# Component Scaling in Mixture Designs

Three scales are used to transform the component levels to a convenient scale
for analysis. The original scale used to input the component levels is the
“Actual”. These are converted to the “Real” scale, with each component re-scaled
so that the total is 1.0. In the real scale, the components are then fractions
of each component in the mixture. If the total of the components is set to 80%
then the “Real” values are the actual values divided by 0.80.

For analysis, the “Pseudo” scale is preferred. In the pseudo scale each
component is rescaled to be a fraction of the “active” part of the mixture.
L-Pseudo is the default scale, but U-Pseudo will be offered if collinearity is
lower in this scale. (See mathematical description below.)

To illustrate, suppose that a three-component nut mixture will always contain at
least 50% peanuts, at least 15% pecans and at least 5% cashews. Therefore, 70%
of the nut mix is predetermined. We are going to do an experiment to determine
the remaining 30%. In pseudo terms,

Peanut pseudo component = (% peanut – 50%) / 30%

Pecan pseudo component = (% pecan – 15%) / 30%

Cashew pseudo component = (% cashew – 5%) / 30%

If there are no lower limit constraints, the real and pseudo scales are
identical.

After building the design you may change the scale via the Display Options menu.

## L-Pseudo vs U-Pseudo

**Lower bounded pseudo values**: the minimum value of each component becomes zero;
the maximum value approaches one. How close it comes to one depends on the
constraints. For a simplex the component minimums are zero and the maximums are
one.

**Upper bounded pseudo values**: the maximum value of each component becomes zero;
the minimum value approaches one. How close it comes to one depends on the
constraints. For an inverted simplex the component maximums are zero and the
minimums are one.