It depends on the change, the competition, whether there are any penalties, and the equity (or perceived value) of the page and website as a whole. Once a page is crawled and processed, ranking changes happen quite quick (I’ve seen as fast as 15 minutes).
For example, if you have a website about the best credit cards – of which there are hundreds of affiliate sites already ranking – a small change will probably have no effect. You’d likely have to chip away in this space for months. On the other hand, if you have a local plumbing business in a town of 3 plumbers, a small change will likely have a much bigger change in rankings.