The Response Surface Methodology,
The Box-Behnken design,
three replicates.
It is important to remark that Response Surface Methodology (RSM) is a modeling empirical method that relates real variables (responses variables) as function of real variables (factors). As example CFU/ml as function of time and temperature. You state that you have four conditions, however the most important is how many factors (as real variables) do you have. Assuming that you four conditions are the result of time (x1) and temperature (x2) combinations, your four conditions may be,
x1 x2
1. -1 -1
2. 1 -1
3. -1 1
4. 1 1
-1 represent a low value of your factor and 1 a high level. This design may be considered as a Box-Behnken but with many limitation. Actually, these four conditions represent a 2^2 factorial design, and you can only fit the following model,
Y=b0+b1x1+b2x2+b12x1x2
If you want to construct a RSM you need much more than four conditions (for two factors). A Box-Behnken design for RSM with two factors require at least 9 conditions,
x1 x2
1. -1 -1
2. 1 -1
3. -1 1
4. 1 1
5. 0 0
6. -1 0
7. 1 0
8. 0 -1
9. 0 1
If your factors are the strains, you cannot use a RSM with strains type because strains type is not a real variable. In this case you can construct a RSM for each strain, or introduce a Boolean variable but it is the same.
First of all, thanks for contributing. Yes, of course I'm gonna to use each strain separately. My four conditions are:
1. Temperature (25, 30, 35 c)
2. Substance concentration (10, 20, 30 mM)
3. pH (6,7,10)
4. Bacterial inoculum (1,1.5,2 CFU/ml).
Thanks,
Alaa
Ok. You have 4 real variables. A feasible Box-Behnken for your 4 variables is,
Treat. Temp. Conc. pH Inoculum
1. 25 10 6 1
2. 35 10 6 1
3. 25 30 6 1
4. 35 30 6 1
5. 25 10 10 1
6. 35 10 10 1
7. 25 30 10 1
8. 35 30 10 1
9. 25 10 6 2
10. 35 10 6 2
11. 25 30 6 2
12. 35 30 6 2
13. 25 10 10 2
14. 35 10 10 2
15. 25 30 10 2
16. 35 30 10 2
17. 30 20 8 1.5
18. 25 20 8 1.5
19. 35 20 8 1.5
20. 30 10 8 1.5
21. 30 30 8 1.5
22. 30 20 6 1.5
23. 30 20 10 1.5
24. 30 20 8 1
25. 30 20 8 2
I suggest to you change the pH levels to (6,8,10) like in the design, in order to approximate the orthogonality.
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