Questions tagged [fractional-factorial]

Experimental designs that use only a subset of possible factor combinations. Typically, some factors are intentionally confounded w/ some interactions, making the interactions impossible to estimate, but requiring a smaller N for the study.

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Are crossed factorial design and full factorial design the same concept?

About crossed factorial design, two factors A and B are crossed, if every level of A can occur in every level of B. A full factorial/crossed experiment is an experiment whose experimental units take ...
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826 views

Algorithm for generating a multi-level fractional factorial design

I would like to perform some black box testing on some software that takes a large number of input variables. These variables can have some interactions (either intentional or non-intentional) so I ...
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182 views

How to calculate (standardized) orthogonal contrast coding in R?

I want to determine efficient fractional factorial designs and blocked designs for factorial surveys and am using the R library AlgDesign. The criteria I'm using to determine if a design is efficient ...
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998 views

Some questions about AlgDesign for Fractional Factorial Design in R

I have a few Design of Experiment type questions about the AlgDesign package in R that I can't find answered online: Will using the center=TRUE option in the gen....
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125 views

How to design a 2-level fractional factorial experiment given some prior knowledge

We're designing a trial to test four factors (call them A, B, C and ...
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57 views

Is it possible to determine how many effects I can estimate in a least squares problem just by looking at the correlation matrix?

I currently have a model matrix $X$ with $6$ columns, which is being used for a factorial design problem, with each column associated with an effect. The ultimate goal is to be able to estimate as ...
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184 views

Experimental design vs factorial design

During my study about experimental design, I detect from some examples that factorial design is a sub-step in an experimental design. However till now the idea seems not fully clear for me. What is ...
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58 views

Augmenting experiment design matrices

Consider a set of users (rows) where we are already testing several treatments (columns): $$\begin{pmatrix} E & U & E \\ U & E &E \\ \vdots & \vdots &\vdots \\ E & E &...
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341 views

How to set up a mixed model with partially crossed factor levels

I would need some help with the analysis of a soil data set. The variable Ms was measured with n=5 over several campaigns (7 levels; i, ii, iii...) throughout a year on an agricultural field that ...
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228 views

Explain fractional factorial design in plain English

I want to begin learning about factorial experiments and, specially, fractional factorial design. What would be a simple, plain English explanation, to get the big picture of this topic? Besides, an ...
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228 views

True replicates or nested data ANOVA - only one experimental unit per condition

I'm in materials science. I have a fractional factorial experiment. I am investigating the main effect of various treatments on a measured response. The exact details are probably not needed to ...
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Identifying method by equation (Related to Factorial Fractional Design)

I'd like to know the name of the method in the picture below. It's the same category as full - and factorial fractional design. It's quite difficult to search the net for this equation - I've tried ...
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112 views

Constructing one-ninth fraction of the $3^{5}$ design

I want to construct a $3^{5-2}$ design with $I=ABC$ and $I=CDE$ as generators. The complete defining relation for this design is: $I=ABC=CDE=ABC^{2}DE=ABD^{2}E^{2}$. This is a resolution III design ...
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Full and fractional factorial designs

I have a data set consisting of six independent environmental variables (all binomial: present / absent) and one dependent variable (binomial: disease present / absent). In order to determine the ...
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237 views

How can I fit a polynomial given some prior knowledge but fewer observations than coefficients?

I want to fit a second degree polynomial to data from a fractional factorial design in five dimensions. Because of the cost of trials, I am initially only going to do eight runs. So I have fewer ...
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383 views

DOE for evaluating a factor with more than 2 levels

I am new to designing experiments. I like the simplicity of 2-level, fractional factorial designs for screening what factors and interactions are important. However, I often conduct competitive ...
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456 views

Fractional Factorial design for 3 factorial

I would like to be assisted on how to go about choosing the treatments to work with in a fractional factorial the following scenario. I have 3 factors ie 3 feeding intervals, 3 larval densities and 3 ...
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114 views

Design of Experiments for Baking

I am very new to design of experiments concept. I would like to design an experiment to understand the relationship between input parameters like amount of various ingredients, cooking temperature, ...
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Arbitrary combination of levels in fractional factorial Experiments

I have a problem figuring out the properties of an existing fractional factorial experiment. I basically have the following samples 1-6 and the properties A-D: ...
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How to quantify the “resolution” of “Fractional factorial design”?

