STATISTICS IN LINGUISTICS

Brian M. Scott BMScott at stratos.net
Sat Feb 6 01:42:10 UTC 1999

```Patrick C. Ryan wrote:

> What I find amazing is that you would think a "100% CORREKATION" does not
> establish a cause and effect relationship.

It obviously doesn't.  Imagine a large, square room whose sides are
oriented east-west and north-south.  The floor of the room is blue in
the northern half and red in the southern half.  The ceiling is blue in
the eastern half and red in the western half.  A track runs through this
room between the SW and NE corners.  Mounted on the track is an opaque
cubical with a window in the ceiling and another in the floor.  You are
riding in this cubical, which moves slowly but erratically back and
forth along the track.  From time to time a buzzer sounds, the window in
the floor opens momentarily, and, as it closes, the window in the
ceiling opens.  You find that every time you see a blue (resp. red)
floor, you also see a blue (resp. red) ceiling a moment later.  The
correlation is perfect, but there is clearly no cause-and-effect
relationship between the floor color and the ceiling color.

> I can see why you prefer not to deal with mathematical models. If you have
> 100 trials, and the same cause has the same effect, the probability of the
> cause creating the same effect again is 100%. Not 99%. Not 98%. Infinity is
> not a factor in this equation.

No.  I flip a fair coin (the 'cause') 100 times and get tails (the
'effect') 100 times -- unlikely, but certainly possible.  The
probability that I get tails on the 101-st toss is still 1/2, not 1.

Brian M. Scott
Dept. of Mathematics
Cleveland State Univ.

```