RM: G'day Graham, until this morning I would have agreed with you
100% about the need to use 11 degrees of freedom for this sort of
thing, but after a few days of developing a small program that shows
me how much data is required to reach the .05 level (or better) under
various circumstances, I realised that we are not going to get very
far in the near future unless we change the way we have been working
for decades and either:
(a) Start gathering enormous amounts of data or
(b) Get rid of degrees of freedom that kill virtually every project.
I found that the latter was far easier to do, and all it requires is
for us to change what we are saying with useful some projects.
In this series of examples which I've started to post here, I'm
deliberately not saying anything about the 12 signs of the zodiac in
any given study, so they don't need to be accounted for with degrees
of freedom. Each observation that I am reporting is for only 2
factors, which *happen* to be signs of the zodiac, but I'm not
comparing any scores with any of them except the one mentioned.
I could easily have substituted "born in the sign of Aries" with "born
in the country of Australia" but if I had done the latter I wouldn't
be asked by any stats expert to use 194 degrees of freedom for the
other 194 countries in the world.
Now if we imagine that I *had* used Australia instead of Aries, and
I'd used New Zealand instead of the sign of Taurus for the observation
about the tendency to gravitate towards basketball, then the
observation stands alone.
I suppose it would stand alone just as much as if I had given a bunch
of subjects in an experiment "A Virgo pill" or "Taurus pill" and we
compared their attitudes towards basketball afterwards.
[By way of example]
The difference here is that I'm not saying that the "Virgo pill" works
better than the "Aries pill" or the "Gemini pill" or any other pills
because I didn't make any such pills. I only made the two - Virgo +
Taurus pills.
Usually of course when we are conducting surveys or experiments we are
saying or implying that a high-scoring sign is better than ALL the
others, but we don't need to do that :-)
Ray
[P.S. I got your snail mail - thanks]