On the A320, during rotation you can find a typical example of this.
The IRS supplies the normal indications of VSI, the ADR is used as backup.
During rotation, the VSI points up almost instantly, while the altimeter tape is showing an initial descent (mind you, 20 feet or so...) as the static ports are slightly on the lower side of the fuselage, the aircraft starts to pitch up, and the static ports are exposed slightly more to the relative wind.
Flex