Thursday, April 2, 2009

Georg Rasch

Georg Rasch was a Danish Mathematician, born 1901, and sadly deceased 1980. He has a Wikipedia entry and a whole web site dedicated to his memory. His best known publication is a book entitled "Probabilistic Models for Some Intelligence and Attainment Tests". It's a great read, but sadly out of print and not widely available second hand.

When people ask what Rasch methodology is all about, I describe it as chaos theory for social scientists or more specifically educationalists and psychometricians. Traditional models in both natural and social sciences were deterministic. An example of a deterministic expression is:

y = f(x)

where y is a function of x.

The function might be x + 2, 2x, x2, or x2 + 2x + 2, it doesn't matter.

In a deterministic model, if the independent variable (in this case x) is known, the dependent variable (in this case y) can be precisely calculated.

Stochastic, or probabilistic, models take a less certain view of the world. They regard events or outcomes as essentially random, but influenced by circumstances. Again put simply, the expression about can be made stochastic by introducing uncertainty as follows:

p(y) = f(x)

where the probability of an outcome y is a function of x. For example if place a fixed number n of blue beads in a box, and vary the number x of red beads in the box, the probability of removing a single red bead from the box is given by:

p(red) = x/(x + n)

A major attraction of deterministic models is the simplicity with the terms of an equation can be rearranged. For example in an expression such as:

y = 2x

you can not only predict accurately a value for y if you know x but also impute a value for x, if you can measure y.

The same is sadly not true for stochastic models. Using the previous example, if you know the number of red and blue beads in the box, you can accurately calculate the probability of pulling out a red one. But if you want to estimate by observation the ratio of red to blue beads, pulling out a single bead is not sufficient. And even if you repeat the experiment several times, the mathematics required to estimate the colour distribution from the distribution in the sample selected is a lot more complicated than the simple equation to calculate the probability of pulling out a red bead if the distribution is known. And that is perhaps why Rasch methodology is not widely used by teachers and educationalists in their day to day assessments of student ability. They do a web search for an article on Rasch methodology, take one look at the mathematics, and run away, never to return.

This blog is about learning Java, and I set out with two objectives in mind.

First I wanted to translate an application I had written for Windows into a format which could be posted on the web. And although the translation is not complete, I have done enough to demonstrate the concept, to myself or anyone else who is interested.

My second objective was build the Rasch methodology into a web application so that children could benefit from a fairer method of assessment without teachers and supervisors having to navigate their way through a mathematical argument comprising a series of exponential expressions.

I should not be the first to build Rasch methodology into a computer model. The Winsteps software has been around for yonks. But I might be the first to put use Rasch methodology in a web application.

1 comment:

Matt Barney, Ph.D. said...

I was pleased to find your blog; and especially intrigued about your Rasch application for the web. If I understand you correctly, you're creating an alternative to Winsteps or Facets?

Can you say more about the application and when it will be available?