There are many pedagogical innovations incorporated in these lectures. Among these, there are THREE main differences, and many minor ones. A more complete list of features is given HERE -- Teachers planning to use these materials should definitely read these features.

An outline is attached at the bottom of the page.

The first lecture (L01) is a general introduction to the Islamic approach to knowledge. The next 8 lectures (L02 to L09) form the first unit, which is an introduction to descriptive statistics, but sets the ideas in a format very different from conventional statistics courses.

1. It is assumed that most data will NOT be normally distributed. This makes the mean and SD very bad measures of location and dispersion. Better alternatives are median and IQR. Many other changes in teaching methodology become necessary when we deal with data which is not normally distributed.

2. We treat data as providing CLUES to reality, instead of being the final determinant. Thus data analysis may start by looking at numbers, but must always proceed to looking at the real world implications. Interpretation of statistics is strongly related to the real world situations which generate the numbers. This link is ignored in conventional texts and is emphasized in our treatment in this text.

3. The main idea of the course is that statistics is a branch of RHETORIC. We learn how to make arguments using data and data analysis. There are no final and conclusive answers available from the data. One must ALWAYS add some subjective elements to create an interpretation of the data analyis. By focusing on these subjective elements and by changing them, we can substantially alter the meanings of any given data analysis.

THERE ARE TWO WAYS TO WATCH/LISTEN to the lectures.

Easy way, recommended. Download and install Open Office. Open the file Lxx*.odp in Open Office and just play the slides, as long as the MP3 files are in the same folder, the presentation will automatically go slide by slide and play the accompanying sound file for each slide.

More hassle, but not difficult. Download the PPT presentation and the accompanying slides. Go through the presentation manually, For each slide, play the accompanying sound file which is clearly marked as LxxSyy.mp3 where xx is the Lecture Number and yy is the SLIDE number.

TWO ADDITIONAL WAYS HAVE BEEN ADDED: Movies are now available for directly watching on internet, on my personal website -- asadzaman.net. Furthermore, Microsoft Powerpoint presentations with EMBEDDED sound files are also available for download from same source.

FEEDBACK: Students complain that the English is too complex -- they cannot understand the audio part of the lectures.

SOLUTION: Teacher should download ONLY the powerpoint AND the TRANSCRIPT of the lecture. The Transcript is a written record of the audio portion of the file. If the Teacher keeps the printout of the transcript in front, he/she can do the presentation themselves, referring to the transcript as a reminder of the points to be covered in presenting the slide. This way, they can use any (level of) language to present the materials. AFTER having presented the material in class, the student should be encouraged to listen to the lecture on his/her own separately; on the second round, they should find it much easier to understand and follow the English.

Description of Course

This is an online course, which has been designed to suit the background and requirements of Pakistani Students. A very complete set of course materials is available on the website indicated below. This material is meant to be used as a resource by teachers of Statistics. Mostly, teachers are so busy with the mechanics of running the course, preparing lectures, and other routine aspects, that they not have time to observe the students learning process, and implement efficient ways to increase their knowledge. The online course provides complete support to the teaching process so that 90% of the routine and mechanical chores are taken care of. This allows the teacher to run the course creatively, in accordance with the needs and capabilities of the students.

Although this course only covers basic concepts (mostly), it does so in a new way, so that even people with advanced training in statistics will find many of the ideas to be very new, and different from what they have been taught. The basic course materials are available from:

https://sites.google.com/site/introstats4muslims/

Some basic familiarity with EXCEL is required as a background for this course. Many students already have the necessary background and do not need to do anything. Those who are new to EXCEL or feel uncomfortable should have a look at the EXCEL LESSONS on the google website referred to earlier:

https://sites.google.com/site/introstats4muslims/excel

In particular there are three PDF files which discuss in detail the EXCEL tasks required for this course. Recent studies of the learning process show that tests play a central role – students do not learn what they are not quizzed on. This make the task of teaching especially difficult and time consuming because preparing and grading good quizzes is a demanding chore. Fortunately, this part has also been automated – each lecture has associated exercises and quizzes which can be taken online and graded automatically without any effort on part of the teacher. This provides for a learning-by-doing process which substantially enhances the learning experience for the students. The links for the quizzes and instructions on how to login and take quizzes are provided for the students. Instructors should contact me to get access to instructor privileges to manage the process and get evaluations of students.

Detailed Outline

A detailed outline of the lectures is given below

L01: Islamic Approaches to Knowledge

Repeated rote learning is closely related to a lack of confidence – students have come to believe that the materials they are studying are too complicated to understand, and therefore, they should just memorize key formula and reproduce them. Students are unwilling or unable to open their minds and actually think about the substance of the course. To restore confidence, this lecture reminds the students of the unique Islamic teachings related to knowledge, which is part of their heritage. This serves as an essential motivational device to prepare students to actually engage with the substance of the course, to think about the concepts and try to use them and to master them.

