Introduction to Statistics: An Islamic Approach

Style of course patterned on MOOC’s

designed by

Dr. Asad Zaman

GOALS: At the most fundamental level, the goal of this course is to demonstrate practically the failure of the secular idea that there are some areas of knowledge which are independent of religion. We demonstrate that even a purely technical subject like statistics is tremendously improved if we adopt the educational methodology of Islam.

There are two intended audiences for this course. Students can directly listen to and watch the lectures, and then do the associated lab. They have text, transcripts and other supplementary supporting materials available to study in case they need further help in understanding.

My main goal however is to reach TEACHERS of statistics in the Muslim World. The course materials are designed to provide complete support, so that in principle, the teacher can run a plug and play course based on ten lectures and ten associated labs. However, there are a lot of different ways that the teacher can inject his/her input into the course, both to get a feeling of ownership and also to adapt it to local concerns and conditions as well as student capabilities and interests. This is the first unit, which deals entirely with descriptive statistics. There is no theory, only methods of looking at and summarizing the data. Later units (planned) will introduce the necessary ideas of probability and statistics.

This course incorporates a VERY large number of innovations and new ideas, in terms of substance, methodology, as well as pedagogical style. Some of the main innovations are briefly discussed below.

Innovations and Features:

1. How does an Islamic approach make any difference to teaching a purely objective, mathematical and scientific subject? first lecture is devoted entirely to answering this question. The prophet Mohammad S.A.W. was sent as a teacher, and the teachings of Islam contain a unique approach to teaching and studying. This approach is fundamentally different from western approaches currently in use everywhere. There are so many differences that one lecture just barely provides an outline, and much detail is left out. Perhaps the most fundamental difference occurs in the theory of knowledge. Western theories reject the unseen, take observations and logic as fundamental, and reject distinction between useful and useless knowledge. Islam requires faith in the unseen, takes the teaching of Islam as the most fundamental and basic source of knowledge, and differentiates between useful and useless knowledge. The goal of the course is to focus on useful portions of statistical knowledge, and to reject and ignore the useless ones, while highlighting why they are useless or harmful.

2. One of the key ideas of the positivist approach to knowledge which underlies current statistical courses is that FACTS are everything and OPINIONS are not knowledge. This idea has percolated into common language in the form “Just give me the facts – (don’t bother me with your subjective opinions). This means that data – objective, concrete, factual – is all important. The first lecture shows that a lot of data is constructed on the basis of subjective decisions. So what look like “facts” are not so factual. Index numbers are used to achieve comparability of different types of series, but there are a lot of arbitrary assumptions required to construct index numbers. Each of these assumptions represents an opinion about relative worth of different factors. Thus “facts” and “opinions” cannot be separated as cleanly as assumed in western methodology. The course highlights all of the different ways that opinions in injected into fact while concealing this reality.

3. The western idea of specialization has led to fragmentation of knowledge. The statisticians studies only the numbers and applies methods from theoretical statistics – the meaning of the numbers and the interpretation of statistical results is left to the field expert. This is an extremely harmful division. Throughout the course we show that right statistical analysis depends crucially on the meaning of the numbers. With exactly the same set of numbers, analysis may be different if these numbers are test scores on exams, and if they are red cell counts. So the statistician cannot afford to be ignorant about the meaning of the numbers, and must learn them from the field expert.

4. This also leads to the crucial distinction between useful and useless knowledge. It is the job of the teacher to show how a given statistical technique is used in the field, and how it leads to the production of valid and useful knowledge. What are the conditions under which the technique works, and when can it be expected to fail. Because of fragmentation, teachers themselves have not been taught about these issues in their courses. This course introduces each technique in the context of a genuine real world example – by genuine, I mean that conventional texts also use real data, but do so superficially. Any data set will do, since they deal only with the numbers. In this text, we pay attention to the meaning of the statistical analysis in context of the real world example, and assess whether or not the results are plausible.

5. Traditional texts assign a central place to the normal distribution, either implicitly or explicitly. It is assumed, without mention, that data sets will be normally distributed, and statistical techniques are developed and discussed with this background assumption. This is because statistics was developed in the pre-computer era, where non-normal data sets required analysis beyond the computational capabilities available. However, this assumption has become embedded deeply in statistical thought and texts. This is why the MEAN and the STANDARD DEVIATION play a central role in conventional textbooks. These are the best estimates of central tendency and dispersion for a normally distributed data set, BUT ARE VERY POOR if the data is not normal. In practice, most data sets we encounter in the real world are NOT normal. Taking this into account, the best measures to use are the MEDIAN and the IQR, and these are given central place in this textbook.The text also focuses on many techniques which are important and required for non-normal distributions, and irrelevant distractions for normal distributions.


6. The structure of the course is currently TEN lectures. Each lecture has an associate LAB session, which requires each student to use EXCEL on a computer to replicate calculations performed within the lecture. Thus a course based on this material will require twenty sessions (Lecture + Lab) and also additional work outside of classrooms. The lecture can be watched as a movie on the internet. It is also available as a powerpoint presentation with audio files for each slide, which can be downloaded and played by students and teachers. It is recommended that teachers watch the lecture together with students. If students have any questions, these can be answered by the teacher. If some issue is generally confusing for all, it is requested that teachers should inform me. Because of the MODULARITY of the course, it is EASY to insert additional slides and explanations into the lecture. Alternatively, a small subunit on a particular concept designed to clarify the issue may be designed. Indeed, one of the ideas of the course is to start with this set of lectures as a base, and to continuously improve it in light of experiences of teachers.

7. The lectures focus on explaining concepts; there is very little in the way of formulae or calculations. There is a text for each lecture which explains the concepts in greater detail, and provides the calculations and the formulae. This is like the traditional textbook. But the real learning should take place in the LAB where the student actually replicates all the calculations required in the lecture on his own. Thus there is a very strong learning by doing component in the course.

8. There is also a TRANSCRIPT of the audio slides for each lecture. This means that the teacher can run the presentation on his own, and just read the transcript (instead of play the audio files). This allows for several different ways that the teacher can provided additional input. First, the teacher can use any language, simply translation the English text into relevant language. Secondly, the teacher can provide additional explanations and detail while discussing a slide. Thirdly, the teacher can modify slides and examples to fit local context. Many examples taken using Pakistani data sets could be modified to use local data sets, to illustrate the same concepts.

9. Some teachers who have used preliminary versions of this material have found the lack of theory disturbing. A lot of time (20 classes) is taken going over basic concepts which are often covered in a very few lectures (3-5 classes) in usual courses. It has been my experience that students do not understand the fundamental ideas of basic courses. They do not have intuitive understanding. Developing a solid grounding in basic data analysis is essential pre-requisite to more advanced studies. Quite often a structure of sophisticated and complex techniques built upon weak foundations proves unstable. Students have a very vague idea of what is being taught, and basically learn to imitate like parrots without developing understanding. More advanced material is under development, and will be made available later.