Perspectives on Faith-Discipline Integration in Statistical Inference

1. Perspectives on Faith-Discipline Integration in Statistical Inference Andrew M Hartley, PhD August, 2011 AD

2. We believe • The fear of the LORD is the beginning of wisdom, and knowledge of the Holy One is understanding (Proverbs 9:10) • …that in everything you were enriched in Him, in all speech and all knowledge (1 Corinthians 1:5) • …for the fruit that the light produces consists of every form of goodness, righteousness, and truth (Ephesians 5:9) But does all this apply to wisdom, knowledge & truth in statistics?

3. Objectives / Framework • Illustrate / explain SOME implications of Christian faith for statistical inference • Catalyze interest & involvement • Not dogmatic; my way is not the only way • Best outcome – Participants will be inspired to investigate implications on their own

4. Agenda • Me • Impacts of Religious Beliefs on Scientific Theorizing • Impacts of Religious beliefs on Statistical Inference • Christian • Humanist • Russ Wolfinger • Counter-points • Alternative approaches • Additional observations • Odds & Ends • Questions / comments at end • Enough time to cover major points only • Will raise more questions than answers • Will focus on statistical inference, not statistics in general

5. As Overview: CSIDG Statement of Purposes (from CFR, 2005) • Promote interaction & fellowship among Christian statisticians • Articulate the relevance of the Christian faith & world view within the statistical community • Encourage Christian statisticians to become more articulate in sharing Godly principles & a Christ-centered lifestyle • Encourage Christians in statistics to explore the relationship of their faith to their discipline

6. Types of Faith-Academic-Discipline Integration • Praying before work / class? • Using discipline to argue for The Faith? • Deepening faith using insights from work? • For example: Explaining the Trinity using the 3 states of H2O? • Evangelism on the job? • Identifying ways discipline can align with faith • Transforming personal practice • Transforming the practice of our co-workers / students

7. Effects of Religious Beliefs on Science Religious beliefs control science indirectly: • Religious beliefs delimit a range of compatible “overviews of reality” (presuppositions about what is, how it fits together, & how we know it) • Each overview of reality, in turn, delimits a range of compatible scientific theories Example from Psychology • Religious belief: Matter is self-existent • Compatible overview of reality: All of human experience is merely physical (atoms & molecules interacting) • Compatible scientific theory (BF Skinner): Only behavior merits study. “Consciousness,” “Soul,” “Perceptions,” “Thoughts,” etc. are merely myths & illusions We usually hold overviews of reality unconsciously

8. Philosophy of the Law Idea (PLI) • Provides a Biblically consistent overview of reality • Developed / expounded by (among others) • Abraham Kuyper • Herman Dooyeweerd • Roy Clouser • Elucidates principles for the sciences • Principles can be categorized as consisting with the Bible’s themes of • Creation • Fall • Redemption

9. Creation & Some PLI Principles • The Bible on Creation • God created all, & it was good • God set man as ruler / caretaker over all creation (Cultural Mandate: Gen 1:28 & 2:15) • Having the right God forms the foundation for all wisdom • PLI • The sciences form part of that ruling / caretaking • Scientific wisdom depends on knowing God • No part of creation is more “important” or “real” than another

10. Creation & Some PLI principles–Science • Humans experience the world in various “aspects” • Aspect = a kind of properties & laws. PLI identifies the following aspects: • quantitative • spatial • kinetic • biotic • emotional • logical • historical / formative • symbolic • social • economic • aesthetic • moral • legal • certitudinal • Each science (mathematics, biology, economics,…) focuses on few aspect(s) • This is “abstraction,” lifting out a part from the “whole fruit” • Concentration on select aspects facilitates new insights & knowledge, BUT…

11. Creation & Some PLI Principles – Scientific & Pre-scientific • Every-day (“pre-scientific”) experience is multi-aspectual, in which • We experience things as a whole (properties of all kinds at once) • All aspects are linked • Each science should enhance, not replace, pre-scientific experience • Theorizing must use pre-sci experience as its starting place • New findings must be integrated back into “the whole” • Replacing pre-scientific experience would reduce it to the science’s aspect(s), making that aspect(s) semi-divine • Example: In economics, “Fiscal Policy A” is theorized to stimulate GDP growth. A responsible, Christian attitude will remind us, though, to put that theory in the larger multi-aspectual context, evaluating it too in terms of justice, sustainability,…