UNIT 1: DESCRIPTIVE STATISTICS

Lecture 2: COMPARISONS Part I: Indexing Facts and Fiction

This lecture deals with the idea of comparing two numbers, to see which is larger. The lecture shows that even this basic concept is not so simple, because multidimensional objects can be measures in different way. To compare them requires creating an index, which makes many arbitrary choices

Lecture 3: COMPARISONS: Part II: Sorting, Ranking and: Percentiles,

Within a given list, the operations of sorting, ranking and computing percentiles provide ways of comparing different lists – such as performances of students in different exams or in different classes. The percentile concept is also a key to understanding distributions of data and random variables.

Lecture 4: REPRESENTING: (Mean, Median and Mode)

The concept of the central value of a list of numbers can be understood via the standard three measures: mean, median and mode. The strengths and weaknesses of each of these three is explained via real world examples where only one or two of the three is appropriate while the others are not. In particular, median is the most appropriate measure in most situations, even though the mean is most widely used.

Lecture 5: Measures of Spread, and Outliers.

Various measures of spread are discussed. The usual Standard Deviation is very sensitive to outliers, while the IQR – interquartile range is robust. How these measures are used in real world data sets to assess variability is demonstrated by practical examples.

Lecture 6: Boxplots.

Mean and SD are often used to summarize data sets, but work well only for normal data sets. Most data sets are not normal, and a graphical summary given be the boxplot works well for these. What is the boxplot and how it is used is illustrated on real world data sets.

Lecture 7: Histograms

Unlike boxplot or other summaries, histograms or data distributions provide a complete description of the data. However, different features of the data appear visible at different bin sizes. How to make and interpret histograms on real data sets is explained in this lecture

Lecture 8: Densities:

Several defects in histograms can be removed by moving to plots of the data density. Making such plots involves choosing a kernel density function and a window size. How to make and interpret such plots with varying window sizes is explained in this lecture.

Lecture 9: Bivariate Relationships

We apply the data summarization techniques developed to the study of bivariate relationships. Graphical techniques allow clear understanding of how two variables relate to each other without making any of assumptions required for a regression analysis. How these techniques can be used to draw inferences from real world data sets is explained.

THIS ENDS THE UNIT ON DESCRIPTIVE STATISTICS. THE NEXT UNIT DEALS WITH BASIC PROBABILITY AND STATISTICS CONCEPTS

UNIT TWO: RANDOM SAMPLING

Lecture 10: Random Draws

We describe random variables as being random draws of a ticket from a box containing n tickets. This provides an intuitive and natural approach to discrete finite random variables which can easily be understood by students. More complex cases are built upon these simple intuitive foundations, which permit easy explananations of otherwise very complicated concepts. This approach provides an alternative to the standard approach based on the Kolmogorov axioms which is extremely hard to understand.

Lecture 11: Random Variables

Building on the idea of random draws, random variables are objects which can be approximated by random draws. Since all variables can be approximated by finite discrete random variables, this allows a natural and intuitive approach to general random variables.

Lecture 12: Probability Laws and Discrete Random Variables

Operations on random variables require the use of probability laws. These are motivated and explained. The addition law applies to exclusive events. Independence is introduced as a primitive concept to be understood intuitively. It allows the use of the multiplication law for computation of independent probabilities. These are motivated and explained by real world examples.

Lecture 13: Binomial Distribution

This lecture develops the Binomial Random Variable, providing detailed examples in simple cases. This is the fundamental building block for all random variables, as the normal distribution can be developed as a limiting case of the Binomial. The Binomial formula is developed and explained in detail, and problems in calculations of binomial probabilities are solved. The independence and identical probability assumptions of the binomial are explained using real world examples

Lecture 14: Expected Values, Averages, and LLN

The concept of the expected value as a theoretical property of a random variable, and the sample average as an observed empirical property is developed. The Law of Large Numbers shows that the sample average converges to the theoretical population quantity. This is explained via simulations and examples.

Lecture 15: Central Values and Unexpected Values

The mechanism of inference depends on identify certain values as central and others as unusual. The unusual values give you cause to suspect the null hypothesis. The boundary separating the central and the unusual values is the critical value. These concepts are illustrated and explained in context of real world examples.

Lecture 16: Normal Approximation to Binomial

Normal distribution is developed as a large sample approximation to the binomial. Relevant calculations are done to show how this approximation is used to make binomial probability calculations in applications of interest.

Lecture 17: Central Limit Theorem

The Central Limit Theorem shows that sums of random variables may be approximated by normal random variables. This is explained and illustrated (but not proved). We show how the theorem is extremely useful in allowing us to make approximate probability calculations in situations where we have minimal knowledge of probabilities of random variables under consideration.

THIS ENDS THE SECOND PART OF THE COURSE ON BASIC PROBABILITY CONCEPTS ESSENTIAL FOR STATISTICS.

Note that there are only 17 lectures. Lecture is Introduction and Motivation, and could be removed from the course as such – that is, students could be asked to watch it in their own time. There are EIGHT lectures on descriptive statistics and EIGHT lectures on Basic Probability Concepts essential for Statistics. Each of these lectures has a COMPUTER LAB associated with it, This makes for 16 x 2 = 32 classroom sessions which cover statistical concepts. The labs give the student hands-on computational practice on the concepts covered in the lectures. At the end of the course, the student should have developed several important skills in extracting information from real world data sets using EXCEL formulae and graphics.