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Introductory Post

All wisdom is rooted in the Quran.. The Noor of Allah is reflected in the hearts of all human beings. Anyone anywhere who succeeds in purifying his or her her heart can find the truth. – Dr Asad Zaman

Assalamo Alaikum

Welcome to our online course on Real Statistics. This course is based on principles I have learned through a lifetime of experience in studying and teaching. It is my hope that this course will initiate a new model for our approach to education throughout the Islamic World. Knowledge is the greatest of the treasures of Allah Subhanahu wa T’aala, and learning is the most exciting of all life-experiences/adventures for which we have been created.

This online course on “Real Statistics: An Islamic approach” is an attempt to reclaim, recapture and recreate our rich Islamic Intellectual heritage. In the process of the “Theft of History”, author Jack Goody explains how Europeans borrowed ideas from other civilizations and claimed them for their own. For instance, the supposedly revolutionary Copernicus was in fact just a copyist of Muslim astronomers – see “Is Science Western in Origin?” by CK Raju.

A heavy set of tasks has been assigned to the groups for the first week. There are three/four tasks of a technical nature, to setup various mailing lists and blog memberships, for use in conducting discussions of the materials in this course. There are three to four main readings. Finally, there are three main pedagogical principles, to learn and to use for the learning process in this course, and in all courses. Details of what needs to be done are specified in outline on the main page of the course website: Real Statistics {Shortlink: bit.do/azrs0}

If there is any confusion about what needs to be done, or how to do it, group should discuss among themselves – it is likely that at least one person in the group has clarity. If no one has clarity, then the group leader should contact me.

Dr. Asad Zaman, Vice Chancellor
Pakistan Institute of Development Economics

Understanding Statistical Distributions: A Summary and Response

Summary

There is a crisis in the understanding of probability that arose because of a mistaken view that was accepted by the economist community. This view was that all uncertainty could be describe with the aid of probabilistic models. The view that was left behind was that of Keynes and Knight who distinguished ordinary risk from a “radical uncertainty” that they saw as “completely beyond” comprehension and analysis by human beings.

The concept of a statistical distribution is a fundamental one but is often insufficiently understood. There are four types of distributions. The first type is the only real type that exists in “reality” as we ordinarily perceive it. The others are only imaginary and do not “exist” in the way that the first one does. This subtle difference between the different types is a source of confusion.

The first type of distribution is a way to understand the characteristics of real, countable population that could be human beings or any other reasonable set of objects in the universe. Human beings live in a finite universe, all real populations are finite and the first real type of distribution is concrete and requires no rules of probability. The core concept behind real distributions is a characteristic function that assigns to each member of the population a category.

Percentage as Probability

The distribution of this function can be defined in terms of percentages – which is an analogous concept to probability. The distribution of the function is the list of percentages of members that belong to each category in the population.

Idealized Distributions are Approximations of Reality

Not the other way round! I was always taught that idealised, mathematical notions were perfect and reality was an approximation.

Real distributions enable us to study the characteristics of the members of a population. The characteristics can be defined by the analyst in any way suitable to his particular goals of the research. The distribution belongs to the characteristic. An example of a characteristic is gender. The characteristic function assigns to each member of the population, a particular category and the set of categories are induced by the characteristic in question. For gender, we have a binary set containing two elements each corresponding to male and female respectively.

Every function F which defines a characteristic for each member of the population has a distribution. Note that the set of possible outcomes of F must be finite, because the population itself is finite. The distribution of the function F is the just the percentage of members of the population which belong to the categories created by the outcomes of F. 

Response

Disconnection

The reason why mathematics classes from the beginning of school to doctoral level studies feel like we are seeing through a fog is because the approach does not begin with reality as we perceive it. In the Quran, the exhortation that is made to the believers is to look at the sky, the trees, the animals (and their anatomies – Surah Nahl for example), the bees, the water, the mountains and to think. Real learning begins with learning to reflect perceived reality and learning to wonder about the creation of Allah. Whereas in the modern western classroom, learning begins and ends with learning to manipulate symbols without learning what they mean. This alteration and sometimes annihilation of meaning has devastating consequences because it alienates most of the young people from formal learning and leads many other to believe that meaning does not actually exist.

Pedagogical Principles

It is not sufficient to simply “cover” all the material and “explain it well.” A pedagogical approach must take into account the experience of the student both inside and beyond the classroom. Teaching too many things at once causes anxiety and teaching too little causes disinterest. Teaching for other than sake of Allah causes regret, disappointment and even depression in the long run. We learn what we do not know when it is taught in terms of what we do know.