12. Creation & Some PLI Principles–Statistical Inference • (I suggest that) Statistical Inference, a science, focuses on • certitudinal aspect (relating to trust, belief) and • quantitative aspect (how many, how much) • the aspects (economical, physical,…) of the sciences whose data Stats Inference analyzes • Example: • A biologist asks you to analyze her bacteria growth and death sample data. She wants to know how sure she can be that, in the population, the mean maximum number of live organisms occurs at some t within [5 hours, 7 hours] • Degree of sureness = certitudinal & quantitative • Mean max in [5,7] = quantitative & logical • Data = quantitative & biological • What statistical reasoning can answer the question & maintain proper relations between these aspects? • A task of Christian philosophy of statistical inference: identify proper relations between these aspects

13. Fall • Man, the caretaker (part of being in “God’s Image”), sinned, so his sin affects all creation – dis-harmony, death, disease,… • A primary type of sin: Idolatry (major OT & NT theme) • At root: Idolatry = Regarding something created as • Self-existent (Divine) • More important than other created things = semi-divine • The sole reason for other created things existing • “The” source of knowledge, happiness, fulfillment • Worthy of our undivided attention • Lovelace: “It is the paradox of earthly blessing that because of our own wayward hearts we can worship the gift rather than the giver” • Calvin: “All the things which make for the enriching of this present life are sacred gifts of God, but we spoil them by our misuse of them” • Man made to worship • Exorcise the demon; seven come to take its place • If we don’t worship God, we worship something else (Rom 1:25) • “Jesus is the only Master Who will not destroy you.”

14. Fall – What People Worship (Candidates for Idolatry) • Money • Sex • Drug abuse • Success at the job • One’s own gifts / profession / outlook • Self-expression / self-fulfillment • Logic / mathematical reasoning • … • Calvin: “The human heart is a factory of idols … Every one of us is, from his mother’s womb, expert in inventing idols.”

16. Fall & PLI Principles • The PLI shows: Many forms of idolatry in science amount to “reducing” parts of life to other parts • Sociology: GC Homans claimed all social principles could be explained by the principles of behavioral psychology & economics • Commercial Psychology: Certain advertising practices seem to increase consumer demand • However, is increased demand always good? • In each case, we are tempted to reduce functioning in certain aspects to scientific findings in other aspects

17. Reduction in Statistical Inference—Examples • BF Skinner: “When a statistician speaks of ‘experimental design,’ he means designing experiments he can analyze with his methods” • RA Fisher: “Statistical methods are essential to social studies, and it is principally by the aid of such methods that these studies may be raised to the rank of sciences” • “The statistician is the guardian of scientific rigor” These attitudes illustrate the general concept of idolatrous reduction in statistical inference

18. Humanism & Associated Overviews • PLI analyzes some non-Christian religions, including humanism, & their effects on science • Humanism’s central claim: Man is self-sufficient • 2 overviews of reality (“Ground-motives”) are consistent with humanism; each idolizes a self-sufficient area of humanness as the path to truth / prosperity / happiness • “Science Ground-motive:” Reduces meaning to logic / math • Truth founded only on logic / math; all else is “mere” opinion • A spirit of the Enlightenment / Modernism • “Personality Ground-motive:” Reduces meaning to self-expression / personal freedom • Universal truth may not exist; if it does, we cannot know it • In any case, what matters is personal truth • A spirit of the Romantic Period / Post-modernism (Rousseau’s “Noble Savage”) • I have tried to show: Each Ground-motive sets its own bounds for statistical schools-of-thought • We MAY have time for discussing

19. Humanism & Science Ground-motive—Example of Reduction in Statistical Inference • “P=0.03, so a relationship probably exists between eating Big Macs and developing cancer.” • Reduces certitudinal & biological functioning to quantitative functioning, as if the data alone could tell us what to believe (without consideration of the pre-scientific, such as prior plausibility of a relationship) about a biological law • We all know that stats rules do not justify such a statement; however, such statements are ubiquitous (textbooks, papers, software user manuals,…) ---WHY?--- • People follow what they love, not what they know (St Augustine of Hippo) A cause for celebration?: “Supreme Court finds Statistical Significance is not Necessary for Causation” (JSM Session 438 on Wednes) Not so fast!

