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.
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
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?
Fig 1C of the Replication Study: Melanoma exosomes educate bone marrow progenitor cells toward a pro-metastatic phenotype through MET uses an odd (to me) three stage normalization procedure for the quantified western blots. The authors compared blot values between a treatment (shMet cells) and a control (shScr cells) using GAPDH to normalize the values. The three stages of the normalization are
first, the value for the Antibody levels were normalized by the value of a reference (GAPDH) for each Set.
Motivation: https://pubpeer.com/publications/8DF6E66FEFAA2C3C7D5BD9C3FC45A2#2 and https://twitter.com/CGATist/status/1175015246282539009
tl;dr: Given the transformation done by the authors, for any response in day_0 that is unusually small, there is automatically a response in day_14 that is unusually big and vice-versa. Consequently, if the mean for day_0 is unusually small, the mean for day_14 is automatically unusually big, hence the elevated type I error with an unpaired t-test. The transformation is necessary and sufficient to produce the result (meaning even in conditions where a paired t-test isn’t needed, the transformation still produces elevated Type I error).
Set up Normal distribution Type I error Power Right skewed continuous – lognormal What the parameterizations look like Type I error Power This 1990-wants-you-back doodle explores the effects of a Normality Filter – using a Shapiro-Wilk (SW) test as a decision rule for using either a t-test or some alternative such as a 1) non-parametric Mann-Whitney-Wilcoxon (MWW) test, or 2) a t-test on the log-transformed response.
Some background (due to Sewall Wright’s method of path analysis) Given a generating model:
\[\begin{equation} y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \beta_3 x_3 \end{equation}\] where \(x_3 = x_1 x_2\); that is, it is an interaction variable.
The total effect of \(x_1\) on \(y\) is \(\beta_1 + \frac{\mathrm{COV}(x_1, x_2)}{\mathrm{VAR}(x_1)} \beta_2 + \frac{\mathrm{COV}(x_1, x_3)}{\mathrm{VAR}(x_1)} \beta_3\).
If \(x_3\) (the interaction) is missing, its component on the total efffect is added to the coefficient of \(x_1\).
