# 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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### Minimum replications for adequate testing power with factorial design

I currently running an agricultural field study using a 2x2x3 factorial design. I need to collect samples for measuring soil bulk density, which takes a lot of time. There are two sites, 4 ...
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### How do Fractional Factorial Designs relate to 'Response Surface Methodology'?

Fractional factorial designs (FFDs) and Response Surface Methodology (RSM) are both approaches to extracting some information about how multiple interacting factors affect a response variable. Their ...
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### Is there a function in R to give the lack of fit and pure error of an ANOVA completed on a half 2^k factorial with centre points?

I have a half fraction factorial experiment for four factors, meaning I have eight experiments that I conduct. I expect that some of the responses are quadratic and not linear, thus I included centre ...
1 vote
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### Fractional factorial design with mixed categorical and numerical variables analysis for more than two levels

I have an experiment setup that consists of multiple continuous and multiple categorical variables. Right now, I am just using two levels for the categorical variables, allowing me to encode them as -...
1 vote
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### Fractional Factorial Design when some factors have more than 2 levels

Let's say I was conducting an experiment with 4 factors. Three of them have qualitative settings, so I can simply designate one as +1 and one as -1. But one of the factors is numeric, and I would like ...
52 views

### 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 $2\times 2$...
1 vote
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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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### 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
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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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### 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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### 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: ...
538 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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### 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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### 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 ...
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### 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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### 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 ... 93 views

### 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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### 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 ...
1 vote
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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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### 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 ...
1 vote
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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 (...
1 vote
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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 "...
1 vote
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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: ...