Solution 2.10 - Chemometrics: Data Analysis for the Laboratory and Chemical Plant
Education Article
- Published: Jan 1, 2000
- Channels: Chemometrics & Informatics
1. A dummy factor is employed because the total number of factors must be one less than a multiple of four. Two level fractional factorials must consist of a number of experiments equal to a power of two, or 16 in this case. The design reduces the number of experiments necessary, which may be important if experiments are time consuming or expensive.
2. A simple way of doing this is by calculating the correlation coefficients between each possible pair of columns, using a correlation matrix. These should equal 0, except for autocorrelation.
3. The design matrix is exactly as the experimental matrix, except with a first column of "+"s added to account for the intercept. The coefficients are as follows.
b_{0} |
b_{1} |
b_{2} |
b_{3} |
b_{4} |
b_{5} |
b_{6} |
b_{7} |
b_{8} |
b_{9} |
b_{10} |
b_{11} |
47.00 |
8.33 |
-2.33 |
0.50 |
8.83 |
-8.17 |
-2.17 |
1.33 |
4.17 |
7.67 |
9.00 |
4.83 |
4. This can be shown for b_{1}.
b_{1} = (-15+42-3+57-38-37-74+54+56+64-65+59)/12 = 8.33
which is the same as in question 3.
5. Apart from b_{0}, there five coefficients that are larger in magnitude than the dummy variable, namely b_{1}, b_{4}, b_{5}, b_{9} and b_{10}. Hence the key factors are (a) %NaOH (b) Stirring (c) Reaction time (d) Catalyst / substrate ratio and (e) Reagent / substrate ratio. Note that the sign of each factor is useful indication also, and reliable as the data is coded and there are no interaction or squared terms.