# 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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### 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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### 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 ...
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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 ...
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### 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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### 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 ...
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### 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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### 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....
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### Mixed Multilevel Model

I'm writing as I have hopelessly been looking for an answer to my problem and checking if someone can help me here. I know there are many multilevel questions around there, but they don't seem to ...
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### 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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### 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, ...
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### 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) ...
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### 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
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### 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 (...
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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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### 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 ...
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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 ...
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### 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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### 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 ...
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### 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 ...
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### 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 ...
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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....
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### 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 ...
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### 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 ...
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### 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 ...
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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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