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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10 views

Do I want a mixed model for fractional factorial designs?

I have created a d-efficient fractional factorial design of 48 combinations from a total of 192 possible combinations (4x2x2x3x2x2). To estimate the model, I plan to have 4 runs in 12 blocks and 40 ...
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How to generate a design for a response surface with a discrete input random variable?

I'm trying to generate a design of experiments for fitting a response surface for a quantity $Y$ such that, $Y = f(X_1, ..., X_6)$. I'm open to a factorial design as well as a random design. $X_1,..., ...
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91 views

Advantages/disadvantages of fractional factorial design vs completely randomized design

I'm new to the design of experiments (DoE) and will be running a screening experiment to estimate the effect of a large number of binary independent variables (approximately 10) on a single continuous ...
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53 views

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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What is a “regular” fractional factorial (2-level)?

What is the difference between a regular fractional factorial design and a non-regular fractional factorial design? I found it several times but especially in the FrF2-package.
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How to study a fractional factorial design? [closed]

I wonder why a DoE/fractional factorial design isn't studied with the help of a linear mixed model? Or an Anova? How to analyze it in general is e.g. given here. Background: I will study several gas ...
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Interpreting interaction effects in Factorial design

I have factor1 with 2 levels fully crossed with factor2 (5 levels). Now samples are collected from same experimental units at 6 different times. Time is used as within-subject variable. When I run ...
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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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73 views

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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How do I do a power analysis for a fractional factorial design?

I want to do a power analysis for my 3x2x2 design, but I am not using the full factorial design, but rather a fractional one, so instead of using the full 12 groups, I actually only have 6. I was ...
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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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logistic and anova

In here, you can see original data. My data is $4\times3\times3\times2$ completely randomized design experiment data. I want to model the probability of survival in terms of the stimulus variables. ...
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Taguchi Designs for differential gene expression

I plan to do a differential gene expression using RT-qPCR of 10 genes on 3 strains cultured in different enviormental conditions of 3 factors (2 levels each one). In order to do so, I want to follow a ...
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Specifying the bandwidth parameter for Local Whittle estimation

In every Local Whittle function I have seen I have to set bandwith parameter usually denoted m such that m = floor(1+T^delta). I am interested in the delta, how do I choose what value to put in the ...
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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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210 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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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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Comparison of treatment differences in fully factorial design

I have a dataset from a fully factorial experiment aimed at looking at mortality rates in fish depending on chemical additions. There are manipulations of Buffers (2 types), Nutrients (Ca and Mg) ...
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Constrained design of experiments

I would like to conduct a 2-level fractional factorial experimental design on 8 factors. I used the FrF2 package in R to do so. I have capacity to do roughly 30 experiments, so I selected a resolution ...
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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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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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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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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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414 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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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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496 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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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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129 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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366 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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166 views

Incomplete treatments in Fractional Factorial Designs

I'm trying to analize a chemical experiment with four factors or independent variables. Initially each factor had three levels, so i proposed a $3^4$ factorial design; the problem was that all the ...
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253 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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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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879 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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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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356 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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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 ...
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325 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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How to combine in a (fractional) factorial design model the blocking effect with a treatment (package planor)

For my greenhouse experiment with potted trees, I am planing a fractional factorial design. The experiment has six factors (treatments) each with two factor-levels, and I want to use a model/package, ...
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Fractional factorial designs: lower $p$ vs. more replications

If you were to choose between a 2(X-1) with only one replication or a 2(X-2) with two replications, what would be preferred and why? The goal is to both predict the values of the effect parameters as ...
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How do I analyze interaction in two-factor factorial data when sample size is not given?

I am looking at two-factor factorial data where the response variable is number of cancer cells after an experiment is performed. The two-factors are: Factor A, which has a = 2 levels: "...
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235 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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244 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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What methods can I use for parameter estimation of fractional factorial design?

I've been asked to estimate the parameters of fractional factorial design model which is normally estimated using least square method in R (code is lm). Question: Is it possible to change the least ...
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Generating a response surface from a fractionated design

Is it possible and valid to generate a response surface through augmentation of a fractionated factorial design, where all main effects and two factor interactions have no bias from any other main ...
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Intuition to the Resolution of a fractional factorial design

In design of experiments, is there an intuitive way to understand (and explain) the idea of the "resolution" of the design?
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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 ...