This is going to be one of those very rare times when I differ from fluttermoth
but only with reference to the frequency.
Partial water changes should always be no less frequent than once every week, regardless of "tests." If a problem should arise, additional water changes are usually recommended as a "first step," but everything being good, once a week is best. The voilume can vary depending upon specifics, but generally speaking 1/3 of the tank water should be the minimum amount changed, and 1/2 would be better. I have been doing 1/2 water changes weekly for 20 years, and I know the fish benefit (plants do too).
There was an article in TFH a few years back that mathematically calculated water change benefits, and the conclusion the author came to was than a 70% change once a week was the best. I probably get very close to this amount, as my "half the tank" is visual so with the water displacement of substrate, wood and rock, and lowering the water in the tank down to and even slightly past the mid-point, I am probably changing at least 60% if not more.
A more substantial change once a week is actually more beneficial than smaller changes more often. The actual volume of water might still be the same per week--i.e., changing 10% daily for 7 days is changing 70% of the water every week--but the benefit of the former is significantly less than the latter. Removing "x" amount of water is only removing "x" amount of pollutants, or "crud" as the TFH author termed it, and this crud is being added every day, so less gets removed with multiple small volume changes than is removed with larger volume changes.
Fluttermoth is very correct in the reasons for water changes. Waiting until a nitrate test shows higher levels of nitrate is waiting too long, as the detriment to the fish from those increased nitrates has already commenced. Water changes are intended to ensure more stability so they must be regular and substantial.
A final point concerns the "detriment" to the fish that I mentioned above. Fish are more closely connected to their physical environment (water) than any terrestrial animal is to its environment (air). The water passes through the fish's gills, and a number of things happen. The fish, like all animals, has to maintain a physiological equilibrium internally, what is termed the homeostasis, which Biology Online defines as “the tendency of an organism or a cell to regulate its internal conditions, usually by a system of feedback controls, so as to stabilize health and functioning, regardless of the outside changing conditions.”
Four important body functions of homeostasis are closely associated with processes in the gills: gas exchange, hydromineral (osmoregulation) control, acid-base balance [pH] and nitrogenous waste excretion [ammonia]. These processes are possible because of the close proximity of the blood flowing through the gills to the surrounding water, as well as the differences in the chemical composition of these two fluids (Bartelme, 2004).
As things change in the water, be they parameters (the GH and pH are highly significant here), temperature, TDS (total dissolved solids), nitrogen elements (ammonia, nitrite and nitrate), and sometimes even light and other fish, the individual fish must spend a lot of energy to adjust its internal physiological equilibrium. One author described this as driving a car uphill; it requires a lot more gas (energy) to climb than it does to run at the same speed (level) on flat ground.
Each species of fish has evolved within a specific environment—and by “environment” in this context we mean everything associated with the water in which the fish lives—and the physiological homeostasis only functions well within that environment. This greater dependence upon their surrounding environment is why fish are more susceptible to stress than many other animals (Wedemeyer, 1996).
Byron.