Real Statistics: Introduction
After the dramatic failure of economists to predict the Global Financial Crisis, Krugman said that “the profession as a whole went astray, because they mistook the beauty of mathematics for truth” (see Quotes Critical of Economics). Many people have independently arrived at similar conclusions – current educational methods train students using mathematical theories not connected to the real world, and fail to teach them how these theories work to resolve real world problems. For one example, see “Memorial: David Freedman”, which describes how David started out with heavily mathematical research, and eventually came to realize that the mathematical assumption on which such research was based did not hold in the real world. He gradually transitioned to a radically different approach, which put real worlds problem first, and statistical theories required to solve them second. His pathbreaking undergraduate textbook on Statistics focuses on real world uses of statistics. Furthermore, this textbook does not contain a single equation, because Freedman believed that mathematics distracts students, and prevents them from thinking about concepts. Personally, I also followed a similar intellectual trajectory. After writing the heavily theoretical and mathematical advanced graduate textbook “Statistical Foundations of Econometric Techniques”, I came to the realization that real world econometrics required far more intuitive and direct approaches to the data. I have described this transition in “My Journey from Theory to Reality”.
Currently, I am process of creating a new approach to Statistics, based on the foundations of an Islamic approach to knowledge. Islam differentiates strongly between useful knowledge and useless knowledge. In teaching statistical theory, we must be careful to focus on useful knowledge, which would be beneficial to mankind. This requires ensuring that the theories we teach have useful applications in the real world. Amazingly, after looking deeply into the question of what portions of statistics can be applied, I came to the conclusion that a lot of the theories we teach have no direct application to reality. I often use the example of studying the complexities of the car engine, while failing to learn how to drive. These two are entirely different skills. Similarly, learning the mathematical proofs of theoretical statistics has very little to do with how statistics is used to solve real world problems. Over the past fifteen years, I have been developing a new approach to statistics and econometrics based on trying to teach students how to drive, rather then teaching them how the car engine is built. This methodology has been extremely successful. I have been able to bypass huge amounts theory that I had to learn myself, and I have been able to get my students to the frontiers of knowledge far more quickly and efficiently. I have learned that we need to reconstruct the discipline from the foundations. Even the basic definition of probability as a limiting frequency is highly unsatisfactory. Students have direct experience of probability in the form of tossing coins, but the definitions and theories we teach seem to have no relation to this experience.
The most fundamental concept in probability and statistics is that of the distribution of a random variable. Many authors have complained that even after many courses on the subject, the students do not understand this basic concept. After thinking about this for a long time, I have come to the conclusion that this is our fault as teachers. There are four different concepts which are closely related, and we mix them all up, causing confusion for ourselves, and for our students. I am now creating a set of posts & lectures meant to clarify this confusion. These lectures would form the introduction and the basis for the planned course on Real Statistics: An Islamic Approach (RSIA). The first of the four concepts is most elementary and very easy to understand, because it does not involve any probability. It deal directly with groups of people and proportions of these groups which fall into different categories. This concept is explained in the previous post on “Understanding Statistical Distributions 1”. After explaining this concept, I have written up a follow-up post on “PP2: Building Confidence”. This provides a short summary of the concept, and provides a detailed discussion of the Pedagogical Principles we need to use, in order to improve student learning outcomes. In particular, we need to build confidence of the students that they can master the subject. Without this confidence, students are reluctant to put in the efforts required to try to understand complicated concepts. In later posts, I will discuss the second, third, and fourth type of distribution that we need to understand and use in statistical theory.
To conclude this post, I will briefly describe an initial draft of the first chapter for the planned new textbook on real statistics. I have been using and developing this new approach over the past ten years, and this lecture is the introductory lecture I have been using. It is broken into four parts, linked below:
- RSIA01: An Islamic Approach to Knowledge – This introductory section explains the many ways in which an Islamic approach knowledge differs radically from the Western approach we have all learned in the process of our own education. It explains how Islam place extreme emphasis on knowledge, comparing the ink of the scholars to the blood the martyrs. Because it is central to Islam, there are large numbers of Islamic rules and manners related to the process of teaching and learning. These rules are very different from the Western approach.
- RSIA02: The Value of Knowledge – The second portion explains how Islamic emphasis on knowledge led Muslims to put in great efforts to acquire knowledge. It was this thirst for knowledge which led the Muslims to Leadership, and created a civilization that dazzled the World for a thousand years.
- RSIA03: Training the Heart – The third portion explains the difference between useful and useless knowledge. Useful knowledge is for the benefit of mankind and enters the heart. Muslims are not allowed to be neutral and detached. Rather, the love of God, drives them to serve the creation of God, using the knowledge and strength they have been given.
- RSIA04: The Struggle for Knowledge – Instead of neutral and detached observation, we must struggle to change the world for the better. Knowledge will be generated in the process of struggle. Islam provides us with many guidelines regarding how we are to struggle to create good, and prohibit the evil. This last and final portion also contains action-exercises for students of “Real Statistics”, to engage them in real world applications of the material under study.
The new textbook that I am planning to write (“Real Statistics: An Islamic Approach”) will have in introductory chapter based on the materials above, which describes the underlying methodology and ideas which led to the creation of the course. The STATISTICS itself will begin with the description of the four types of distributions which form the foundation and basis of the discipline. The first type is the “Real Distribution” which has been explained in the previous post on “Understanding Statistical Distributions 1”. This shows how basic probabilities can be understood simply as percentages, within real world populations – concepts which are immediately intuitively understood, and form part of the life experiences of students. This allows much clearer and deeper understanding of probability than standard axiomatic approaches. A follow-up post on “PP2: Building Confidence” provides a short summary of the concept, and provides a detailed discussion of the Pedagogical Principles we need to use, in order to improve student learning outcomes. An Islamic approach requires us to engage with the students, find out about their progress, and help them take the next step in their personal journey towards knowledge. It does NOT involve taking a pre-packaged, canned, set of ideas and force-feeding it to all students, regardless of their interests and capabilities. In this connection, see my posts on “Teaching Fish to Fly” and “Brainwashing VS Meta-Level Analysis” for more differences between Islamic and Western approaches to education. Later posts in this sequence will introduce the more complex concepts of distribution.