The Design Expert software gives me the picture of resolution for the fractional factorial design, in which Resolution III, IV and V are most critical. But can I ask, how can I determine the ...
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271 views

Optimum approximate theory D-Optimal design

I am using optFederov, from package AlgDesign, to create D-Optimial designs. However, I am a bit confused on what measure to use as efficiency measure. I'd like to use D-Optimal but I don't know which ...
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286 views

Half-Normal Plot of Coefficients from Binary Factorial Experiments

After I wrote this all up I debated whether or not I should post it because I think I know the answer to this question (after looking at the two models I'd end up with), but since I don't really know ...
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543 views

Control group in Incomplete Factorial Design

here, in title of Incomplete Factorial Design, it is written that " it is actually impossible to implement a group that simultaneously has several levels of treatment factors and receives no ...
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167 views

Fractional Factorial Design

In a $2^5$ design, it is believed that only the main effects $(A,B,C,D, E)$ and $AB,AC$ interaction effects are non-zero. I need to construct a fractional factorial with minimum number of runs which ...
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$2^{5-2}$ Design : Alias Structure

$2^{5-2}$ Design Design Generators: $D=AB\quad E=AC$ Defining Relation: $I=ABD=ACE=BCDE$ $$\text{Aliases}$$ $$A=BD=CE=ABDE$$ $$B=AD=ABCE=CDE$$ $$C=ABCD=AE=BDE$$ $$D=AB=ACDE=BCE$$ $$E=ABDE=AC=BCD$$...
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Factorial design name

I was just wondering, as I have been using ordinary least squares regression a lot lately, could anyone explain why a factorial design called a "factorial" design? What part of the calculation is ...
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How to find the levels (+ or -) using the words in a Fractional Factorial?

I'm stuck on this question and would appreciate any help! Q: Given the partial defining relation I = -ABD = -ACE = BCF for a $2^{6-3}$ fractional factorial design, obtain the complete defining ...
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62 views

Controled Factorial Experiment Design: which name or resource?

I'm designing an experiment which has to factors (A,B) with respectively 4 and 5 levels. Since this is quite a large amount, I figured I use a factorial design. However, it is unclear whether the ...
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1answer
125 views

What is the meaning of $A(B^2)$ interaction in a 3 level factorial with 2 factors $A$ and $B$, when the factors are qualitative?

I understand that when the factor is quantitative the $AB$ interaction can have a linear component and a quadratic component and so $AB^2$ makes sense there. But when we have qualitative elements how ...
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How to analyze experiment (based on DoE and via mixed model)?

I am about to deploy my DoE which is based on six parameters with two whole plots: Temperature and relative humidity. The experiment aims at studying a sensor due to the presence of several gases (...
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1answer
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Adding center points in $2^k$ models

I'm not sure I understand this concept. In $2^k$ designs, the independent variables have only two values and are coded as either being -1 (low value) or +1 (high value). We can add a center point to ...
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13 views

Does a factorial design work for factors that have discrete levels, but can't be classified as “high” or “low”?

