Causal Inference via Causal StatisticsCausal Inference via Causal Statistics

Center for Applied Social Science

Center for Applied Social Science

"The development and utilization of Causal Statistics will eventually be as important to the non-experimental sciences as the codification and utilization of the scientific method was to the physical (i.e., experimental) sciences." 1969

“It is beyond incredulity that, in the approximately 150 year history of the modern social sciences, so little money, thinking, and work have been devoted to the development of tools and techniques for making valid causal inferences in non-experimental research.” 1999

“Since both the Government and private foundations seem incapable of supporting revolutionary research to found, develop, and operationalize methodological tools, designed to draw causal inferences for the purpose of surmounting the most devastating impediment to progress in the social sciences, I will devote the rest of my life to accomplishing these ends and if that eventually proves insufficient I will contribute at least $1,000,000 toward the completion of this research effort.” 2006

“100 years from now, research results and theories in the non-experimental sciences will consist mostly of large arrays of variables, connected by multi-equation causal models, inferred from a single large or a compounded succession of smaller applications of Causal Statistics in empirical research studies.” 2007


Introduction to the Web site

Causal Statistics is a mathematical inquiring system which enables empirical researchers to draw causal inferences from non-experimental data, based upon the minimum required assumptions, explicitly stated. The non-experimental sciences (e.g., the social sciences, epidemiology, etc.) are and have, for well over a century, been in desperate need of a tool to make valid causal inferences. To understand the difficulties in drawing causal inferences from non experimental data and the potential of Causal Statistics for surmounting these difficulties, see Working Papers #1 and #2, below, on the right hand side of the page.  For examples that illustrate the need for and value of Causal Statistics, see Working Papers #3 and #4.

Causal Statistics is the only completely founded causal inquiring system.  It is an axiomatic, deductive, logical construct, in the sense that Euclidian geometry is such a construct. 

At its core, Causal Statistics is based on epistemology, the philosophy of causality, subatomic and quantum physics, both experimental and non-experimental research methodology, social science insights into theoretical and operational definitions, deductive and inductive logic, a penetrating investigation into the concept of inference and it's applications, axiomatic mathematics, and both classical and Bayesian statistics.  See Working Paper #6 below, for a discussion of how Causal Statistics is founded on and derived from these disparate conceptions and disciplines, as well as how this causal inquiring system relates to other statistical paradigms.

The initial purpose of this web site was to make my dissertation, entitled Foundations of Mathematical Epistemology: A Derivation of Causal Statistics, published in 1972, easily accessible. A downloadable, selectable, and searchable copy of the dissertation is presented below, on the left half of this web page. To the right of the dissertation are links to (1) draft Working Papers intended to clarify and expand on various aspects of and issues relating to Causal Statistics and (2) other papers of interest on various subjects, all at various stages of completion.

The dissertation presents Causal Statistics at a level that highly analytic and dedicated researchers could extract the implied causal inquiring system and apply the paradigm in non-experimental research and obtain valid causal inferences. Nevertheless, greater simplification is necessary for the vast majority of social science researchers to utilize Causal Statistics with complete understanding and confidence.

Hence, as work on the web site has progressed, the ultimate goal of the site has become more far-reaching.  The goal has evolved toward making a sea change in the way non-experimental scientists conduct their research. Specifically, it is desired that social scientists, epidemiologists, and other non-experimental researchers, when appropriate, utilize Causal Statistics in the design, conduct, analysis, and reporting of their empirical research; a consummation I anticipated 40 years ago, but has not been realized.  See Working Papers #7, #8, #9, and #10, below, for discussions of previous efforts to push causal inference methodology forward, for impediments, for the sources of these impediments, etc.

In an effort to accomplish this goal, I have established five objectives (“Objectives” are steps on the path toward accomplishing the overall goal.):

  1. To make the dissertation readily available to all (accomplished via the presentation of the dissertation, below);
  2. To extract from the dissertation portions that are, in sum, necessary and sufficient for formulating a causal inquiring system based on epistemology, philosophy, physics, definitional analysis and construction, research methodology, logic, axiomatic deductive mathematics, and statistics;
  3. To utilize these extractions to formulate Causal Statistics in a complete, coherent, and interrelated (i.e. with consideration of how Causal Statistics related to its epistemological environment) form;
  4. To present this formulation of Causal Statistics in an easily accessible way (even multiple ways) to research methodologists, to the researchers themselves, to research consumers, to social science theorists, and to applied social scientists. (The initial presentation will be accomplished through the collaborative development of a definitive book on Causal Inference, entitled Causal Inference via Causal Statistics and through various Working Papers available to the right of the dissertation, below.  The book is being developed by Dr. Portwood at in cooperation with members of Analytic Bridge and in a manner that can be viewed by anyone);
  5. To challenge non-experimental scientists and research methodologists to do the hard work to study, understand, analyze, critique, extend, and apply Causal Statistics.

