'd suggest for the occasional one-off though. Note that graphviz does not seem to have had any development for around six years, but Instaviz, an IOS version, is available on the Apple store; it has shape recognition so finger sketches can become graphs for flowchart.
The Graphviz (Mac version) description on their web site was last updated in April 2008. InstaViz, on the other hand, is selling for $8 on the App Store, and was last updated with version 3.8 in 2016.
Configurations: PPC (older versions), Intel (current)
Current Version: 4.6.3
Listing updated: 7-7-13
Program updated: 4-18-13
gnuplot is open source scientific plotting software. It is available online from many sources
Current Version: 2.2.1
Last update: 4-6-2013
Listing updated: 4-24-2018
StatCrunch is a freely available for web-based use, currently without advertisements, with a $5 per user fee for use on your own server, or $5/six months. It has the usual range of basic statistics, from t-tests to regression to ANOVA and nonparametric tests, with a wide range of graphs also available, and works from Excel or text files. StatCrunch will also store your data within reason. For those with low budgets or infrequent needs, StatCrunch's fairly easy to use interface and price are extremely attractive (it also makes sharing data easy).
Free - open source - for Mac OS X
Current version: 1.2.1
Report updated: 7/2013
Matplotlib is a pure python plotting library with the goal of making publication quality plots using a syntax familiar to matlab users. The library uses Numeric for handling large data sets and supports a variety of output backend.
On August 28 2012, John D. Hunter, the creator of matplotlib, died from complications arising from cancer treatment, after a brief but intense battle with this terrible illness. Please consider making a donation to the John Hunter Memorial Fund.
SciPy is a library of scientific tools for Python which supplements the Numeric module. SciPy includes modules for graphics and plotting, optimization, integration, special functions, signal and image processing, genetic algorithms, ODE solvers, and others.
VTK (Visualization Toolkit)
May be compiled from source code for OS X, Linux, etc
Latest version: 7.1
Listing updated 1/2017
The Visualization ToolKit (VTK) is a system for 3D computer graphics, image processing, and visualization with several interface layers. In VTK applications can be written directly in C++, Tcl, Java, or Python.
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“VTK supports a wide variety of visualization algorithms including scalar, vector, tensor, texture, and volumetric methods; and advanced modeling techniques like implicit modelling, polygon reduction, mesh smoothing, cutting, contouring, and Delaunay triangulation. Moreover, we have directly integrated dozens of imaging algorithms into the system so you can mix 2D imaging / 3D graphics algorithms and data.”
- Graphing and visualization software (including packages that do statistical routines, e.g. Aabel)
About our test survey file
Our test survey file: The “survey file” has 1,000 cases, with 40 questions on a five-point scale, two irrelevant variables (screen width and height), and a couple of demographics (shown here as “job type” and “new or old hire”). We are planning to run the same tests on each package as time goes on.
Books by MacStats maintainer David Zatz • MacStats created in 1996 by Dr. Joel West; edited since 2005 by Dr. David Zatz of Toolpack Consulting. Copyright © 2005-2020 Zatz LLC. All rights reserved. Contact us.