# Teaching Statistics

[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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