20. Humanism & Personality Ground-motive—Example of Reduction in Statistical Inference • “P=0.08>0.05, but we can conclude H0 is false, since a p-value is subject to interpretation.” • Reduces certitudinal functioning to feeling (a function of the “sensory” aspect) • Before we calculated P, we knew it was subject to interpretation & would give us freedom to conclude what we wish about H • Calculating P has allowed us to take advantage of that, without explaining that we could have produced other, more restrictive (prescriptive) statistical results • These 2 examples (of the 2 GMs) pre-suppose idolatrous relations between quantitative, certitudinal & other aspects • Part of the Christian task: Identify Biblically-consistent relations between those aspects

21. Redemption & Some PLI Principles The Bible on Redemption • The fall did not cancel the Law & Prophets (Mt 5:17). Redemption is not the destruction of creation, but its fulfillment,renewal & restoration (Mt 17:11 & 19:28; Acts 3:21) • Bringing out the good in creation continues as part of loving God (Rom 8:19) • Christians will reign with Christ (2 Tim 2:12; Mt 19:28), the “new Adam” (Rom 5:12, 1 Cor 15:20) who came partly to fulfill the Cultural Mandate (Gen 1:26 & 2:15) PLI • “The redemption by Jesus Christ means the radical rebirth of our heart and must reveal itself in the whole of our temporal life” – H Dooyeweerd • Christ’s atonement, reconciliation & Spirit-filling restore creation (including science) to the right path (“already” & “not yet” tension)

22. Redemption & Some PLI Principles for Statistical Inference • Sketch of Biblically consistent statistical inference • Immersion (to the extent possible) in field of application & • Data collection / analysis & • Synthesis of all relevant considerations …all help to ensure… • Justifiable (quantitative) degrees of (certitudinal) beliefs • Maxims for statistical inference in a Humanist World • Positive: Statistical Inference should enhance pre-analytic experience, but not replace it. The data alone cannot indicate what to believe or what to do • Negative: Inference places limitations on beliefs. We are not free to believe whatever we want

23. Redemption, The PLI & Subjective Bayesian Inference • SB requires pre-analytic statements (“priors”) of strengths of belief • SB’s priors help ground statistical inference in the pre-scientific • SB’s results are natural enhancements of (not replacements for) the pre-scientific. Example: • Prob (11 <  < 15 | prior) = 0.2 • Prob (11 <  < 15 | prior, X=x) = 0.7 • SB’s results are about generalities (hypotheses / parameters) given data and the prior • Results meet definition of statistical inference directly • SB meets “maxims” mentioned earlier • Positive: SB claims that data should update pre-existent strengths of belief, but not create belief ex nihilo • Negative: SB’s results prescribe beliefs, conditional on the prior & on data • Therefore, consistency of SB with PLI seems possible (though not guaranteed)

24. Summary • Religious beliefs set bounds for overviews of reality, which in turn set bounds for scientific theories. • The PLI provides a Biblically consistent overview of reality which offers implications for science • God calls us (& we want to) worship Him alone, so that no aspects are reducible to others, yet all aspects are interconnected • Science should enhance pre-scientific experience, but not replace it • Humanism claims that man is self-sufficient. Two overviews of reality are consistent with humanism: • Science Ground-motive: Logic & math are the path to truth / reliability • Personality Ground-motive: Freedom & self-expression are the way to happiness / fulfillment • Some interpretations of statistical results are consistent with the Science Ground-motive; others are consistent with the Personality Ground-motive • Two principles (maxims) may guide statistical inference in cohering with the PLI and avoiding some humanist reductions

25. Suggested Reading • Roy Clouser, “Is There a Christian View of Everything From Soup to Nuts?” • Lecture delivered at Dordt, 2002 • http://www.dordt.edu/publications/pro_rege/crcpi/93211.pdf • Roy Clouser, Myth of Religious Neutrality • Herman Dooyeweerd, Roots of Western Culture • http://www.reformationalpublishingproject.com/pdf_books/Scanned_Books_PDF/RootsOfWesternCulture.pdf • Andrew Hartley, Christian and Humanist Foundations for Statistical Inference • Robert Knudsen, “Dooyeweerd’s doctrine of science” • http://www.asa3.org/ASA/PSCF/1979/JASA12-79Knudsen.html • Short but dense

