# Questions tagged [latin-square]

Latin squares (and rectangles) are two dimensional patterns often used in the design of experiments. They allow for more efficient use of experimental units than a full factorial design, allowing for control of row and column effects, which made them popular in agricultural experiments.

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### Justifying uneven group sizes in an incomplete counterbalanced measures design using a balanced Latin square

I'm working on the statistical analysis of an experiment where we showed 6 videos to a group of people and asked them to rate their effectiveness. In order to handle bias due to the order, we divided ...
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### Usefulness of Latin Square Design

I want to understand the usefulness of the Latin Square Design. Suppose there are two block factors, each with three blocks. There are three experimental groups: A, B, C. One realization of the Latin ...
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### How to derive the Sum of Square for Latin Square with repetition

I am studying the Latin Square Design with n repetitions from https://online.stat.psu.edu/stat503/lesson/4/4.4 Let say we talk about the repetitions case 3 i.e. we ...
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### Experimental design for a 96 well plate

I am designing an experiment that will include an assay on a 96 well plate and could use some advice on the optimal layout. In our experiment we have 12 biological replicates, and each replicate has ...
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### How to generate a latin square for a user study?

I have to do a user study for a paper to see how using or not using tool X affects the quality of something (defined in my study). The study goes like this: participant 1 uses tool X to do task A and ...
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### How to Analyze Latin Hypercube Results

After running an experiment generated by a Latin Hypercube design, what next? Just pick the best point? I guess there’s no ‘modeling’ or ‘curve fitting’ going on right? So you basically just choose ...
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### How many sets of variables do I need to assess all pairwise correlations in a planned missing design

I have 54 variables that I need to correlate, but due to constraints I can only put up a maximum of 16 variables at a time for data collection. At the end of the day, I need estimates of the 1,431 ...
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### How do I write sum of squares and degrees of freedom for multiple Latin squares put together?

I have notes from my professor in which a Latin square model ($s$ treatments in an $s \times s$ square) is described as follows: \begin{align*} Y_{ijk} &= \mu + \alpha_i + \beta_j + \gamma_k + \...
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### Can I use lmer if my experiments include 4 latin square blocks in a single experiment?

(Please understand I am a real novice) I ran an experiment to investigate the interaction between factors. I used 6 factors, namely A,B,C,D,E,F. The whole experiment has 5 blocks and each block by ...
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### How many points for statistical significance in design of experiments

I am running an experiment that includes 27 input data points. The function yields results if we input $2 \leq x \leq 27$ points. I divide my data points in 9 sets of 3 points each. Now, I want to ...
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### 3 Treatment Agronomic Experiment: Latin Square or Randomized Complete Block Design with 4 replicates?

I need help with designing an experiment. Suppose I am testing 2 fertility programs against a control in Lettuce, for a total of 3 groups (Program A, Program B, and Untreated Control). Let's assume ...
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### Using Latin Hypercube Sampling with a condition that the sum of two variables should be less than one

I am building an experimental design with 4 variables defined on (0,1). In notation, $x_i \in [0,1]$ with $i=1,..., 4$). Two of these variables must satisfy the condition that $x_1 + x_2 \leq 1$. ...
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### Repeated measures design: Must each participant receive ALL 4 versions of a given stimulus? [closed]

I am creating a 2x2 repeated measures design where a given stimulus object has four possible versions (2 factors with 2 levels each create 4 unique object versions). In the ideal repeated measures ...
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### Dividing CDF rather than PDF equally in Latin Hypercube Sampling

Returning back to the basics of Latin Hypercube Sampling, I wanted to ask why LHS is a division of CDF into N intervals rather than PDF. I'm having some trouble understanding what the difference is ...
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### Is there a way to check if sample obeys the Latin Hypercube Sampling rule?

