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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Difference between confounding and aliasing in 2^k factorial design

In statistics, particularly in experimental design, what is the difference between confounding and aliasing in 2^k factorial designs? Also how is a principal block related to the two concepts? I've ...
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Question on $2^2$ factorial experiment( replicates)

I am looking at a question, and it seems that the questions is making some assumptions and that they are providing extra information that is not necessary. Here is the question: Consider a $2\times 2$...
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717 views

How do I estimate a factorial design with empty factors?

I'm trying to analyse data from a factorial design, but I don't have all combinations of factor levels, and I have repetition for the combination. As this configuration differs from book's examples I'...
1 vote
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Possible to treat ordinal variables as continuous for fractional design defining relation?

I am looking at performing a DOE using the Response Surface approach (control and noise modeled together) for a group of 2 Continuous Control, 1 Continuous Noise and 3 Categorical variables. 2 of the ...
3 votes
1 answer
46 views

Design of Experiments: Factorial design 2^2 with center point added. Does it make sense?

This question is about factorial design of experiments, let's say with two factors $x_1$ and $x_2$ in the following picture. In a $2^2$ factorial design there would be only the black circles. But what ...
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How to deal with statistically insignificant factors?

I used $2^4$ factorial design to screen significance of the factors $A$, $B$, $C$ and $D$. It turned out that $A$ and $B$ were significant, whereas $C$ and $D$ were not. Since there is no need to ...
1 vote
1 answer
213 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. ...
1 vote
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15 views

Blocking in $3^2$ fractional replicated design of experiments

I'm new to design of experiments and I'm planning an experiment which involves 2 factors at 3 levels ($3^2$ design). I'm using 3 levels as I think that there will be some non linearity, but I cannot ...
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AlgDesign-implementation never moves below 90% D-efficiency (Factorial Survey)

I'm currently researching Factorial Surveys and am trying to implement D-efficiency-designs in the AlgDesign-package. My first step was to run simulations as to uncover the relation between the number ...
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1 answer
29 views

Help with Excel's Regression Output

I'm a junior engineer at a small biotech company and have some (real) data from a fractional factorial DoE (3 factors, 2 levels, 4 test conditions with six replicates each). Currently, we use excel to ...
1 vote
1 answer
743 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 ...
3 votes
1 answer
339 views

What are the advantages/disadvantages of design of experiments (DoE) versus stochastic optimization methods

I am working in a project to assist an experimental team in optimizing reaction conditions. The problem involves a large number of dimensions, i.e. 30+ reactants which we are trying out different ...
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Does it make any sense to consider bootstrapping a $3^2$ factorial design?

Suppose I have two factors, $A = (A_1,A_2,A_3)$ and $B=(B_1,B_2,B_3)$, each at three levels, associated with a response $Y$, which is averaged over $N$ values. For example, the pairings would look ...
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Suggestion Needed about Design Experiment

As a part of my coursework, I'm supposed to be designing an experiment for an online cab service provider to understand the following: Whether letting the cab driver know the drop location of the ...
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2k factorial experiments with Yates Algorithm and One-way ANOVA test

I studied for a Six Sigma Certification, and I'm stuck on the 2k factorial Design of Experiment with Yates Algorithm and the One-way ANOVA hypothesis test. I correct replicate, on my excel, the Yates ...
3 votes
2 answers
411 views

Why are models based on coded (-1,1 etc) and non-coded variables (as they are) very different? What should I use for publications?

I am doing factorial experiments in R. I noticed when I use my variables as they are vs. coding them into -1,1, they are all very different. Here is my sample code. ...
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1 answer
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How to select runs from a full factorial experiment design matrix to build a fractional factorial design

I have a design matrix with 18 runs. A and B are three-level categorical variables (low, mid , high and small, medium and large), and C is a two-level categorical variable (male, female). Here's an ...
1 vote
1 answer
53 views

$2^k 3^l$ factorial design

I'm looking for a reference for a $2^k 3^l$ fractional factorial design. Do such things exist? I could use a D-optimal but would prefer a clean aliasing structure. Any tips on software also good. Use ...
2 votes
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How to deal with large combinations of factors

I am faced with a new problem that I cannot really tackle with the way I usually do my analyses and would appreciate any input you may have. The research goal is to identify the factors and ...
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16 views

How to categorize data by combining the IVs (Independent Variables) to run a factorial ANOVA test on JASP?

How do I clean up a Likert scale data set taken from qualtrics survey platform to run a factorial ANOVA test to make it 2x2 (2 levels)? NOTE: Questions are randomized and structured as: High Normative,...
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Finding maximum (maxima) for result data with multi-dimensional in- and output and multiple levels (fractional factorial)

I have a rather expensive simulation with six or more variable input parameters (with up to five different levels), and two output parameters. I already scanned over a large range of parameters and ...
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1 answer
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Confidence interval for the gender effect with management employment area

Suppose we have the following Factorial Experiment: A university wants to assess the starting salaries of their MBA graduates. The study looks at graduates working in four different employment areas: ...
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Individual Covariate in Fractional Factorial Design?

