I rarely get to blog here, so I am taking the opportunity to point out something above the general decline in mathematics students - the losing of knowledge.

Take a look at these feeds from the Australian:

Mathematics Students in Serious Decline

Equation for maths warns of disaster

I was teaching at University when we as a society ripped these students off, replacing core problem solving with vapid histories and philosophies. Such a change had a lot to do with the academia of mathematics becoming disconnected with the application of its theory. And this is where the problem lies.

I’ll give you an example. I sought to take a Graduate Certificate in Applied Statistics recently. Not because I wanted another piece of paper, but because I am looking for some more knowledge to protect myself and my clients from stupid misapplications of theory. I couldn’t find one that was more than a simple training course in certain statistical software packages. Needless to say, I haven’t enrolled. I need, as do all analysts more than the mindless application of a software package.

The need arose when the tried and proven ANOVA test failed on me. ANOVA is the draught horse of multiple testing applications. I had a test returning p values that experience tells were way too small. The underlying data, was violating a number of assumptions of the ANOVA test, and I could find a transform that would fix it. I still haven’t found a transform, and have had to move on without that test, making my story that much longer as I now have to justify the use of “unorthodox” testing procedures.

This is not the first time that I’ve come across underlying short-comings in standard procedures. My argument comes from the fact that often I have to go right back to 1930’s papers by deities like Fisher, or early works by Tukey to find underlying mechanics and discussions. Far too many papers simply state the software package they used, and the outcomes, never addressing whether the package should have been applied in the first place.

I wonder how often it is that an assumption has been made regarding validity, and never checked.