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For example, in answering: "a) How does Method A improve students' performance?", I would cite a general underlying factor linked to performance. For example, I generally recommended when I have my tutoring cap on (disclosure, I am not a professionally trained teacher) is to suggest brain exercises and even a proper diet, that supports brain ...


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Equivalent null hypotheses Yes When you are asking the question about significance then you relate to hypothesis testing. For your situation, the hypotheses $H_0: \Delta = 0$ and $H_0: \Delta\% = 0$ are equivalent if you assume that 'mean of control' is non-zero (and if you do not assume that, then the $\Delta\%$ becomes a problematic definition due to the ...


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The absolute (delta) and relative (delta%) changes are different random variables, so you should try to calculate the ratio-based standard errors, CIs, and p-values if you care about the latter. This will not change your decision most of the time, but you will come across examples where it does matter (wider CIs, higher p-values, etc.). Ratios can be tricky ...


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The most straightforward way would be to specify a caliper. A caliper is the maximum distance two units can be apart from each other before they are not allowed to be matched. Any treated units that do not receive a match because there are no remaining units within their caliper are left unmatched and discarded. The tighter the caliper, the more units are ...


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I try to sum up what I‘ve learned from the comments to close the question: Linear mixed effect models do not necessarily need normally distributed data; here is a link to another Post dealing with the same question Not the data itself but the residuals of the model should be normally distributed One of the most important things to look at while working with ...


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Here are two important things to consider: As in all statistics contexts, we assume that data are measured with error. The larger the experimental region, the more accurately we are able to estimate the equation of the response surface, assuming that our model is correct. As has been stated by GEP Box and others, all models are wrong, but some are useful. ...


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Do you know about 'propensity score matching'? I think it does what you want. Here is an example https://www.researchgate.net/publication/223906464_Family_Group_Decision_Making_a_propensity_score_analysis_to_evaluate_child_and_family_services_at_baseline_and_after_36-months


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Your post misses some essential information, such as the nature of the variables and the goal of the experiment. But one approach you can try is to first generate the full factorial design, and then choose some fraction by D-optimality. D-optimality is implemented in R in the package AlgDesign and certainly many other places. On this site you can find some ...


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Trial here is the single experimental unit, we could say the "atom of the experiment", which leads to one observed value each. So here it is ... presenting three rhythmic patterns (each consisting of 5 sounds) to participants and they're supposed to say which one is different from the other two ... which results in one observed value, which here ...


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I would model the fixation time with a mixed effects model, with a random intercept for ID, and maybe also a random slope within ID. Using the R package lme4 such a model could be written as lme4::lmer( fixation ~ index*answer + (1 | ID), data=your_data_frame ) which means that index, answer and their interaction are fixed effects while there is a random ...


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MichiganWater mention this is a split plot design, Temperature is the plot and the recipe is the subplot. Using R to design the experiment: library(agricolae) library(tidyr) Temp <- c("T1", "T2", "T3") Recipe <- c("R1", "R2", "R3", "R4") #Oven <- c("O1", "O2", ...


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Here are some similar questions with answers, maybe a duplicate: How to use Design of Experiment (DoE) to reduce the number of simulations? Best DoE method to fit Gaussian Process Regressor Is there an equivalent to LHS for a discrete input space? User @neverKnowsBest have this answer in a comment: I've seen people use JMP to fit gaussian process ...


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How many runs can you do before you have to change the parts that run down? Maybe define those runs as a block, and use a split-plot design, see Understanding the split plot. If I have misunderstood, and you never change those parts, then maybe you just needs to model the correlation and take account of it in the analysis.


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One standard way of expanding an experiment is to use D-optimal designs. The AlgDesign R package (on CRAN) supports that. You should probably have the new runs in an additional block.


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You could look into response surface designs, see this posts and this excellent book: Response Surfaces, Mixtures, and Ridge Analyses. You could start by doing some slight extrapolation from your estimated model and do some preliminary experiments along that extrapolation.


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You are looking for split-plot design. The name comes from agricultural land experiments where there is a treatment that have to be applied at large plots of land, an example could be fumigation by aircraft. Then those large plots are further split in smaller plots where other treatments are applied. Your difficult-to-vary variable corresponds to the large ...


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In the same way we don't know the form of the outcome model (which is why we use propensity score matching in the first place), we don't know whether regression completely removes all confounding in a matched sample. Matching makes it more plausible for confounding to be removed by regression; this is the main thesis of Ho, Imai, King, and Stuart (2007), the ...


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You want to make linear regression using only one categorical regressor. Of course you can do it, maybe it is better if you create dummy variables before performing the regression. https://www.moresteam.com/whitepapers/download/dummy-variables.pdf for some information about the use of dummy variables


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