Why have there been so many changes to the Statistics Curriculum, especially with regards to the Central Limit Theorem and Confidence Intervals?
Currently statistics teaching is entering a very interesting period because statistical practice is changing from normal based methods to computer-based methods, which for many reasons are superior. This quote from a paper we have written will perhaps give you some idea of what is happening.
Technology has unleashed access to computing power that can cope with unthinkable and tedious amounts of computation necessary to produce confidence intervals and tests of significance using new methods such as bootstrapping and randomisation. These methods, although algorithmically simple, are powerful: more exact than norm-based methods as they do not rely on normal distribution assumptions — they are distribution free — and in the case of randomisation do not rely on sample size assumptions. Even more importantly, the same thinking can be applied across a wide range of seemingly different situations.
“The new methods set us free from the need for Normal data or large samples. They also set us free from formulas. They work the same way (without formulas) for many different statistics in many different settings. They can, with sufficient computer power, give results more accurate than those from traditional methods”(Hesterberg, Moore, Monaghan, Clipson & Epstein [3, p. 16-2]).
The range and effectiveness of these new methods are so great that they are “rapidly becoming the preferred way to do statistical inference” (Hesterberg et al. [3, p. 16-2])
Quite a few introductory courses in the USA are making a complete change to the new methods. Also the emphasis in teaching is changing from calculating confidence intervals to understanding the concepts underpinning them. Research has also shown consistently over the last 20 years that students do not actually understand the sampling distribution of sample means and the central limit theorem.
What should teachers in NZ do? We think teachers should be encouraged for the reasons above to adopt the informal confidence interval for the median and from an empirical multiple sampling perspective see that it works, having been introduced to Year 11 ideas that sample size and spread (IQR) matter when ascertaining the extent of the sampling variability that needs to be taken account of when making an inference about the populations.
This year (2012) the University of Auckland will be starting to adopt these new methods. The focus in the teaching will be on the thinking and reasoning inferentially. In fact the CLT will no longer be taught.
See this paper by Cobb, which sets out the rationale for changing to the computer-based methods.