Media screen update

I was thinking about my previous post and decided to use the data set as a test of my proposed approach.  I began with a fractional factorial screening design and put then moved the associated data into the appropriate experiments:

The ANOVA indicates that the model is a poor fit and there were no statistically relevant terms.
ANOVA of Screening Results

Source	DF	Sum of Squares	Mean Square	F Ratio
Model	5	79.46656	15.8933	1.0621
Error	2	29.92813	14.9641	Prob > F
C. Total	7	109.39469		0.5503

Parameter Estimates from Screening Results

Term		Estimate	Std Error	t Ratio	Prob>|t|
Intercept		7.66875	1.367665	5.61	0.0304*
Glutamine		-0.35625	1.367665	-0.26	0.8189
EAA		1.00625	1.367665	0.74	0.5385
NEAA		2.76875	1.367665	2.02	0.1802
ITS		0.98125	1.367665	0.72	0.5476
Lipids		0.40625	1.367665	0.30	0.7944

At this point, we'd say there was insufficient information in the data to determine what was the impact of the factors on the VCD.  JMP can be used to make an augmented design to determine what effects are in place.  Here are screen shots from the process:
Steps for Augmenting Screening Design

A

B

C

D

 Transcribing the data in the appropriate runs allows another attempt to identify what's driving the VCD.  One point to make is that main effects are now estimable as well as pairwise interactions with glutamine (see figure B).  We have good model that indicates that lipids don't play a significant role nor does the interaction between glutamine and NEAA.
ANOVA Results from Augmented Design

Source	DF	Sum of Squares	Mean Square	F Ratio
Model	7	172.18733	24.5982	35.8350
Error	7	4.80500	0.6864	Prob > F
C. Total	14	176.99233		<.0001*

Parameter Estimates from Augmented Design

Term		Estimate	Std Error	t Ratio	Prob>|t|
Intercept		7.475	0.219692	34.02	<.0001*
Glutamine		-0.55	0.219692	-2.50	0.0408*
EAA		0.8125	0.219692	3.70	0.0077*
NEAA		2.575	0.219692	11.72	<.0001*
ITS		0.7875	0.219692	3.58	0.0089*
Lipids		0.2125	0.219692	0.97	0.3656
Glutamine*EAA		-2.1125	0.219692	-9.62	<.0001*
Glutamine*NEAA		0.05	0.219692	0.23	0.8265

Re-running the analysis gives an even better estimation of the model effects.  If the center points are compared against the predicted model, it's clear there is some higher order activity.  Which of the terms might be squared?  At this point, we're stuck because our design doesn't support evaluating square terms due to aliasing.  Next blog post will include results from another augmentation of the experiment!
ANOVA Results from Augmented Design (significant factors only)

Source	DF	Sum of Squares	Mean Square	F Ratio
Model	5	171.46708	34.2934	55.8601
Error	9	5.52525	0.6139	Prob > F
C. Total	14	176.99233		<.0001*

Parameter Estimates from Augmented Design (significant factors only)

Term		Estimate	Std Error	t Ratio	Prob>|t|
Intercept		7.45875	0.205443	36.31	<.0001*
Glutamine		-0.53375	0.205443	-2.60	0.0288*
EAA		0.79625	0.205443	3.88	0.0038*
NEAA		2.55875	0.205443	12.45	<.0001*
ITS		0.80375	0.205443	3.91	0.0036*
Glutamine*EAA		-2.09625	0.205443	-10.20	<.0001*

Location of Center Point Data within the Augmented Design (significant factors only)