Paired t-test as a special case of linear model and hierarchical (linear mixed) model

Update – Fig. 2A is an analysis of the maximum endurance over three trials. This has consequences. Figure 2A of the paper Meta-omics analysis of elite athletes identifies a performance-enhancing microbe that functions via lactate metabolism uses a paired t-test to compare endurance performance in mice treated with a control microbe (Lactobacillus bulgaricus) and a test microbe (Veillonella atypica) in a cross-over design (so each mouse was treated with both bacteria).

What does cell biology data look like?

If I’m going to evaluate the widespread use of t-tests/ANOVAs on count data in bench biology then I’d like to know what these data look like, specifically the shape (“overdispersion”) parameter. Set up library(ggplot2) library(readxl) library(ggpubr) library(cowplot) library(plyr) #mapvalues library(data.table) # glm packages library(MASS) library(pscl) #zeroinfl library(DHARMa) library(mvabund) data_path <- "../data" # notebook, console source("../../../R/clean_labels.R") # notebook, console Data from The enteric nervous system promotes intestinal health by constraining microbiota composition Import read_enteric <- function(sheet_i, range_i, file_path, wide_2_long=TRUE){ dt_wide <- data.

GLM vs. t-tests vs. non-parametric tests if all we care about is NHST -- Update

Update to the earlier post, which was written in response to my own thinking about how to teach stastics to experimental biologists working in fields that are dominated by hypothesis testing instead of estimation. That is, should these researchers learn GLMs or is a t-test on raw or log-transformed data on something like count data good enough – or even superior? My post was written without the benefit of either [Ives](Ives, Anthony R.

Should we be skeptical of a "large" effect size if p > 0.05?

Motivator: A twitter comment “Isn’t the implication that the large effect size is a direct byproduct of the lack of power? i.e. that if the the study had more power, the effect size would have been found to be smaller.”1 2 A thought: our belief in the magnitude of an observed effect should be based on our priors, which, hopefully, are formed from good mechanistic models and not sample size“.3

“A more efficient design would be to first group the rats into homogeneous subsets based on baseline food consumption. This could be done by ranking the rats from heaviest to lightest eaters and then grouping them into pairs by taking the first two rats (the two that ate the most during baseline), then the next two in the list, and so on. The difference from a completely randomised design is that one rat within each pair is randomised to one of the treatment groups, and the other rat is then assigned to the remaining treatment group.

The statistical significance filter

1 Why reported effect sizes are inflated 2 Setup 3 Exploration 1 4 Unconditional means, power, and sign error 5 Conditional means 5.1 filter = 0.05 5.2 filter = 0.2 1 Why reported effect sizes are inflated This post is motivated by many discussions in Gelman’s blog but start here When we estimate an effect1, the estimate will be a little inflated or a little diminished relative to the true effect but the expectation of the effect is the true effect.