Something I posted elsewhere in problems about the use of statistical reasoning..... for posterity.....

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I have a problem though with the idea that, just because a course of development has been charted and identified statistically, that course is the one true developmental path. Much in child development courses is based on this notion when it's really not a proven thing: God (such as there is one, and that's a personal thing) may have set things out in the bell curve pattern, but man invented the standard deviation, and that is something we in child development (yes, I had to do it for my psychology degree equivalent) need to remember, and we forget that at our peril.

In the course of development, as you'll know, there are many factors impinging on a child and some of these are biological, and some are non-biological; some are social and some are environmental, and some we just don't fully understand, because they are events at the interface of the child and his/her environment... which do not have set predictable outcomes.....

For this reason, I have a problem with terms like "normal development" being given to mean "that development which, if it were measurable and measured, would fall between 1 s.d. either way of the mean", when EVERYTHING that is under a "normal" distribution is - by definition - normal. Unfortunately, not a great many psychologists (in child development or elsewhere) are that familiar with the mathematical concepts and so on that underpin the statistics that they are taught to use (without too much thought as to where they come from, I'm afraid).

In any case, statistics is a very poor way to describe developmental trajectories over time: the best way is by using state-space analysis, which is what the physicists now use (many having given up on statistics as being basically useless). In such an analysis, what we see as the "normal" distribution is in fact a cross section of a set of state-space trajectories and a given point in space-time around a point-set which is known as an attractor. This attractor may or may not ever be coincided upon by the data points which describe a given trajectory through that space-time and it merely represents a hypothetical line segment which suggests a trajectory that we could think of as the mean trajectory of a hypothetically infinite data set based on an infinite number of observations of, in the case of child development, a child's development.

Because of the fact that there is a chance for any observed child's development to veer anywhere under the "normal" distribution purely by chance we have to accept that a child's development is NOT a linear function of "you do this, and he or she does this and time happens and you get this...." - and we deceive ourselves cruelly if we let ourselves think that it is. Chaos theory has more of a role to play in child development than anything we think of based only on our limited understanding (in psychology/child development/education/etc) of statistics and what they actually tell us.

Einstein once said, "God does not play dice with the universe!"

Many of his students (and their students) are now finding out the rules of this incredible poker game that God was trying to tell Einstein how to play.

No way can we predict, and no way should we really try. I am not a God-person; I don't have any belief in any God. But - if there is one - then quantum mechanics and chaos theory are the rules by which that God determines what happens. And those rules are way outside of the scope of any statistics course in psych/educ/ChiDev/etc training that any of us have here (unless we all went to Oxford and studied under Frank Close, Roger Penrose and the likes).

What I'm ultimately trying to say, I think, is that we shouldn't see previous development as a predictor of later development.

As to what ends up bringing about autistic states... the jury is actually still out on that (although they'd like us to send in more coffee! ).


Anecdote: I remember when my daughter was being assessed at Cambridge Uni by Fiona Scott BA(Hons) PhD C.Psychol (one of SBC's team) and talking about this with Simon and Sally (who came up with the device we know as the CHAT (CHecklist for Autism in Toddlers). Sally was still thinking very clearly in terms of statistical distributions, and Simon was trying to get his head round the idea of state-space analysis but he was still trapped in this idea of standard deviations.... and he could not quite grasp the idea (most physicists know more than I even care to know about this: I know just enough to know what statistics sucks )... anyway, he had the origin of the graph as z=0, and equal divisions for z along the horizontal axis. And he couldn't handle that idea that the values on the axes are not statistically derived quanitities: they're raw scores used as co-ordinates in the space whose state we're actually analysing. The statistical stuff happens when you cut across the attractor.... then you get something that will (under a nearly infinite run of observations) approximate this so-called "normal" distribution we can't (so it seems) help but fail to ignore....

I let him buy the sandwiches at that point. Sally sorted out the tea. Earlier, Fiona and I had spent a break in the ADI-R "taking the piss out of Skinner"

That was actually a good day. I stumped a Cambridge Professor!