Factorial Experiments

Dec 11, 2013

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Dependent variable Yk Categorical independent variables A, B, C,

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Factorial Experiments

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Multiway ANOVA Factorial Experiments

Multiway ANOVA. It is certainly possible to consider more than one categorical variable at once.In fact, if you are interested in the effect of several variables, you can get much more information out of a carefully designed experiment manipulating all the variables than separate experiments manipu

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Factorial Experiments

Factorial Experiments. Factorial Design = experiment in which more than one IV (factor) at a time is manipulated Uses all possible combinations of the levels of the factors The factors are “orthogonal”. Factorial Designs. Main effects The effect of each IV alone Interactions

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Factorial Designs

Factorial Designs. Chapter 11. Class Temperature & learning. Add a second factor (gender). What about another factor (test level)?. Factorial designs. Allow experiments to have more than one independent variable. Example. Example.

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FACTORIAL ANOVA

FACTORIAL ANOVA. Overview of Factorial ANOVA. Factorial Designs Types of Effects Assumptions Analyzing the Variance Regression Equation Fixed and Random Effects. FACTORIAL DESIGNS. All combinations of levels of two or more independent variables (factors) are measured.

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Factorial Experiments

Factorial Experiments. Text reference, Chapter 5 General principles of factorial experiments The two-factor factorial with fixed effects The ANOVA for factorials Extensions to more than two factors Quantitative and qualitative factors – response curves and surfaces.

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Design of Engineering Experiments – The 2 k Factorial Design

Design of Engineering Experiments – The 2 k Factorial Design. Text reference, Chapter 6 Special case of the general factorial design; k factors, all at two levels The two levels are usually called low and high (they could be either quantitative or qualitative)

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Multiple Comparisons in Factorial Experiments

Multiple Comparisons in Factorial Experiments. If Main Effects are significant AND Interactions are NOT significant: Use multiple comparisons on factor main effects (factor means). If Interactions ARE significant: 1) Multiple comparisons on main effect level means

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7-2 Factorial Experiments

7-2 Factorial Experiments. 7-2 Factorial Experiments. 7-9 Factorial Experiments with More than Two Levels. 7-9 Factorial Experiments with More than Two Levels. Two-Way Factorial Model where = A main effect, i = 1, = B main effect, i = 1, = Interaction effect

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Factorial

Factorial. factorial_of(0,1). factorial_of(N,Ans) :-N>0, N1 is N-1, % “ is ” eval numerical expressions like N-1. factorial_of(N1,PrevAns), Ans is PrevAns*N. ?- factorial_of(5,Ans). ?- factorial_of(3,6). ?-factorial_of(X,120). Integer Operation.

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FACTORIAL EXPERIMENTS

FACTORIAL EXPERIMENTS. THIS APPROACH HAS SIGNIFICANT ADVANTAGES AND DISADVANTAGES. BASIC APPROACH. Access to the system or simulation k control-able independent variables (Factors) Each has an on/off, hi/low, present/absent CAUTION: These are not conditions or cases, they are decision-able.

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Fractional Factorial Experiments (Continued)

Fractional Factorial Experiments (Continued). The concept of design resolution is a useful way to categorize fractional factorial designs. The higher the resolution of the design the better. However, as expected, to achieve higher resolution more experimentation is sometimes necessary.

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Factorial Experiments

Factorial Experiments. Analysis of Variance Experimental Design. Dependent variable Y k Categorical independent variables A, B, C, … (the Factors) Let a = the number of categories of A b = the number of categories of B c = the number of categories of C etc.

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Experiments with both nested and “crossed” or factorial factors

Experiments with both nested and “crossed” or factorial factors. Example 14-2 Nested and Factorial Factors (Hand insertion of electronic components) Three assembly fixtures Two workplace layouts Four operators for each fixture-layout combination

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Factorial Experiments

Factorial Experiments. Analysis of Variance (ANOVA) Experimental Design. Dependent variable Y k Categorical independent variables A, B, C, … (the Factors) Let a = the number of categories (levels) of A b = the number of categories (levels) of B

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VII. Factorial experiments

VII. Factorial experiments. VII.A Design of factorial experiments VII.B Advantages of factorial experiments VII.C An example two-factor CRD experiment VII.D Indicator-variable m odels and estimation for factorial experiments

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Factorial Experiments: - Blocking, -Confounding, and -Fractional Factorial Designs.

Factorial Experiments: - Blocking, -Confounding, and -Fractional Factorial Designs. Emanuel Msemo. Wednesday, July 30, 2014 4:30pm – 6:30 pm 1020 Torgersen Hall. ABOUT THE INSTRUCTOR. Graduate student in Virginia Tech Department of Statistics. B.A. ECONOMICS AND STATISTICS

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Fractional Factorial Designs of Experiments

Fractional Factorial Designs of Experiments. P M V Subbarao Professor Mechanical Engineering Department. Selection of Few Significant Parameters for Experimentation…. Full Factorial Design : Design Matrix. Full Factorial Design : Result Matrix. Most Significant Factor.

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Factorial Experiments

1.76k views • 173 slides

Factorial Design of Experiments

Factorial Design of Experiments. Kevin Leyton-Brown. Terminology: variables. response variable outcome of an experiment. The thing being measured factor a variable upon which the experimenter believes that one or more response variables may depend, and which the experimenter can control

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Factorial Experiments

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free read (✔️pdf❤️) Factorial Survey Experiments (Quantitative Applications in the Social Sciences)

Download here : https://great.ebookexprees.com/1452274185 | Factorial Survey Experiments (Quantitative Applications in the Social Sciences) | Filling a gap in the literature of the field Factorial Survey Experiments provides researchers with a practical guide to using the factorial survey method to assess respondents beliefs about the world judgment principles or decision rules through multidimensional stimuli vignettes that resemble reallife decisionmaking situations Using insightful examples to illustrate their arguments authors Katrin Auspurg and Thomas Hinz guide researchers through all re

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