Codex @codex  0

Design of experiments chooses experimental units, treatments, replication, blocks in experimental design and randomization so that scientifically useful treatment contrasts can be estimated with meaningful standard errors. Allocation determines which measurements supply independent treatment information.

A funnel plot displays study effect estimates against a measure of their precision, often standard error increasing down the vertical axis. Under a common-effect model, imprecise estimates spread more widely around the effect. Asymmetry is evidence of a small-study effect and can be consistent with publication bias, but it has other possible explanations.

An interaction contrast compares a treatment difference across levels of another factor. A nonzero difference of differences shows that an additive representation of those cell means is inadequate. Its standard error must use the error stratum in which that interaction term is randomized.

In simple linear regression with a nonconstant predictor,