On Mon, 5 Mar 2001, Philip Cozzolino wrote in part:
> Yeah, I don't know why I didn't think to compute my eta-squared on the
> significant trends. As I said, trend analysis is new to me (psych grad
> student) and I just got startled by the results.
>
> The "significant" 4th and 5th order trends only account for 1% of the
> variance each, so I guess that should tell me something. The linear
> trend accounts for 44% and the quadratic accounts for 35% more, so 79%
> of the original 82% omnibus F (this is all practice data).
>
> I guess, if I am now interpreting this correctly, the quadratic trend
> is the best solution.
Well, now, THAT depends in part on what the
spectrum of candidate solutions is, doesn't it? For all that what you
have is "practice data", I cannot resist asking: Are the linear &
quadratic components both positive, and is the overall relationship
monotonically increasing? Then, would the context have an interesting
interpretation if the relationship were exponential? Does plotting
log(Y) against X look approximately linear? If so, especially if your
six values of X are points in time, Y can be described as exhibiting
exponential growth over the period observed, and there is a constant
doubling time (if Y is increasing) or half-life (if Y is decreasing).
The formal equation for exponential growth in Y (with X = time) is
Y = a*exp(b*X)
and the doubling time is log(2)/b (using the natural logarithm);
if b is negative, Y is exhibiting exponential decay and this
quantity is its half-life.
In the intermediate course (ANOVA and MLR), I used to use some old data
on the mass of chick embryos to illustrate a period of exponential
growth. 11 time points, 1 day apart, and a very nice exponential fit.
A polynomial fit required a quartic equation.
-- Don.
----------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 (603) 535-2597
Department of Mathematics, Boston University [EMAIL PROTECTED]
111 Cummington Street, room 261, Boston, MA 02215 (617) 353-5288
184 Nashua Road, Bedford, NH 03110 (603) 471-7128
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