C. Sterling Portwood, Ph.D.
October 18, 2006


Foundations of Mathematical Epistemology: A Derivation of Causal Statistics, by Charles Sterling Portwood III. © 1972


Dissertation Title Page, Table of Contents & AbstractTitle Page, Table of Contents, Abstract, Definitions, and Symbols

Dissertation Part I (Introduction) and Chapter 1 (Setting and Summary of Dissertation)Part I (Introduction) & Chapter 1 (Setting and Summary of Dissertation)

Dissertation Chapter 2Chapter 2 (Setting and Significance of the Causal Statisitcs Project)

Dissertation Chapter 3Chapter 3 (Importance of the Dissertation)

Dissertation Part II Philosophy of Causality and Chapter 4 The Definition of CausePart II (Philosophy of Causality) and Chapter 4 (The Definition of Cause)

Dissertation Chapter 5 Analysis of the Causal PhilosophyChapter 5 (Analysis of the Causal Philosophy of David Hume)

Dissertation Chapter 6Chapter 6 (Analysis of the Causal Philosophy of John Stewart Hill)

Dissertation Part III & Chapter 7Part III (A Derivation of Causal Statistics) and Chapter 7 (Derivation of Continuous Causal Micromathematics)

Dissertation Chapter 8Chapter 8 (Derivation of Discrete Causal Micromathematics)

Dissertation Chapter 9Chapter 9 (Derivation of the Universal Model of Discrete Causal Micromathematics)

Dissertation Chapter 10Chapter 10 (Derivation of Discrete Causal Macromathematics)

Dissertation Chapter 11Chapter 11 (Derivation of the Universal Model of Discrete Causal Macromathematics)

Dissertation Chapter 12Chapter 12 (Derivation of the Universal Model of Causal Statistics)

Dissertation Part IV & Chapter 13Part IV (Concluding Remarks) and Chapter 13 (Contributions and Conclusions)

Dissertation Chapter 14Chapter 14 (Recommendations for Further Work)






1.  A Simplified Explanation of the Causal Inference Problem

2.  A Simplified Explanation of Causal Statistics

3.  Examples Illustrative of the Inadequacies of Associative Statistics and the Acute Need for Non-experimental Researchers to Use Causal Statistics

4.  An Application of Causal Statistics to Pesticide Data

5.  Origin of my Entry into the Development of Causal Inquiring Systems

6. The Relationship among Statistical Paradigms and an Intuitive Presentation of the Foundations of Causal Statistics

7.  An Abbreviated History of Non-Experimental, Statistical Causal Inquiring Systems Through the Mid 20th Century

8.  An Analogy Illustrative of how Methodologists have Failed to Develop, Perfect, and/or Recommend Causal Inquiring Systems: A Parable of Failure

9.  One Methodologist’s Experience with Attempts to Develop a Causal Inquiring System

10.  Shame

11.  502

12. 503

13. 514

14.  What is Mathematical Knowledge?

15.  An Epistemological Approach to Evolution/Intelligent Design in Education

16.  The Preparation and Characterization of Electron Beam, Vapor Deposited, Germanium Films

(Click below for faster downloading)

Title Page through Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

Chapter 8-11

17. Operational Intelligence

18.  Keeping Tropical Fish in Farms Alive in a Cold Snap

19.  A Radical Departure from Classical Statistical Significance

20.  A General Model of Product Evaluation

21.  Manifesto of the Center for Applied Social Science

The Start of a 1975 Causal Statistics Textbook



Recently I ran across a treatment for a causal statistics textbook which I designed in 1975, after teaching an graduate causal statistics course at the University of Hawaii; as far as I know the first causal statistics course ever taught.  This treatment was a first draft of the preface, the table of contents, and part of the first chapter and is presented at the bottom of this webpage.


In 1975 I gave the draft to a representative of Prentice-Hall to see if they would be interested in publishing such a book.  When they got back to me they noted that there were no current courses in causal statistics and they were not interested in trying to build the market.  They felt therefore that the proposed textbook didn't seem to them to be a financial winner.  They mentioned that they did like my writing style and would like me to write a classical statistics textbook for them.  I thanked them, but responded that I had no interest in such a project.


In 2008 I designed another causal statistics textbook (to initial sketch of 2008 textbook) without reference to the 1975 version.  When I rediscovered the earlier textbook it was interesting to see the extreme differences between the two books.  The 1975 draft was much more mathematical and application oriented and the 2008 design was more philosophical, foundational, and derivational; focusing more on required assumptions and on the understanding of the nature of causality and causal inference.


Each of the two approaches is important in their own respects.  After considering the comparisons and contrasts between the original designs, I developed three different syntheses of the two approaches.  The original 2008 table of contents and the three syntheses are presented here.


Immediately below are first drafts of the preface, the table of contents, and a portion of chapter 1 for the 1975 Causal Statistics textbook.

Causal Statistics for Application

Preface and Table of Contents


Chapter 1




Some areas of the website are still under construction.