[From Bill Powers (941225.0300 MST)]
All the present or ex EABers:
I don't know why I didn't think of this before, but so it goes: I
didn't.
Here is a little test for EABers, to see if they understand basic system
analysis. I've already been claiming that they don't, so there's no
added loss of face here in failing the test.
Suppose we have a simple fixed-ratio m schedule. We know that the
apparatus equation is simply
R = B/m,
where B = mean behavior rate
R = mean reinforcement rate
m = ratio
We observe that in the steady state with m = 5, R = 16.67 and B = 33.3
per unit time, and that with m = 10, R = 10 and B = 100. The question
is, what is the best LINEAR organism-function that will account for
these observations? The organism function will express B as a function
of R.
A linear function can be expressed either as a slope-intercept form or
as a point-slope form. The slope-intercept form is y = ax + b, and the
point-slope form is y - y0 = c(x - x0). These forms are both the
equation of a straight line, and the forms are mathematically
equivalent. Either form can be transformed into the other.
There is only one possible linear form for the organism function, given
the two sets of observations above. What is it? Use either form for the
answer.
No trick or complications here; forget about collection time, satiation,
all the fancy stuff. This is a basic and simple exercise in system
analysis. There is a unique answer and it can be obtained using high-
school algebra. What we want is a linear formula expressing behavior
rate B as a function of reinforcement rate R, nothing more. There is
only one right answer.
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Best,
Bill P.