ill be the pessimistic guy and say: No, without some really expensive lab equipment and months/years of studying it wont be possible.
microscopic analysis, and to solve it and centrifuge it, that are just basic steps. Thats preparation, what follows is biochemical analysis, you search for chemical markers or for specific proteins, produced either by parasites themselves or by immune responses to the parasites. Often if they find something under the microscope or during preparation, they follow up with a biochemical test to confirm it and to make it a solid diagnosis.
But you can cut out the middle-guy, which would be the vet. Here is how vets do it: They get test kits from the lab, get a poop sample properly collected and prepared using the test kit, send it in to the lab, get back the results. The price of the lab testing is included in the price of the test kit. So you can just buy the test kits directly and send it in directly, without a vet. Some excellent pet stores have them for sale, otherwise: internet. Its the best way when people want to screen a larger collection for certain issues, and want professionalism and a reliable result but low cost.