TABLE OF CONTENTS "If your experiment needs statistics, then you ought to have done a better experiment."
ERNEST RUTHERFORD (NOBEL PRIZE FOR CHEMISTRY 1908)
The attitude of elite chemists toward statistics has not improved much from when Rutherford made this insulting statement. Perhaps the reason is that the standard methods for design of experiments don't work very well on mixtures. For example, let's say you get a new ultrahigh-shear blender and start tossing in various fruits to see if you can make a tasty "smoothie" drink. Table 11-1 shows the experimental layout for a fanciful concoction that might be branded "BanApple." Is this a good design?
| Std Order | A: Apples | B: Bananas | Proportions A/B | Fraction (A, B) |
|---|---|---|---|---|
| 1 | 2 | 1 | 2/1 | (0.667, 0.333) |
| 2 | 4 | 1 | 4/1 | (0.8, 0.2) |
| 3 | 2 | 2 | 1/1 | (0.5, 0.5) |
| 4 | 4 | 2 | 2/1 | (0.667, 0.333) |
Aside from the dubious choice of ingredients for this mixture design, it makes no sense when you consider that the taste will be simply a function of the proportions of ingredients. Notice that standard orders 1 and 4 end up being the same in terms of the fractions for each fruit. In other words, all that's been done is a scale-up of the same recipe. Yuk! Who would want double the dose of a BanApple smoothie? The total amount varies, but will have no effect on responses such as taste, color, or viscosity. Therefore, it makes no sense to...
