as you suggest
1. log the data
2. use fit model
put ln(vcd0), ln(time)
adn also the interaction term:
ln(time)*ln(vcd0)
a significant interaction means the slope are significantly different
you can obtain the separate equations for each batch by looking at the coefficients (parameters)
BUT i find it simpler to do a linear regression with VCD0 as a by variable
best
diana
On 17 Jun 2005, at 05:41, Davern, Sean wrote:
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
<Growth Rate Analysis.JMP>
Professor Diana Kornbrot
Head of Health & Human Sciences Research Institute
University of Hertfordshire
College Lane, Hatfield, Hertfordshire AL10 9AB, UK
voice: +44 (0) 170 728 4626
fax: +44 (0) 170 728 5073
email: d.e.kornbrot@herts.ac.uk
http://www.psy.herts.ac.uk/pub/D.E.Kornbrot/hmpage.html
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