Each point sits at (X = physiological effect, Y = sighting reports, Z = local pollution, drawn as depth). Both X and Y are generated purely from Z plus independent noise — there is no direct X→Y or Y→X wiring in this model. Rotate freely, or hit "View along confound axis" to look straight down the Z axis: from that angle the cloud flattens into the same misleading X–Y trend a 2D analysis would show, because depth (the true driver) is hidden.
The slice controls do the opposite of hiding Z — they isolate it. Restrict the sample to a thin pollution band and only points sharing nearly the same Z remain lit. Within that band, Z is (almost) constant, so it can no longer drive X and Y apart — and the correlation computed on just those points should sit close to zero, matching the full-sample partial correlation:
r(X,Y|Z) ≈ r(X,Y | Z restricted to a narrow band)
r(X,Y|Z) = [ r(X,Y) − r(X,Z)·r(Y,Z) ] / √[(1 − r(X,Z)²)(1 − r(Y,Z)²)]
- Confound strength — how hard pollution pulls X and Y apart from the origin; higher values stretch the cloud into a longer, more convincing diagonal streak.
- Slice centre / width — choose which pollution band to isolate and how thick it is; a narrower slice more cleanly isolates "same pollution, does X still predict Y?"
- View along confound axis — snaps the camera to look straight down Z, reproducing exactly what a 2D scatter (which never measured pollution) would show.
Real-world relevance: slicing by a suspected confound is the manual, visual version of stratified analysis or regression adjustment — the standard toolkit for checking whether an association survives once a shared cause is held fixed.