I want to make a marketing experiment (sending an e-mail) with fractional factorial design. I will send this e-mail to a mailing list consist of 660 members. I have 6 factors and use the 1/2 fraction....
0 votes
1 answer
48 views

Picking interaction effects for PB design and Hamada-Wu analysis

I am trying to use Plackett-Burman design to construct a design matrix for $OA(12, 2^{11})$. However, my experiment has only $6$ main effect factors. Similar to the well-known Cast Fatigue experiment, ...
1 vote
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32 views

Setup and analysis of deterministic simulation (Design of experiments, ANOVA)

My problem is as follows: I have a time series simulation (implemented in Python), which is roughly about an abstract modeled storage object digesting and creating energy flows. These (resulting) ...
6 votes
1 answer
573 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 ...
0 votes
1 answer
81 views

Making sense of an actual equation obtained after Box-Cox transformation

I have recently performed and analysed an experiment and I am currently stuck on making sense of the outcome. Any help would be much appreciated. The experiment consists of a simple DC voltage source ...
1 vote
1 answer
63 views

Quasi-random sequence with discrete variables with differing number of levels

My question is probably worded incorrectly but here it is: I have (say) 3 discrete random variables: x1: has 15 levels (uniform pdf for simplicity) x2: has 3 levels (uniforms) x3: has 4 levels (...
2 votes
1 answer
59 views

How do you analyze an unbalanced fractional factorial design?

I'm interested in learning about unbalanced fractional factorial designs. If they are possible to analyze, what are the drawbacks to using them? Just usual loss of orthogonality? How does analyzing ...
5 votes
1 answer
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A theoretical question on fractional factorials

Very much in need of help interpreting this if anyone is available.. Thank you! Fractional factorials that include many factors can sometimes have a surprisingly low number of experimental conditions ...
1 vote
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13 views

Variance of effects in $2^kr$ factorial design

I'm working through The Art of Computer Systems Performance Analysis, a statistics book focused on analyzing computer performance, and I don't follow the logic for computing the variation of effects ...
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71 views

Treatment combinations in different blocks for a $2^6$ design with partial confounding

Let us consider a $2^6$ design in 8 blocks with ABCD, BCE and ADEF as independent effects are chosen to be confounded with blocks. Q.1 $\:$ Write down the treatment combinations in the principal ...
1 vote
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One corner point duplicate and two level full factorial design main effects calculation

I conducted a series of experiments corresponding to a full factorial design with 3 factors and two levels per factor. I entered the data in a software (minitab, not sure if relevant) the calculation ...
1 vote
0 answers
72 views

Response surface design for factors with two levels

I would like to fit a response surface to a system (actually, a computer model of a complex physical system) with 15 parameters that can be either on or off (ie 2 levels only). There could be ...
2 votes
0 answers
72 views

De-aliasing two-factor interactions in a Plackett-Burman design

what I've got so far is a 2-level experiment design with 10 factors and 32 experiments, which is made of a resolution III Plackett-Burman design that I folded (complete foldover) so that it is a ...
3 votes
1 answer
93 views

How to extend Plackett-Burman design to further explore the interactions?

My situation is as follows: I have built a 2-level Plackett-Burman design with 10 factors (some are actual 0/1-variables, the others are numeric and I used the minimum and the maximum) and 32 ...
5 votes
1 answer
184 views

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,..., ...
0 votes
2 answers
357 views

How to test for a synergistic effect of A & B with proportions of treatment effects, if I don't have the full 2x2 table?

I currently have a 2x2 table of proportions for treatment effects that looks like: \begin{array}{lll} & \text{Treatment } A & \text{Without Treatment } A \\ \text{...
1 vote
0 answers
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Is there value in assigning a dimension-specific weighting when calculating the main effect?

I've been looking into factorial designs and noticed an interesting property. Is this simply a mathematical trick or can we attribute some 'meaning' to it? Say we have a $2^k$ design where k = 3 here....
1 vote
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318 views

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, ...
1 vote
1 answer
94 views

Why is there aliasing in a full-factorial design?

I am using the R package AlgDesign to evaluate the design of a simple full-factorial experiment, tweaking an example from R Bloggers. I've specified ...
3 votes
1 answer
862 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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232 views

Bayesian updating of log-normal parameter after observation of poisson process

I am trying to update my estimate of a parameter (error rate) which has a prior log-normal distribution using an observation of errors (presumed to be Poisson distributed). However, I am having some ...
4 votes
1 answer
174 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). For the experiment, I plan to have 4 runs in 12 blocks and 40 ...
3 votes
1 answer
139 views

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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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 (...
0 votes
1 answer
109 views

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 ...
5 votes
1 answer
3k 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 ...
1 vote
1 answer
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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 (...
0 votes
1 answer
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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 ...