Garden centers often advertise applying gypsum to your lawn to “decompact” the soil by improving the structure of clay soil. This only works in soils common in the arid western US where there is much more sodium than calcium in the soil. This does not work in Indiana because the parent material for most of Indiana soils is limestone and thus calcium (Ca++) is far more common than sodium (Na+) in our soils. Instead of gypsum, consider aerifying every spring and/or fall to reduce compaction and improve plant health. Aerifying with large tines and punching 20-40 holes/sq. ft. will produce the best results.
Really want to know why gypsum doesn’t work in Indiana? In arid parts of the country, sodium occupies many of the cation exchange sites in the soil and since it is only a +1 charge, soil colloids tend to disperse and are easily compactable because of poor soil structure. Adding gypsum (CaSO4) allows the Ca++ to replace the Na+, the Na+ is leached out as Na2SO4, and the soil tends to flocculate (glued together on the microscopic level) with more Ca++ on the exchange sites, improving soil structure and thus less prone to compaction. Since there is far more calcium than sodium on exchange sites in Indiana soils because limestone is our parent material, adding calcium via gypsum has little or no effect on the soil.