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The short answer is that there is no formal definition of experimental design. You have as many possible experimental designs as you have experiments. The list you provided is quite exhaustive, but many of these elements will be irrelevant for simple experiments. Conversely, if you perform sequential experiment design (i.e. if the design of experiment $t$ ...

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It seems that the OP is mainly concerned with conducting a t-test for unequal sample sizes. However, imbalanced sample sizes are in general not a huge problem when applying the t-Test. The t-test is actually very stable against sample size characteristics as deviations from normal distribution and imbalanced sample sizes (if sample sizes are large enough!)....

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If your group sizes are large enough, you are well powered to detect effects so small as to essentially be useless. Here is an example in R. I generate 200,000 observations from two groups whose means differ by 0.01. library(tidyverse) replicate(1000,{ x = rnorm(200000) y = rnorm(200000, 0.01, 1) t.test(x,y)$p.value<0.05 }) %>% mean I ... 0 With these sorts of experiments there is always the question of external validity. To which extent are associations (and theories about what causes these associations) amongst Berkeley undergraduates willing to take part in experiments transferable to more interesting populations? Leaving that aside: It is indeed an observational study with respect to ... 0 I would set up the analysis this way (using R) library(lme4) mod <- lmer(score ~ condition*day + (1 | subject), data=your_data_frame) summary(mod) You say want to evaluate interactions between "condition" and "day", but the model you have written does not admit interactions. Within the main effects model you have estimated (no effect for day), the null ... 3 Start by considering how precisely you need to know the variability among runs. That should be informed by the differences in sensor resistances you ultimately want to be able to detect among gases. When you eventually get to the point of comparing gases, note the following rule of thumb* for the number needed in each group ($n$) to detect a difference in ... 1 This is a really good question. There probably isn't a clear answer. It comes down to: Which is more consistent, the set of differences or the set of ratios. If one experiment goes from a mean of 5 to a mean of 10, and another goes from a mean of 20 to a mean of 40, do you think those are consistent (becuase they both are doublings) or do you think those ... 1 You say " ... that the classical ANOVA (and ANCOVA) experimental design techniques can be expressed as linear regression ... ". I think this is a confusion, fundamental experimental design concepts such as blocking, randomization, replication (and also treatment design concepts), have nothing to do with linear models in itself. This concepts are equally ... 0 Tentatively, we could write a model for this experiment like $$Y_{ijt}=\mu + \delta_i + \alpha_t + \epsilon_{ijt}$$ as a starting point, where a completion of the model need some distributional assumptions on the error term$\epsilon_{iijt}$. In addition you could include an interaction term$(\delta\alpha)_{it}\$. You have not told us about any ...

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This is often called algorithmic design or optimal design. The last name hints on some optimality criteria, and there are many to choose from! Much used is D-optimality. Some related posts here is Motivations for experiment design in statistical learning? and Is DoE applicable to collect data for machine learning model?, look at the links and references in ...

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