The design of experiments (DOE) is the study of how to structure an information-gathering exercise where variation is present. In statistics, controlled experiments are usually implied, meaning that study units are randomly assigned to conditions where levels of a variable have been independently ...

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Do I still need ergodicity if I have multiple/infinite time series of the same data generating process?

The main reason we need ergodicity (and therefore stationarity) is, as Shalizi puts it: The ergodic theorem is important, because it tells us that a single long time series becomes ...
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Nested mixed experimental design with crossed factors for laboratory validation procedure: how to model it?

I have been asked to analyze the following laboratory experiment: 14 donors’ red blood cell samples are typed for rare antigen-asset recognition by an automated procedure (machine), which returns a ...
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the Randomised Complete Block Design

I got the following output using the Randomised Complete Block Design: ...
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One-way Fixed model

Duppose we have 12 treatments, and to start the experiment we choose these treatments, randomly. However, after selecting one treatment, all the samples are gathered and we shift to the next treatment ...
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What is my study design

I have two sample groups and I will not be manipulating the participants in any way so this is not an experimental design. However I wish to compare the results of the two samples (between subject ...
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17 views

What is the proper way to increase power when randomizing at the village level?

Let's say that we have a hypothetical RCT with the following information: --We are interested in seeing whether a particular belief held among some individuals in a developing country can be ...
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Pros and cons of various designs

Help me with this question. I'm clueless. CROSSOVER DESIGN PROS- Gain in precision- compare approaches within students, so variation between students is eliminated. CONS- Susceptible to carry-over ...
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How to correctly analyzed a mixed within-subjects/between-subjects design?

I recently ran a perceptual study in which I aimed to measure how emotion recognition accuracy from whole-body motions changed when two type of body representations were used. Five actors Ai with ...
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Confounding variable that is the focus of experiment

The wiki defines confounding variable as an extraneous variable in a statistical model that correlates (directly or inversely) with both the dependent variable and the independent variable ...
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1answer
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Ranking Data Comparison

I'm currently analyzing my experimental data and I have a question about comparing two variables. In the experiment I have a question which asks respondents to rank a set of pictures based on their ...
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39 views

When is there a point for using regression with controls to analyze experimental data?

Many randomized controlled trials in economics (and probably other sciences as well?) use regressions to analyze data obtained from experiments. In the simplest setup with binary treatment, assuming a ...
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Why use Coded Variables in Experimental Design?

Full-disclosure, I'm not sure if this ENTIRELY on-topic. Often times, most texts will suggest that we code our variables. i.e. If we move from 345 to 350 to 355, we code our variables as -1, 0, and ...
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regarding generating synthetic data simulating the real data

We are trying to develop some predictive models. The current scenario is that we have to rely on synthetic data at first since the real data set will not be available quite soon. It is understandable ...
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22 views

Questions about mixed model design with repeated measures/nesting/incomplete design

I have data from a incomplete factorial experiment with repeated measures and potential nesting and am trying to figure out 1) the right way to design the mixed model to analyze the data, and 2) how ...
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Which analysis do I use for this experimental design?

Seeking feedback from those with a better quantitative mind than my own! Currently preparing my doctoral research proposal. I want to determine the impact that various levels of technology ...
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12 views

Regression Discontinuity Design Using Time of the Policy Change as the Assignment Variable

I am trying to study the impact of a policy change on user behaviour. In my context, a new policy is implemented on a specific week. Hence, everyone is exposed to the new policy at the same time. I ...
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1answer
34 views

Experimental Design with Factorial Block Structure

I'm designing a language-learning study with maybe 30 participants. My collaborators want each person to experience both of the methods we're using, so we are planning a crossover design. In addition ...
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Degrees of freedom in general full factorial design of experiments with missing observations

I am trying to calculate the total sum of squares SST and the degrees of freedom of an experiment with four features and three levels for each feature. It results in 3x3x3x3 samples (of course). ...
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32 views

Basic question about central limit theorem and sampling distributions

The CLT states that "if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population, then the distribution of the sample means will be ...
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1answer
38 views

2x2 experimental design: t-tests vs. mixed anova analysis

I have conducted an experimental study, with 1 within-variable (time: T1 and T2) and 1 between-variable (group: control and treatment), measuring just one dependent variable. I understand that this ...
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Incomplete randomized designs with uneven block sizes

Say we aim to estimate the effect of a treatment on the population and that we have, e.g. the following 12 experimental units: ...
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How to analyze $2^k$ design with replicates in SPSS (or R)?

I want to tune the parameters of an optimization algorithm. Since there are $4$ parameters: A, B, ...
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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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20 views

What analysis to use? IV: multiple interdependent levels, DV: continuous variable

My dependent variable is a continuous variable, ranging from 0 to infinity. However, my independent variable has multiple interdependent levels. To illustrate, A person has 6 attributes: A1, A2,... ...
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14 views

Power analysis for polynomial regression

There are two variables, $X$ and $Y$. I am interested in the shape of the relationship between $X$ and $Y$, specifically whether it is linear, curved, or some higher order polynomial function, because ...
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Factorial ANOVA Hypothesis

If say I have an experiment with two categorical factors, a and b, in response to the variable x, and I set it in such a way that I try all possible combinations of the two factors, this is factorial ...
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2answers
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What statistical test is appropriate for paired data where the same subjects are tested at multiple times?

