1/2 " difference in side wall height is an approximation. Higher tyre walls make up the 1" difference in diameter between 15" and 16" wheels , ie 1/2" more height between the wheel and the road, and 1/2" more at the top of the wheel where it makes no difference to handling etc.
To be more accurate the profile of the tyre as shown in tyre size , eg 185/60/R15, is a percentage of the tread width. . Thus 60% of 185 mm is 111m side wall while its 16" equivalent 185/55/R16 is 55% of the same 185mm tread width ie only 101.75 mm . 10mm less (approx) , which is 0.4 " , not quite half an inch. Not only that but measurement will be of a curved rubber side wall, not just the extra height between wheel rim and road surface.
Things get more complicated if tread width changes. For instance a 195/60/R15 tyre side wall is 60% of 195 = 117 mm not 111mm