ANOVA can be used in parametric procedures to compare 3 or more samples and to test if the population means are equal.
MANOVA is an extension of ANOVA and is used in order to test simultaneously the relationship between several categorical variables (treatments) and two or more metric dependent variables. Is is useful when we design an experimental situation to test hypotheses about the variance in group responses on two or more metric independent variables. As an example of an experimental situation think of the handling of several non-metric treatment variables.
The quality of statistical analysis heavily depends on the alternatives presented in the experimental design. An experimental design is a plan for running an experiment. Experiments are performed to study the effects of the factor levels on the dependent variable. The factors of an experimental design are variables that have two or more fixed values or levels of the factors. In Conjoint analysis, the factors are the attributes of the hypothetical products or services, and the response is preference or choice
Conjoint analysis is a technique for measuring consumer preferences for products or services. It is also a method for simulating consumers possible reactions to changes in current products or newly introduced products into an existing competitive market. One of the fundamental problems in performing Conjoint analysis is how to generate experimental designs. The purpose of an experimental design is to give a rough overall idea as to the shape of the experimental response surface, while only requiring a relatively small number of runs. These designs are expected to be orthogonal and balanced in an ideal case. In practice, though, it is hard to construct optimal designs and thus constructing of near optimal and efficient designs is carried out. In this paper it will be present the basic criteria of the design efficiency and some algorithms which can be used for its construction. Special attention will be paid to the algorithm we developed and implemented in Visual Basic application as the procedure in MCON softwar
A response surface design is a set of advanced design of experiments (DOE) techniques that help you better understand and optimize your response. Response surface design methodology is often used to refine models after you have determined important factors using factorial designs; especially if you suspect curvature in the response surface.
Response surface with no curvature
Response surface with curvature
There are two main types of response surface designs:
- Central Composite designs
- Central Composite designs can fit a full quadratic model. They are often used when the design plan calls for sequential experimentation because these designs can include information from a correctly planned factorial experiment.
- Box-Behnken designs
- Box-Behnken designs usually have fewer design points than central composite designs, thus, they are less expensive to run with the same number of factors. They can efficiently estimate the first- and second-order coefficients; however, they can't include runs from a factorial experiment. Box-Behnken designs always have 3 levels per factor, unlike central composite designs which can have up to 5. Also unlike central composite designs, Box-Behnken designs never include runs where all factors are at their extreme setting, such as all of the low settings.
How can I use a response surface equation?
The difference between a response surface equation and the equation for a factorial design is the addition of the squared (or quadratic) terms that lets you model curvature in the response, making them useful for:
- Understanding or mapping a region of a response surface. Response surface equations model how changes in variables affect a response of interest.
- Finding the levels of variables that optimize a response.
- Selecting the operating conditions to meet specifications.
For example, you would like to determine the best conditions for injection-molding a plastic part. You first used a factorial experiment to determine the significant factors (temperature, pressure, cooling rate). You can use a response surface designed experiment to determine the optimal settings for each factor.
What is a response surface design? - Minitab
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Response surface with curvature. There are two main types of response surface designs: Central Composite designs: Central Composite designs can fit a full ...[PDF]THE RESPONSE SURFACE METHODOLOGY - Semantic ...
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Subsection 5.4.4: First-Order Gasification Response Surface With Curvature. Subsection 5.4.5: Coal Gasification Response Surface Conclusions. Section 5.5:
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The present study aimed at maximizing cellulase production by Penicillium funiculosum using sequential experimental design methodology for optimizing the ...
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