# Bootstrap confidence intervals when sample size is really small

TL;DR A sample table from the full results for data that look like this Table 1: Coverage of 95% bca CIs. parameter n=5 n=10 n=20 n=40 n=80 means Control 81.4 87.6 92.2 93.0 93.6 b4GalT1-/- 81.3 90.2 90.8 93.0 93.8 difference in means diff 83.

# Analyzing longitudinal data -- a simple pre-post design

A skeletal response to a twitter question: “ANOVA (time point x group) or ANCOVA (group with time point as a covariate) for intervention designs? Discuss.” follow-up “Only 2 time points in this case (pre- and post-intervention), and would wanna basically answer the question of whether out of the 3 intervention groups, some improve on measure X more than others after the intervention” Here I compare five methods using fake pre-post data, including

# Using Wright's rules and a DAG to compute the bias of an effect when we measure proxies for X and Y

This is a skeletal post to work up an answer to a twitter question using Wright’s rules of path models. Using this figure from Panel A of a figure from Hernan and Cole. The scribbled red path coefficients are added the question is I want to know about A->Y but I measure A* and Y*. So in figure A, is the bias the backdoor path from A* to Y* through A and Y?

# "Nested" random factors in mixed (multilevel or hierarchical) models

Setup Import Models as nested using “tank” nested within “room” as two random intercepts (using lme4 to create the combinations) A safer (lme4) way to create the combinations of “room” and “tank”: as two random intercepts using “tank2” Don’t do this This is a skeletal post to show the equivalency of different ways of thinking about “nested” factors in a mixed model. The data are measures of life history traits in lice that infect salmon.

# Estimate of marginal ("main") effects instead of ANOVA for factorial experiments

Background Comparing marginal effects to main effect terms in an ANOVA table First, some fake data Comparison of marginal effects vs. “main” effects term of ANOVA table when data are balanced Comparison of marginal effects vs. “main” effects term of ANOVA table when data are unbalanced When to estimate marginal effects keywords: estimation, ANOVA, factorial, model simplification, conditional effects, marginal effects Background I recently read a paper from a very good ecology journal that communicated the results of an ANOVA like that below (Table 1) using a statement similar to “The removal of crabs strongly decreased algae cover (\(F_{1,36} = 17.
• page 2 of 7

#### R doodles. Some ecology. Some physiology. Much fake data.

Thoughts on R, statistical best practices, and teaching applied statistics to Biology majors.

Jeff Walker, Professor of Biological Sciences

University of Southern Maine, Portland, Maine, United States