Environmental Engineering Reference
In-Depth Information
ANOVA. Sequential F-tests are performed, initially using linear model and
adding terms (quadratic and higher if appropriate) (Hogg and Ledolter, 1989).
Once a model is selected a simple linear regression technique (least squares) is
used to fit the model to the data having rough linear relationship. ANOVA is
performed and an overall F-test and lack-of-fit test confirm the applicability of
the model. Also, summary statistics (r
2
, adjusted r
2
, PRESS, etc.) and the
standard error for each model coefficient are calculated. After the model fitting
is performed, the next step is validation of assumptions used in the ANOVA
residual analysis. This analysis includes calculating case statistics to identify
outliers and examining diagnostic plots such as normal probability plots and
residual plots. If these analyses are satisfactory, the model is considered
adequate, and response surface (contour) plots can be generated. Contour plots
can be used for interpretation and optimization.
1.5. Optimization
The immobilization of toxic substances in hazardous jarosite waste and
processing into value added products may depend on the types of additives
used, their quantity, concentration and process technique under which the
synthesis is completed. Optimization may be performed using mathematical
(numerical) or graphical (contour plot) approaches, graphical optimization
being limited where there are only a few responses.
Numerical optimization requires defining an objective function known as
desirability or score function that reflects the levels of each response in terms
of minimum (zero) to maximum (one) desirability. One approach uses the
geometric mean of the desirability functions for each individual response,
where
n
is the number of responses to be optimized (Derringer and Suich,
1980):
D= (d
1
d
2
d
n
)
1/n
(4)
Another approach is to use a weighted average of desirability functions:
(w
1
d
1
w
2
d
2
w
n
d
n
)
D=
n
Search WWH ::
Custom Search