since 1940

Fuel consumption method

So your friend just installed a new tuned exhaust system and claims a 25% increase in engine power and you think this is a little much. 

Given that the indicated horsepower of an engine is proportional to the weight of mixture induced into the engine per unit time for a constant fuel/air mixture, there should be a corresponding increase in fuel consumption at full throttle. For those with fuel flow transducers you should be able to accurately measure the increased horsepower.

Cylinder head temperature method

Power requires heat and more power produces more heat. Some of this excess heat finds its way into the cylinder head. To maintain a constant average cylinder head temperature, the mass flow of air must be increased approximately in direct proportion to the indicated horsepower. During climb at full throttle using the same airspeed, air temperature, air density and approximate mixture ratio, cylinder head temperatures should be proportionally hotter with the increase in indicated power.

Because of the heat capacity of the cylinder materials, the CHT doesn't react instantly to changes in engine or cooling conditions. For comparison purposes the cylinder temperatures need to reach equilibrium conditions.