Is Scientific Methodology Axiomatic? A Summary and Response

This is continuing from Dr. Zaman’s comments on my post about certain observations on the introductory chapter in the Econometrics textbook by Greene. In the post, I had raised a question regarding a footnote in the textbook where Greene mentions that modern econometric analysis begins with “behavioural axioms.” This means that there are certain “axiomatic truths” about human behaviour that we take as given before we propose an econometric model. This seems contrary to the scientific principle of believing in nothing without empirical evidence. In this regard, I read Is Scientific Methodology Axiomatic? on the WEA Pedagogy blog. Here is a summary/repose of that post:

Is Scientific Methodology Axiomatic? A Summary

The Axiomatic Methodology starts with some simple postulates and then derives complex theorems using logic. A well known example of the use of the axiomatic method is in Euclidean geometry. The theorems of Euclidean geometry constitute what may be called “analytic truths” which do not rely on empirical evidence to sustain a notion of verity. They hold true based on the foundations of the original axiomatic postulates and the framework of logic without any reference to the real world.

There is common misconception in the modern world that scientific methodology is axiomatic. The subject of science is the real world as perceivable by human beings as opposed to the conceptual world of Euclidean geometry and mathematics. For a scientific theory to emerge, we must construct a mapping of axiomatic truths to the real world. For example, we might map the surface of the oceans to the geometry of the plane to the real world and attempt to navigate from point A to point B using the Pythagoras theorem. However, beyond small distances, our mapping will be invalid and our navigation will fail. This will require a new mapping that sufficiently accounts for the curved surface of the oceans. A “scientific theory” is an assertion regarding the nature of the real world that arises on the basis of a successful mapping. This theory is a “synthetic truth” which means that it needs empirical validation. Synthetic truths do not lend themselves to “proof” in the way that analytic truths do. In fact, synthetic truths can never be proven. They can only dominate the intellectual discourse until a reality is encountered which they do not explain or to which they do not apply. At this time, a new mapping must be constructed and a new synthetic truth must emerge. Any truth that can be replaced by a new one is not absolute.

Is Scientific Methodology Axiomatic? A Response

I will recall the footnote in question from Greene to motivate my response.

Modern economists are rarely this confident about their theories. More contemporary applications generally begin from first principles and behavioral axioms, rather than simple observation.

From Econometric Analysis by William Greene, Fifth Edition, pp 2

The suggestion seems to be that contemporary applications of econometrics follow the axiomatic method. The analyst postulates certain “universal truths” about human behaviour and proposes a model using them as a foundation. The problem with this idea is that human beings do not behave deterministically like material objects. Their behaviour is subject to historical, social and cultural context. It is often paradoxical and self-contradictory and changes without any apparent reason. It is impossible to formulate a set of axioms about human behaviour that can be taken as “true” in the way that one can formulate axioms about conceptual entities like numbers, points, lines, and surfaces.

If econometrics cannot follow an axiomatic approach, then perhaps it can go the way of science and work through mapping human behaviour to axiomatic truths. This is confounded by the fact that human behaviour is motivated by many “unobservables” which defy measurement. This makes empirical validation of mappings very difficult. For example, we might construct a model of how human beings value clean air and then map it to a hedonic pricing model but how do we measure the notion of “value?” People have tried to measure how people value clean air by the amount they are willing to pay for it. This may be some indication of how much they value clean air but in no way does it constitutes a “theory of human behaviour” in the scientific sense. It cannot be proven. In fact, the empirical evidence presented is only evidence for the validity of the author’s model, not for the behaviour of people. In order to arrive to useful economic policies you would need to supplement this knowledge with many other things like a context-specific understanding of the reasons why people value clean air and how their social, economic and cultural situation affects their decision.

Textbook Analysis: Econometric Analysis by William Greene

How exactly are generations of really zaheen students indoctrinated through graduate programs in economics? How are obviously questionable ideas internalized by the best of the best at the best schools across the world? Many economists admit that there is something seriously wrong with the theories and ideas being taught and yet they continue to teach them. So where exactly does it go wrong? From my experience, it is usually at the beginning. Also, the indoctrination occurs sometimes as pedagogical oversight and not as deliberate deception. The particular oversight that occurs most frequently is the glossing over of the critically important introductory part of the textbook where the assumptions, history and context of the subject are introduced. What happens as a result is that ideas that were heavily debated and only believed by a small group of people at the time of inception are taught if they were “true without question” to large groups of students and the further away in time we get from the origin of the particular ideas in question, the more “generally acceptable” they become. I’ve had two different experiences at the beginning of courses in classrooms where I was attending lectures.

  1. The teacher spends time at the beginning of the course explaining and clarifying the assumptions, the limits and the scope of the science of neo-classical economics and then moves on to the quantitative techniques and never returns.
  2. The teacher skips the introduction and context goes directly to the quantitative techniques.

The second scenario is more common. A case in point is the current class I am taking in econometric methods. The teacher is using the textbook by William Greene and began teaching somewhere in the middle of chapter 2 although the precious little context and background that is included in the textbook is in chapter 1. I have made a practice of reading introductions to textbooks on my own and writing small responses to them. This helps me to stay focused during lectures and avoid falling into despair. Here is my response to the introduction by Greene. I have tried to frame it by including ideas taught during the lecture 1,2 and 3 of this course.

