This second part of the Talk at ISOSS by Dr. Asad Zaman is continuation to the discussion on nature of real statistics and how it can be approached Islamically.

**Inversion Methodology**

Real statistics is founded on inversion principle that requires to reverse the general teaching methodology by putting practice first and theory second. The first ten lectures of this course are developed in the same manner.

David Freedman a distinguished statistician, has also used this methodology. His intellectual trajectory is like mine, both of us have studied heavy mathematical and theoretical statistics with no concern to numbers. He realized that working with real issues is radically different. He faced questions about the usefulness of statistical theories in his undergraduate classes. It motivated him to address this issue in his pathbreaking book “Statistics”. He studied real problems without using mathematical formulas and equations. He observed that some background knowledge is required to see effectiveness of polio vaccine. Polio has a rare and highly fluctuating occurrence frequency, so a large sample is required for significant estimates. Instead of discussing the sampling errors, if students have real data they will better observe and understand if incidence of polio is reduced after using medicine or not. There is no complicated theory, formula or equation but only inclusion of real aspects.

In my textbook I adopted similar approach using Household Integrated Expenditure Survey (HIES) data of a village in Attock district. In a sample of 100 persons 99 people have Rs. 4000 income and one is millionaire. Average income of them is more than Rs. 10,000 but it represents none from this sample. As 99 people have income much lower than the average and one person has far higher income. Here, median or mode are meaningful measures and accurately represent average income. Averaging is studied by many but meaning of numbers is clear when we use real examples. This approach has created very good outcomes for students by developing intuitive and hands on understanding to the problems.

**Effects of Inversion: Focus on Real-World Application**

While compiling the textbook I realized that several of passionately taught statistical theories have no practical uses. For instance, I could not find any real illustration of CORE theorem (Gauss-Markov theorem that states regression estimators are BLUE-best, linear, unbiased estimates). There are several supposedly important yet practically useless theories even from my field of specialization. For example, Stein and Shrinkage estimations are based on assumptions of equal variation therefore, not applicable to heterogeneity. But all the real world problems have heterogeneity. There is no theory developed for latter cases, because derivation of elegant formulas is not possible, this can only be solved by hands on simulations methods and rule of thumbs. Approximations are rough and cannot be verified therefore, these methods are not published even as journal articles. Better solutions from approximate methods in real cases refers that inversion methodology is ultimately beneficial. It increases the interest and practical knowledge of students and accomplishes the valuable task to solve real problems.

**Useful Knowledge enters heart !**

Useful knowledge enters heart of the learners. To abandon theory/practice barrier we must see the real world that involves heart. Consider wage discrimination that affects our lives, can we remain neutral about this? If something is affecting our life, there comes role of heart and morality. That is required to know the harms and benefits of something. To understand the concept of secular knowledge we see how it has emerged. Till 17^{th} century due to religious dominance in Europe, knowledge of every kind was considered within religious domain. Breakout of civil wars in Catholics and Protestants made it a historical necessity to develop a knowledge that is agreed upon by all, this suit is still followed. In a strong western society religion is a private matter with God. It is awkward to discuss religion in casual talk given that it creates disputes.

Islam emphasize to seek useful knowledge that is subject to the purpose and requires to discuss the goals of life. Otherwise we cannot differentiate useful knowledge from useless. In pursuit of Islamic approach, I learned many things. As if we do not talk to a student sitting in the class and start teaching the book by discussing the data and formulas. We follow current standards of teaching, that describes a student to sit in a class only to pass the course. He has no interest to study if a concept is useful, but only if it will be asked in exam. Acquisition of such knowledge is required to pass the exam that is necessary to get a degree, secure a job and make money. If we do not discuss life goals it is acknowledgment to the money making as sole objective.

Purpose of education in capitalist mode of production is to develop human resources not human beings. It needs standardized parts of a machine that keep it running and making money for itself and its owners. Developing human being actually interrupts this pursuit therefore, students are taught that they are marketable commodities that are priced according to their worth. In this approach we must teach about the value of humans in Islam. Humans are precious and best of all creations, and value of one life is equivalent to whole humanity. Therefore, they must learn to be humans not resources. It seems conflicting to teach humanity within subjects like statistics and requires understanding the connection of both. Prophet Muhammad (SAW) has described a person like a mine with hidden treasures. A student is not aware of this, his potential is realized only by a teacher who recognizes it. As a human can render even to the lowest of the low, it becomes the responsibility of a teacher to shape him in whatever form. It is his duty to make this belief in student’s heart that he is valuable and can become whatever he wants. There are big opportunities by Allah but if we only want to earn a living, we will merely sustain this goal.

To read 1st part of this talk click here.

For more discussion on teaching intentions see Teaching Statistics as an act of worship. For detailed discussion on Nature of Useful Knowledge