Our team is preparing to perform unmoderated usability testing on our website and are looking for any insight on the number of participants we need to recruit to obtain a significant sample to represent the population we are testing.
Jakob Neilsen wrote an article in 2000 called "Why You Only Need to test With 5 Users":
As soon as you collect data from a single test user, your insights shoot up and you have already learned almost a third of all there is to know about the usability of the design. The difference between zero and even a little bit of data is astounding.
When you test the second user, you will discover that this person does some of the same things as the first user, so there is some overlap in what you learn. People are definitely different, so there will also be something new that the second user does that you did not observe with the first user. So the second user adds some amount of new insight, but not nearly as much as the first user did.
The third user will do many things that you already observed with the first user or with the second user and even some things that you have already seen twice. Plus, of course, the third user will generate a small amount of new data, even if not as much as the first and the second user did.
As you add more and more users, you learn less and less because you will keep seeing the same things again and again. There is no real need to keep observing the same thing multiple times, and you will be very motivated to go back to the drawing board and redesign the site to eliminate the usability problems.
After the fifth user, you are wasting your time by observing the same findings repeatedly but not learning much new.