Econometric Analysis by William Greene: Response to Chapter 1

In the introduction, Greene outlines how a linear regression is brought into being. He says that “econometric analysis will usually begin with a statement of a theoretical proposition.” He then offers the following excerpt from Keynes’s (1936) General Theory of Employment, Interest and Money.

We shall therefore define what we shall call the propensity to consume as the functional relationship f between X, a given level of income and C, the expenditure on consumption out of the level of income, so that C = f ( X ).The amount that the community spends on consumption depends (i) partly onthe amount of its income, (ii) partly on other objective attendant circumstances,and (iii) partly on the subjective needs and the psychological propensities and habits of the individuals composing it. The fundamental psychological law upon which we are entitled to depend with great confidence, both a priori from our knowledge of human nature and from the detailed facts of experience, is that men are disposed, as a rule and on the average, to increase their consumption as their income increases, but not by as much as the increase in their income.

From General Theory of Employment, Interest and Money by John Maynard Keynes, 1936

The particular theoretical proposition that Keynes is making in this excerpt is that there exists a relationship between the level of income of an individual or society and their expenditure on consumption. He calls this relationship the “propensity to consume.” Keynes admits in part (iii) that this depends, at least partially, on the subjective attitudes and propensities of particular people. In this, Keynes is correct but he nullifies the effect of this admission of subjectivity in the very next line by asserting, without proof, what he calls a “fundamental psychological law” which states that men are disposed to increase their consumption with their income. This is a subjective judgment that belongs to Keynes and Keynes alone. He says that he knows this “a priori” from his “knowledge of human nature and from the detailed facts of experience.” It is his experience and the “facts” that he has gathered through it that is the basis of the theoretical proposition about propensities to consume. The entire exercise is based on this subjective judgment and all “objective” statements that are later numerically actualized through the regression are null and void if we separate them from this subjective foundation. The fact that Keynes does manage to demonstrate the “law” for the particular sample does not prove it in general. Counterexamples to this “law” can easily be found by casually observing the spending habits of even a small randomly chosen group of people. Any generalization to a larger group is rhetorical and the regression results are a part of that rhetorical device.

In a footnote to this, Greene adds the following:

Modern economists are rarely this confident about their theories. More con-temporary applications generally begin from first principles and behavioral axioms, rather than simple observation.

From Econometric Analysis by William Greene, Fifth Edition, pp 2

The first statement is saying that modern economists doubt themselves more than Keynes and this, by the Cartesian ideal of doubt as intellectual virtue, is suggesting that modern economists apply more rigor in testing their theoretical propositions. This maybe true and is definitely an improvement but it changes nothing about the way regressions work. They begin with subjective assertions, beliefs or conjectures of the analyst. While the results of the regressions can be shown to be ”mathematically correct,” they cannot be used to show the validity or the verity of the theoretical proposition that preceded the regression.

The second statement states that modern applications do not rely, unlike Keynes, on subjective observations but are based on axiomatic ”truths” or ”first principles.” This is a statement with enormous implications so it is puzzling that Greene chose a footnote as its resting place. What the statement seems to be saying is that there are such things as”first principles” or ”behavioral axioms” that must be taken to be true without empiricalevidence and must serve as starting points for the development of a statistical device thatwill provide empirical evidence. Is it not an axiom of modern science that nothing is takento be true without empirical evidence? If we have to violate this axiom to develop thestatistical device that will provide the empirical evidence needed to uphold the axiom, weseem to have a contradiction.

Week ONE Tasks

Dear Shraf Group Members

Reminder: Punctuality adds more to competencies and learning capabilities. Tasks for the first week has been conveyed by Dr Asad Zaman in an email . Following is the to-do list for the first week.

Technical Tasks

Readings and Building the basics of Real Statistics :

Readings: MAIN Readings for 28th July to 3rd Aug

Lecture

  • Real Statistics (1/4) Fundamentals of an Islamic Approach: Some essential differences between Islamic approach to education and Western approaches.
  • Real Statistics (2/4) Teaching Statistics as an Act of Worship: To teach statistics as an act of worship, we must acquire useful knowledge for the benefit of the creation of God, out of the love of God.
  • Real Statistics (3/4) Statistics as Rhetoric: Western statistics seems to be about analysis of numbers, but it really is a method of making arguments using numbers to conceal subjective value judgments. Considering arguments in the real world context, and revealing the value judgments, makes the rhetorical aspect clear, and prevents the use of statistics for deception.
  • Real Statistics (4/4) Comparing Fictional Numbers: {to be written up]

Note: It is required to make notes and discuss points for understanding and future teaching.

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