[from Gary Cziko 930413.1725 GMT]

Bill Powers (930412.1000 MDT) said

Fascinating about the chi-squared phenomenon. I suppose it could

be argued that in counting votes there is never an instance of a

fractional vote, but what if the measure consisted of points on a

continuous scale, like temperature? Then your chi-squared measure

would depend on whether you used kelvin, centigrade, or

fahrenheit units.

The way that chi-square is used here is limited to frequency data and so

the problem of scaling you mentioned would not arise. Each unit counted

into the frequency totals must be INDEPENDENT which is why you inflate the

results when you count tenths or hundredths of votes (you can't get

one-tenth of a vote, you must get ten tenths for each vote).

The chi-square is also used for other hypothesis tests which don't involve

frequencies (such as testing the variance of a population) in which case it

is not sensitive to the scale being used (as one would hope and expect).

The common attribute of all inferential statistics tests that my students

find most troubling (and which I have fun emphasizing) is that you can

ALWAYS get a "statistically significant" finding if your sample is large

enough. But of course the practical significance of such findings is

usually zilcho.

I am teaching an introductory statistics course this semester for the first

time in about 4 years. That means it is my first statistics course since

learning about PCT and the meaning of "independent" and "dependent"

variables. I am hoping to gradually introduce PCT concepts into this

course as a way of making students more critical of the use of statistics

in the behavioral sciences. The rubber-band demo is great fun after

discussing what "independent" and "dependent" variables are supposed to be.

We'll see how much I can get away with before my department finds out what

I'm up to!

Of course, eventually such considerations will be a standard part of all

statistics courses (in the same way that it is always emphasized in

statistics texts that correlation doesn't imply causation, it will also be

emphasized that group statistical findings do not imply anything about

individuals as perceiving-behaving systems).--Gary

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