In the test in question, we have data [measurements of discomfort] for the same subjects with different virtual reality experiences. We took multiple measurements of discomfort over the course of the ...
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Statistical design of experiments revealed some surprises — what next?

I recently became the manager of a complex piece of laboratory equipment. It has many knobs and dials to turn, and the different knobs and dials affect the significantly affect the responses I try to ...
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Experimental design: Same randomly selected stimuli versus different randomly selected stimuli in every subject

In an experiment, we’re going to present randomly generated stimuli to multiple subjects one trial at a time and measure neural responses to them. The stimuli are randomly generated to satisfy the ...
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Which tests should I use for my experiment

For each participant in my trial I have 35 parameters ($P_1,\ldots,P_{35}$), each measured at 4 different time points. Furthermore, the participants are partitioned into two groups $A$ and $B$, each ...
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How to model a multiple continuous factor, single response between 0 and 1 experiment

I have a fractional factorial design experiment that varies 12 continuous factors high and low that result in a single response which is 0 <= y <= 1. The distribution of the response appears ...
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12 views

Two groups: first with one measure, second with two measures: how to test between group difference?

In my research I have two groups: 1) Healthy group 2) Patients with disease I have a variable (quantitative) that measures some skin property for each patient. But diseased patients have two types of ...
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35 views

Create balanced incomplete block design with groups in R

I found the below R function on surveyanalysis.org. It creates balanced incomplete block designs (BIBD). I am trying to figure out how to alter the code to be able to partition the items per block ...
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Factorial experiment in GLR model

I am reading some lecture notes on Factorial Experiments. This is perhaps a stupid question. Remark 6.1 In this course we only treat the linear model. The response variable may however be a (Poisson) ...
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25 views

What would be a proper statistical test for multiple models and model selection?

Suppose I have a data set of N observations (n = 1...N) for out-of-sample estimation and values of ($y_n$). I have also ...
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Is the cluster experimental design the same as the block experimental design?

Is the cluster randomised controlled trial the same as the randomized block design? They seem to both have the same goals.
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selecting statistical test

I wish to analyse data regarding physical activity levels of a population (unaware yet if it will be parametric or non parametric) at baseline, week 12 and follow up at three months. My research ...
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1answer
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Variance of subsample from a distribution

I've simulated $N$ variables from a distribution $X_i \sim N(0,\sigma^2)$. I now take a subsample of size $n$ from this sample. Let the indices of this subsample be denoted $S_n$. I was wondering ...
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What is good modern book/resource on advanced experiments?

I am looking for resources (doesn't have to be a single book) that would cover some of the more challenging cases of experimental design and statistical analysis. Some of the cases I would like to be ...
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9 views

Experimental design multilevel

I am creating a vignette study with three instances per person who are randomly assigned to one of 12 conditions. The 12 conditions are different combination (fully-crossed design) of dummy codes ...
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12 views

Experimental Power Calculation with Uneven Split and Correlated Observations

I want to run an experiment. I have prior knowledge that the treatment is better, so I will run the experiment with my $N$ units with 80% of the response in treatment and 20% of the response in ...
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2answers
89 views

Statistical rationale for a 3+3 design

I am starting to learn about design of experiments for clinical trials and in particular I am interested in understanding the statistical rationale for the 3+3 design used for dose escalation in Phase ...
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22 views

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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Optimization using Multiple Regression Equation from DOE vs Reponse Surface Methodology

IF my understanding is correct, to optimize a response, we normally use Response Surface Methodology. However, I came across this article : ...
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28 views

Does Imposing a Constraint Make a Method More Powerful?

Suppose we have 100 patients in a randomized trial. Fifty of them are in the treatment group and the rest are in the placebo group. This is a longitudinal study so that we measure the response from ...
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44 views

Split-Split-Plot or nested ANOVA using lme

I have a simple design but I do not know how to handle it. I have a nested anova (or a split-split-plot anova). I have three grazing treatments (Grazing, coded as Gra1, Gra2, Gra3), replicated each ...
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1answer
49 views

Book recommendations for Design of Experiments

What are some good books on general design of experiments ? Currently I am reading "Design and Analysis of Experiments" by Douglas Montgomery , it has too much mathematical details which are little ...
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24 views

Quasi-experiment: sample size & statistics

I am conducting a quasi-experimental research in a school, where I have access to 100 students who are chosen as classrooms and who will be the participants of the study. I am interested in the ...
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1answer
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Which test to use for 2 groups with 2 subgroups each?

I recorded the pumping rate of two types of worm: normal and mutant, with n=6 the number of worms per type. Then, I exposed these types of worms to a drug. BUT I used a different batch of worms this ...
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17 views

Defining Contrast Matrix

Suppose I have a binary Covariate $X$ which is defined as $$ X = \begin{cases} 1, & \text{if treatment group} \\ 0, & \text{if placebo group} \end{cases}$$ The model is $$\mathbb E[Y] = ...