1. no significant effects of variables
2. no significant relationship between the controlled design variables and the measured response variables
3. inaccurate predictions

This can be reflected in three statistics:

1. R² is too small (R² is the percent of variation explained)
2. The F ratio statistic is too small to be statistically significant
3. Predicted versus actual residuals are too large (even when R² may be large)

When these problems occur it may be due to model mis-specification. That is, the assumed underlying model may be inadequate to fit the data.

All tests assume an underlying model.

Using commercially available software currently enables the experimenter to assume only a linear (1^st order) or quadratic (2^nd order) model to analyze the data. This is a very limiting assumption.

What is needed is the ability use higher than 2^nd order test designs and models. This can be done in two ways:

1. Initially choose a higher order test design to allow higher order model terms
2. Or design the test sequentially to allow higher order test points to be added as needed

DOES has developed new higher order test designs which allow higher order model terms to be added.

The DOES test designs may be done sequentially:

1. 1^st Order (linear)
2. 2^nd Order (quadratic)
3. 3^rd Order (cubic)
4. 4^th Order (quartic)

This is a powerful approach to testing combining the small sample sizes in Phase I with the excellent data fitting in Phases III and IV.