I have eight factors, four with 2 levels and four with 3 levels. These levels are not "high" and "low" in the sense that they can be turned off and on—but are instead things like "voiced" and "...
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341 views

Experimental (factorial) design not exploiting the variance

I want to construct a design to use Choice Based Conjoint Analysis. I want to focus on D-Optimality, for that reason I use the R package AlgDesign which uses Fedorov Algorithm. I create 7 attributes ...
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306 views

Machine Learning for optimization of configuration file

For my master's thesis I am using a 3rd party program (SExtractor) in addition to a python pipeline to work with astronomical image data. SExtractor takes a configuration file with numerous parameters ...
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2k views

Automated calculation of a fractional factorial design with 9 factors

In my research I want to employ a choice experiment using factorial design. However, I struggle to derive a fractional design from the full factorial design. There are 9 factors on 2 levels, which ...
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78 views

Alias Structure of one-fourth replicate of a $4^2$-Factorial Design with interaction $\text{A}{B}^3$ confounded

For finding the Alias of main effect A , i started as the following : $\text{A}$$\times$ $\text{A}{B}^3$$=\text{A}^2\text{B}^3={(\text{A}^2\text{B}^3})^2=\text{A}^4\text{B}^6=\text{B}^2$(mod $4$)$={(\...
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182 views

Fractional factorial design. only main effects considered

I have 15 factors which I want to optimize. Instead of running a fractional factorial design consisting of 32 runs, if I run a design consisting of 16 runs, will I only get main effects or any second ...
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Full factorial repeated measures ANOVA

I have a Full factorial design where factor1 has 2 levels and factor2 has 5 levels fully crossed (10 treatments in total). Then the samples are collected from same individuals (plots) at 6 different ...
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“Incomplete Design” Problem: 2(between) x 2(within) x 2(within--but only in one between group!)

Problem: I am trying to analyze an experiment with the design in the title: 2(between) x 2(within) x 2(within--but only manipulated in one group) My initial hunch was to run two separate 2 (between)...
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Fractional factorial DOE in pythonDOE problem

I need to do a fractional factorial DOE analysis for my data that will come at the end of the post as image, I am using this code in python . It would need to pip install diversipy if you haven't ...
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Multi-level factor design of experiments

How should I select interactions in order to be able to encode multi-level features using interactions of main features in my design? I'm wanting to create an experimental design to be used to create ...
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Factorial experiment design with incompatible levels in IVs

Is it safe to run a Factorial ANOVA if you cannot collect data for some cells? Scenario: There are two independent variables, and one dependent variable. All independent variables are nominal: D (...
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Simulate responses for fractional factorial design

I want to simulate responses for fractional factorial design. As an input for simulation I want to use estimated effect sizes of main factors and some interactions. I know there is a formula for ...
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Central composite design

I'm a data scientist who has not used central composite design before, I only heard of it, but I'm not able to grasp for what it can be used and how it can be used. Can someone please explain this to ...
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When do three-factor interactions or higher be assumed negligible?

I am referring to fractional factorial designs where some two-factor interactions are aliased with three factor-interactions, and three-factor interactions are aliased together. To simplify the ...
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247 views

2x2x2 (reduced) design to study main effects

I'm at the point of conducting a 2x2x2 factorial design to study corporate adoption decisions. I am only interested in the main effects and run a ANCOVA. This experiment is only one part of a bigger ...
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87 views

confounding ABC in factorial experiment

Consider a $ 2^3 $ factorial design lay out in 2 blocks ,each of size 4, as follows Block I: {1,a,b,c} Block II: {ab,ac,bc,abc} Here,the treatments combinations are written in Yate's notation. ...
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DoE - full factorial with less levels or fractional factorial with more levels?

I am planning on doing a variance components analysis (random effects anova). I'm wondering if anyone has any advice regarding balancing the number of levels to include in the design vs. the type of ...
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Question regarding a factorial design and the main effect of one of its factor

Suppose we consider the following $2^4$ factorial design with factors A, B, C and D in the usual order. $Block1 - (0,0,0,0),(0,1,0,1),(1,0,1,0),(1,1,1,1),(1,1,0,1),(0,0,1,0).$ $Block2 - (0,0,1,1),(...
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How to interpret Experimental design created by AlgDesign?

I'm doing an experimental study of 5 factors with a different amount of levels in each. More specifically: 9, 13, 12, 6 & 15. Using the AlgDesign library in R, i ran the following syntax to ...