This site gives a number of tools for teaching introductory statistics at university level. These tools support a particular philosophy on teaching statistics which has been built up over some sixty combined years of statistics teaching experience! Over the past five years this underlying philosophy in tandem with the associated spreadsheet modules has been introduced at UCT in one of the largest first year courses, STA1000F/S, involving some 2000 students per year.

Our observations over the years have led us to conclude that teaching statistics via theory followed by apparent application (in the form of a paper exercise involving manipulation of theory) can give misleadingly good students grades. In fact, students are often seen to achieve remarkably good grades at relatively advanced levels of statistics but, as some gentle probing at postgraduate levels has revealed, in many instances fail to understand the foundational concepts of their discipline! In addition, our current teaching methods need to take cognisance of the fact that, for a variety of reasons, a large portion of our students are mathematically poorly prepared for first year university; and many students have to cope with learning in a language other than their mother tongue.

The Modules

Note that these are written for MS Excel 2007 (or later versions). The modules roughly follow chapters in the first year statistics textbook, Introstat (LG Underhill) and essentially support and supplement that book. They are to a significant extent self explanatory for those with some knowledge of statistics and simulation. In cases where the modules require additional explanation, the spreadsheets themselves have accompanying notes. These modules are essentially crafted as teaching tools and the experience of first year students would be of the lecturer leading the students through the simulations at an appropriate pace, allowing plenty of opportunity for discussion and clarification. Lab based tutorials also support this process.

Description of Available Modules

1. Module 1: We discuss the question: - What are random numbers and what is a statistical distribution? We introduce the Uniform distribution, the most simple of statistical distributions.

2. Module 2: In order to test a claim that a set of 5 mice have been taught how to navigate a maze, we explore the chances of different numbers of successful mice, under the assumption that the mice are making purely random choices. This supports a discussion of how the Binomial distribution arises.

3. Module 3: We sketch the following scenario: a stretch of road is surveyed to determine the number of potholes. Unfortunately information on the individual positions of the potholes is lost but the total number of potholes is correctly recorded. We manage to salvage the situation from embarrassment by employing the Poisson distribution to good effect!

4. Module 4: The same situation pertains as in module 3; however we focus our efforts on the chances of finding stretches of road without potholes, and discover the exponential distribution.

5. Module 5: We explore the magical effects of averaging and find a surprising commonality across the distributions of averages arising from a multitude of different situations (give or take a few assumptions they all seem to converge to that bell shaped curve?).

6. Module 6: We consider hypothesis testing and attempt to pin down the chances that we’re wrong when we think we’re right…or is it right when we think we’re wrong? Oh yes, we also look at statistical power…do we have enough information to attempt to adjudicate between these two hypotheses anyway?

7. Module 7: We find a relationship between two variables and express this as a mathematical straight line formula. But the actual line we get depends on the sample we have. We explore how certain we can be that we know anything about the relationship between our two variables at all.

More about our teaching:

Our approach has been to, as far as possible, make the teaching of statistics visual and experiential. Keeping it visual is of particular relevance where there are language challenges and the experiential approach aims to address the undesirable ‘black box’ of theory effect. A key part of this approach is to provide students with tools whereby they can interrogate theory using a ‘what if’ approach.

The basis of our teaching philosophy is to shift from a pen-and-paper/chalk-and-board paradigm to a “virtual statistics laboratory”, in the form of a spreadsheet platform.

Teaching mathematical and statistical principles through a spreadsheet platform offers significant advantages, particularly for those with weak grounding in basic algebra. The structuring of a spreadsheet develops a general algebraic way of thinking as the process requires skill in expressing numerical relationships using algebraic notation. However, the richest feature that a spreadsheet offers to the teacher of statistics is its ability to show how one can mimic the process of repeated statistical experiments. By simulating statistical sampling one can elucidate a range of subtle and often misunderstood ideas which are central to basic statistical knowledge, such as those of randomness and statistical distributions.

We argue for a two-stage approach in which statistical understanding is built by initially empowering students to use simple spreadsheet operations in MS Excel, followed up by the use of more sophisticated statistical simulation tools in a Visual Basic for Applications (VBA) programming environment. Teaching sessions are built around a set of structured spreadsheet exercises as well as a suite of VBA-based simulations which demonstrate the concept of random variation, as well as show how statistical tools can be used to explore the concept of uncertainty.

At this stage we will list and discuss the currently developed suite of VBA simulation programmes used at first year level and offered on this site. Note that these are written for MS Excel 2007 (or later versions). The modules roughly follow chapters in the first year statistics textbook, Introstat (LG Underhill) and essentially support and supplement that book. They are to a significant extent self explanatory for those with some knowledge of statistics and simulation. In cases where the modules require additional explanation, the spreadsheets themselves have accompanying notes. These modules are essentially crafted as teaching tools and the experience of first year students would be of the lecturer leading the students through the simulations at an appropriate pace, allowing plenty of opportunity for discussion and clarification. Lab based tutorials also support this process.