26. Parting thoughts • Christian philosophies other than PLI may lead to other implications for statistics • Catholic (John Paul II, G.K. Chesterton…) • Eccl 3:1 – There is a time for everything, and a season for every activity under the sun. • 1 Tim 4:4 – For everything God created is good, and nothing is to be rejected if it is received with thanksgiving • Satisfaction in God reduces our impulse to idolize, e.g., logic/math or our feelings/preferences

27. Contact Information Andrew M Hartley, PhD Associate Statistical Science Director, PPD 910-558-7147, khahstats@yahoo.com BACKUP MATERIAL (TIME PERMITTING)…

28. Definition of Statistical Inference • Statements about generalities / hypotheses, based on particulars / data • “What should we (I) believe about H given x?” • Inferences should serve decision-making (James 2:14 – faith and works) • Therefore, conclusions must be probabilities concerning those generalities, OR, at least inform us about such probabilities • Dutch Book: In the presence of uncertainty, decisions using systems other than probabilities of hypotheses cannot do better than (in terms of expected gain) systems using those probabilities

29. Some Popular Statistical Paradigms • Subjective Bayesianism • Direct Frequentism • Indirect Frequentism Covered in following slides

30. Frequentism • Results are frequency statements about data given hypotheses or parameter values • Example (confidence intervals): If we repeated the experiment many times, about 95% of the 95% Conf Intervals would contain  • Do not meet definition of statistical inference directly • “Inferential” implications are • Imposed (invented) • Open to interpretation, to suit the preferences of the audience or the analyst • Disraeli: Lies, damned lies & statistics • Augustine: We follow not what we know, but what we love

31. Direct Frequentism: Results indicate what to believe concerning parameters • Examples • “p-value = Prob (H | x)” • (“transposition of conditioning”) • “p-value = probability results are due to chance alone” • Thinkers/Adherents: RA Fisher (earlier), Guilford, SAS Inst., US Federal Register, US National Cancer Institute, many introductory stats books (Huntsberger, Ware, Maksoudian, Hogg/Tanis, Mendenhall, Kocher/Zurakowski) • Plays to Humanist Science ground-motive • Difficult to align with PLI

32. More examples of Science Ground-motive & Stats Inference • “P=0.03, so a relationship exists between eating Big Macs and developing cancer.” • Reduces certitudinal functioning to quantitative functioning • “P=0.03, so a significant relationship exists between eating Big Macs and developing cancer.” • Reduces certitudinal functioning to quantitative functioning AND tries to hide it by pretending “statistical significance” =“practical significance” • “P=0.03, so we should act as if H is false.” • Reduces functioning in the aspect of application to quantitative functioning, as if the data alone could tell us what to (without consideration of prior plausibility of H, or of utilities) • “In hypothesis testing, Method B is more powerful than Method A, so we should use Method B.” • Reduces functioning in the aspect of application to quantitative functioning, as we should reject a false H0no matter how close it is to being true

33. Indirect Frequentism: Scientist decides what the results suggest about parameters • Example: “p-value = 0.13, and before the experiment, I strongly believed H0, so H0 is still plausible.” • Thinkers: RA Fisher (later), Jacob Cohen, Yates • Fisher: “We have the duty of formulating, of summarizing, and of communicating our conclusions, in intelligible form, in recognition of the right of other free minds to utilize them in making their own decisions.” • Plays to Humanist Personality ground-motive • Difficult to align with PLI

34. Other inferential interpretations of frequentist results • Do they exist? • Can we show them consistent with the PLI? • Can we bring them into consistency?

35. Warnings from Other Disciplines • Failures to identify / elucidate Christian approaches have allowed evil to prevail • Slavery in USA • Libertarianism / Individualism • Abuses of industrial labor • Populism • “Educationism” • Can statistics be different?

36. Might a Christian approach to statistical inference have mitigated / avoided • Transposition of Conditioning? • Irrelevant statistical results that can be re-interpreted to suit the desires of the powerful? • Arbitrary standards such as  = 0.05? • Misleading / confusing terminology such as “statistically significant”?