[From Rick Marken (971124.1100)]
Martin Taylor asked some questions about my spreadsheet in a
private post. I'll answer these questions on the net since I admit
that it's rather difficult to understand the spreadsheet without
knowing many more details than I gave in the post that included
the spreadsheet.
Martin said:
When I open the file, I get a window with several (14? from memory)
"sheets".
I double-click on sheet 1 and I get what seems to be your spreadsheet.
That's it!
But it makes no sense. There are columns headed "10" "20" "30",
which are clearly your IVs.
Yes. The numbers under each of those columns are the measures of
the DV for each subject (there are ten DV numbers under each IV
number representing the 10 subjects in each condition).
In the grayed-out cells there are columns of values starting at 2
and increasing by 2 per row
Yes. These are the values of the perceptual variable (CV) controlled
by each subject. The number you see corresponds to the subject's
reference for the value of that perception; if the CV value is
2 it's because the subject has a reference for that perception
being 2. Each subject, going down a column, has a reference that is
2 higher than the reference of the previous subject in the column.
So the subjects are not really assigned to groups randomly (in terms
of their references). You can change the references for each subject
by changing the formula in the cell to the right of the corresponding
CV value. That formula (as you note) is "self + 0.5*(left neighbour-X)"
where "self" is the cell that contains this formula, "left neighbour"
is the cell to the left of this cell and X is a number which is the
reference value. By changing the number that you call X you will
change the subject's reference for the CV. I could have made X a
random number (using the RAND() function) but this function generates
a new value on each iteration of computation so the reference would
be changing while the control system (subject) is acting to
bring the perception to the reference.
By the way, the formula "self + 0.5*(left neighbour-X)" is the
integral output function for each subject (control system). In
more familiar notation it is just o := o + .5 * (p - r). I
computed error as p-r rather than r-p so that the outputs (the DV
values observed in the experiment) would tend to be positive.
and in the neighbour column there are cells containing formulae
of the form" where X equals the fixed value of the left neighbour,
so that the formula is really "self + 0.5*0".
These "neighbor column" cells are the cells that compute the
perceptual variable (CV) that is controlled by each subject (control
system). An example of the formula in one of these cells is:
=($J14*$A$24+$K14+$B$24+$L14+$C$24+$M14*$D$24+$N14*E$24)-B4
It is important to understand this formula in order to understand
the spreadsheet. This formula computes the value of the perceptual
variable as a linear weighting of the values of the environmental
variables. The "fixed" environmental variable values are stored in
cells A24-D24; they show up in the formula as $A$24, $B$24, etc.
The "variable" environment values -- the values of the IV -- are
in cells E24-G24. The formula above applies to a subject in IV
condition 1 so the perceptual variable is a function of E24;
the variable environmental value for subjects in conditions 2 and 3
come from cell F24 and G24, respectively.
The environmental variables are weighted by coefficients from
what you describe as the "big matrix of "perceptual weights"" .
The coefficients are in rows J through N of the spreadsheet; each
subject's perceptions represent a weighting of the environmental
variables by coefficients from a different row of this matrix.
In the formula above, the enviromental variables are weighted by
the coefficients in row 14 of the perceptual weights matrix
($J14*$A$24+$K14+$B$24...note the row indication associated with
columns J, K ...).
The subject's perception is also assumed to be influence by the
subject's own actions (the output variable). In the formula above,
the subject's output (the one generated by the formula: self +
0.5*(left neighbour-X) in the cell to the right) is in cell B4.
This output is added to the weighted combination of environmental
variables, producing the value of the controlled perceptual variable,
CV. This value (which, in this case, is in cell A4) is used in the
formula that determines output (the formula in B4, which is
=B4+0.5*(A4-2)). So cells A4 and B4 are in a negative feedback
relationship to one another; cell B4 generates output that brings
the perceptual value in A4 to the reference value, which is 2.0
in this case.
Note that there is considerable variation in the outputs (DVs)
over subjects in each condition. This "within subjects" variation
in output is due entirely to the fact that each subject is controlling
a different _input_ relative to a different reference value. All
subjects in the spreadsheet have the same output amplification
(0.5) so the variance in output is not a result of differences in
"response processes".
I think that the most interesting experiment you can do with the
spreadsheet right now (I plan to make improvements and eventually
write a paper about it) is type in new values for the fixed
environmental variables (cells A24 - E24) and see what happens
to the average results. A change in the value at which the
environmental variables are held constant can change the average
results COMPLETELY. This shows dramatically that the group results
tell us NOTHING about the nature of the individuals in the group.
Changing the _constant_ environment changes nothing about the
individuals but it gives a completely different piture of the
average behavior of the group. If you take the group results as
an indication of what is true of the individuals, your conclusion
about those individuals will differ substantially depending on the
level at which "extraneous variables" were held constant in the
experiment.
Best
Rick
···
--
Richard S. Marken Phone or Fax: 310 474-0313
Life Learning Associates e-mail: rmarken@earthlink.net
http://home.earthlink.net/~rmarken