I was wondering if there is a way to check if a certain sample of a large size obeys the Latin Hypercube Sampling rule. I know that for smaller samples, I can easily visualize the sample points to see ...
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### Experimental design – Reducing the number of conditions per participant

Let's say I have an experiment where there are 3 conditions, A, B and C. If using a Latin square design, participants would be subjected to all 3 conditions in different orders. However, if the cost ...
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### Experimental Design with two treatment levels, random effects, and technical constraints

I'm trying to plan an experiment and the experimental design is giving me headaches because it's too complex to wrap my only-statistics-101-capable head around. Basically I want to subject plants of ...
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### When should a randomised Latin Square be used rather than a standard Latin Square

I'm looking at Latin Squares. I've seen standard Latin squares, and Latin squares when the rows are randomised, then columns are randomised. When would one be used over the other? It seems as ...
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### WIth Latin square design, is this situation valid?

I have no background in statistics so I would like to know whether I get it right: Q: suppose I evaluate 3 Teaching methods in 3 schools and in 3 classes (First, Second and Third). I know that the ...
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### Repeated randomized 4 by 4 latin square

I have a field setup with 4 treatments in a latin sqaure setup repeated 5 times. A B D C C A B D B D C A D C A B This field setup is enclosed. The setup is ...
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### Can Latin Square combine between- and within-subject design?

I´m doing an experiment and I´m not entirely sure if my design is still the Latin Square Design. I have 2 independent variables: medium and ...
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### Modification to Latin Square Design

I have an experiment where I am having participants rate the readability of 10 different texts. I have 37 participants and I would like them to rate the readability for 6 texts each so that each text ...
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### Cells means model in R for unbalanced Latin square design

I used a 4 x 4 Latin square experimental design recently and have been advised that a cell means - rather than sum of squares - approach is more appropriate because I have an unequal number of ...
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### Balancing out in an orthogonal design

A definition of orthogonality in the context of statistics is An experimental design is orthogonal if the effects of any factor balance out (sum to zero) across the effects of the other factors. ...
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### Latin Square Design ANOVA in R

I have been searching online for an appropriate way to analyse data obtained using a 4x4 latin-square design (and more specifically how to do this in R). I have some sources online that say the data ...
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### Why in latin squares the rows, treatments and columns are said to be orthogonal

I have always heard "orthogonal" in the area of geometry (also please note I am not a native English speaker). I do not understand the following for latin squares (a quote from a text book): ...
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### Orthogonal arrays

This is from a note I found I have one question, could t=3?
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### Latin Hypercube Sampling Asymptotics

I am trying to construct a proof for a problem I am working on and one of the assumptions that I am making is that the set of points I am sampling from is dense over the entire space. Practically, I ...
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### $2^3$ Factorial Design conducted in a Latin Square Design

When does the situation occur to conduct a $2^3$ Factorial Design in a Latin Square Design? What would be the procedure of analyzing data of a $2^3$ Factorial Design conducted in a Latin Square ...
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### 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 is LSD an incomplete three-way layout?

How is the Latin square design(LSD) an incomplete three-way layout? In this context, let me ask also what is a complete layout?
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### What would be a better alternative to two balanced latin squares (human subject experiment)?

Instead of running a certain balanced latin square twice (if you have m experimental conditions but 2 m subjects), what would be a better approach (to cover twice as many of the possible orderings and ...
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### Increase the sample size of a Latin Hypercube study?

I want to create a climate model ensemble, testing 5 parameters (real, uniformly distributed between two values), using a latin hypercube approach. The problem is that I'm not sure how many ...
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### Are non-square latin hypercubes viable?

At https://github.com/OpenMDAO/OpenMDAO-Framework/issues/599 it is stated that non-square Latin Hypercube experimental design is not well defined (I assume that for higher dimensions that means ...
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### Is Latin hypercube sampling effective in multiple dimensions?

I am currently using a Latin Hypercube Sampling (LHS) to generate well-spaced uniform random numbers for Monte Carlo procedures. Although the variance reduction that I obtain from LHS is excellent for ...
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