 # Standardized and Normalized Factorial Effects¶

In general, an effect is the change in the response caused by changes in the factors. A linear effect is the average value of a response at the high setting of a factor less the average value of a response at the low setting of the factor. An interaction effect is an adjustment to the linear effect depending on the setting of another factor.

Standardized and Normalized effects are seen on the half-normal plot and effects list when analyzing factorial designs. The standardized effects are used for two-level factorial designs. The normal effects are used for multilevel categoric designs.

Standardized effects are calculated by dividing the effect by the standard error of estimating the associated coefficient and then multiplying this quotient by the standard error of estimating the first linear coefficient in the model. The effects are standardized to the first alphabetical linear effect in the model. This stabilizes the effect estimates for non-orthogonal designs.

Normalized effects are calculated by subtracting the sum of squares for each term from the total sum of squares and dividing by the corrected total degrees of freedom less the number of degrees of freedom used to estimate the term’s sum of squares. This value is compared to a χ2 distribution to produce a provisional p-value. The provisional p-value is converted to a standard normal score to produce the normalized effect.