Think about that. If the bar was 25mm OD with .25" wall thickness that would mean that the inside diameter (hollow section) would be 12.3mm. That would leave an equivalent stiffness of 12.7mm i.e. the 25mm hollow bar is WAY less stiff that a stock 20mm bar. (all hypothetical bar sizes) The math is quite complicated.
My saying that a 25mm hollow is roughly equivalent to a 22mm solid is a gross oversimplification. The actual wheel rate of a bar is also influenced by the lever arm of the bar. A bar with a 12" lever arm is going to be much less stiff than a bar with a 1" lever arm as that arm (as measured from the center of the portion of the bar that spans the bushings) due to the mechanical advantage of the longer arm. Example: a 50mm bar with a 12" lever arm could actually have an equivalent stiffness that is less than a 10mm bar with a 1" lever arm. (just for reference and very likely not the case, but you get the point)