> Wayde, I hate to sound stupid in front of all these people, but I don't
> understand what you're saying. If you change only one variable, and leave
> everything else constant, then you see the effect of changing that
> variable, no?
Yes, sort of, but you only get information about how that variable affects
the process for one very specific condition. This completely ignores the
possibility that a change to some other variable will change this
response. If the variable being tested is NOT dependent on other parts of
the process then a simple test changing this one variable is sufficient.
Unfortunately, this is seldom the case. When the variables have
dependency between each other, the "let's only change one variable
approach" won't show this in your test data, and can be deceiving. You
may conclude from such a data set that you know the effect of changing the
one variable, when in fact you only really know its effect for one very
specific case. If I understand you correctly, this is what you are
saying as well.
My point is that many people running experiments on a system with
dependent variables ignore important tests that would have shown this
dependency. Anderson obviously made this mistake. He set the
dichromate concentration variable to zero assuming that it had no affect
on the staining without checking this assumption.
Perhaps the following example might help, suppose that you had four
variables: A, B, C, D; and that you wanted to test them at values of 0 and
1 (nice binary sequence). The possible tests that you could make are:
A B C D Test Number
------------------------
0 0 0 0 1 baseline test
0 0 0 1 2 change variable D
0 0 1 0 3 change variable C
0 0 1 1 4
0 1 0 0 5 change variable B
0 1 0 1 6
0 1 1 0 7
0 1 1 1 8
1 0 0 0 9 change variable A
1 0 0 1 10
1 0 1 0 11
1 0 1 1 12
1 1 0 0 13
1 1 0 1 14
1 1 1 0 15
1 1 1 1 16
As you can see, only changing one variable at a time leaves out 11
possible combinations. More importantly, it is these 11 ignored tests
that would show how changing more than one variable affects the process.
What I've described above is the "classical" scientific method. However,
as you can see, we already have 16 possible tests to perform for a very
simple problem of four variables having two values. "Real world" problems
are much more complicated, and the combinatoric approach gets unwieldy.
You may simply not have the time or resources to try every possible
combination. This is where the use of statistical experimental design
(Taguchi methods, etc.) come into play. Basically you try to choose a
subset of tests from the large number of possibilities to provide the
most information with the fewest number of tests.
> If you put dabs of pigment-in-gum on the paper without dichromate, and
> then do the same pigment and gum *with* dichromate, you have changed one
> variable. It's true you have to decide whether to increase the pigment so
> that it's the same relative concentration, or cut the gum volume so you
> stay with the same total volume of liquid. But those are NOT crucial
> variables, as the absence of the dichromate is.
Yes, so the staining depends not only on the ratio of pigment to gum, but
also the dichromate concentration. Changing one affects the other. Your
experiment needs to account for this.
> That first test I suppose would be still without exposure. To add
> dichromate *and* exposure would be two variables. Of course as noted,
> that's what you'd have to do in order to have a meaningful gum test in any
> event.... so I'd suggest scrapping the nonsense of the gum and pigment
> alone, and start fresh.
Exposure is another variable that effects the staining in combination with
the others. Can't leave it out if you really want to understand the
process.
> That's NO variables for the first test, just pick
> your amounts and times.
Now you've lost me on that one.
> Tho I'll mention that I've standardized gum tests at 100 units exposure on
> the NuArc and one hour still development. Saves a lot of writing notes,
> when exposure and development are not the variables being tested... if
> they are, I do 3, 6, or 9 strips at a time, to get all the variables at
> one shot.
Yes you can always choose to hold part of the variables constant, but
remember that tests based on these conditions may not accurately predict
the results obtained if these conditions are changed.
> And after making a "decent" gum print, you could bear to do anything ELSE?
> Say not so...
Oh I don't know. I made a carbon print yesterday that is a significant
improvement over my previous prints. I don't think I'll be able to give
that up for gum <grin>.
- Wayde
(wallen@boulder.nist.gov)