Sean,
I wrote a short article on that topic for JMP'er Cable
(http://www.jmp.com/news/jmpercable/15_summer_2004.pdf ).
You might find it useful.
Cheers
Gunter
-----Original Message-----
From: jmp-l-owner@lists.biostat.wustl.edu
[mailto:jmp-l-owner@lists.biostat.wustl.edu] On Behalf Of Davern, Sean
Sent: Friday, 17 June 2005 2:41 PM
To: 'jmp-l@lists.biostat.wustl.edu'
Subject: [jmp-l] Comparing Regression Slopes
<< File: Growth Rate Analysis.JMP >> I have a relatively
simple analysis that I can't determine how to
appropriately do with JMP.
I'm measuring log-phase cell growth in two different vessels.
So, from
first principles I know:
VCD = VCD0 * exp( a * time)
Where VCD is viable cell density, VCD0 is the initial cell
density and a is
the growth rate constant.
I want to compare growth rate (a) in two vessels. Lets say I
run 2 (1
replicate) of each vessels. So, I inoculate 4 vessels and
measure VCD0.
Daily I take samples, record time and measure VCD (a
measurement with large
variability). I take measurements for 3 days giving 4 points
for each
curve. Lets not assume that VCD0 is the same for all tanks
even if I
inoculate them with a common inoculum.
I now want to know if a is a function of vessel type. I
believe that I
might also be able to determine if differences of growth
between two vessels
of the same type was measured.
This site references J. Zar and describes a statistical
analysis for
comparing slopes and intercepts of linear regressions:
http://www.curvefit.com/1_model__2_datasets.htm
I haven't gotten the reference yet, so I haven't read the
background.
I'm wondering if I can use the Fit Model platform if I use a
log
transformation the VCD data as Y. Then I want to determine if
the slopes of
a linear regression are distinguishable. The question is how
do I structure
the model effects? I believe that if I include "time [vessel]"
(the nested
combination) and "vessel" as my model effects I'll get the
ANCOVA analysis.
p-values for the "vessel(type):time" parameter estimates will
tell me if
slopes (a) are statistically distinguishable. Furthermore, if
I also nest
"Run ID" appropriately I'll also get the within-vessel
comparison.
How do I specify the nesting correctly? Will this give me
the correct
statistical analysis? It seems to me that the p-values will
tell me if the
model terms are significant with respect to the model but it
isn't obvious
to me that they tell me the instances are statistically
distinguishable.
The attached JMP ver 5.1.2 file contains example data.
<<Growth Rate Analysis.JMP>>
Thanks, in advance, for any guidance.
Sean
Sean Davern
Amgen
1201 Amgen Court West
Mail Stop AW2/D2152
Seattle, WA 98119-3105
Phone: (206) 265-7074
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