# Solution 2.14 - Chemometrics: Data Analysis for the Laboratory and Chemical Plant

## Education Article

• Published: Jan 1, 2000
• Channels: Chemometrics & Informatics

1. The first column, representing the levels (or concentrations) of the first factor is as follows.

The blocks are indicated. The cyclic permuter relates the levels of the first factor between blocks. For example experiment 9 is related to experiment 3 by one permutation as 0 à -1 in the permuter of this example.

2. The 14 factor design is as follows:

3. The difference vector is {3 1 0 2}. Table 2.30 suggests that this difference vector is acceptable, for an orthogonal design.

4. The correlation matrix is given below.

The graphs are presented below.

In the top graph all possible combinations of levels are represented, resulting in orthogonality and a correlation coefficient of 0.

Between factors j and j+6, the correlation coefficient is 0.5, and the bottom graph is obtained. Using a repeater of –2 it is impossible to produce orthogonality between a minority of combinations of factors. A solution (for up to 12 factors), would be to choose a repeater of 0, and cyclic permuters as given in Table 2.30.

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