Hi Laura,
Analogous estimations are higher level and the estimate is a very broad stroke. "This project is very much like the ABC Project... The estimate for that project was $XXX, so we can use that." So, the estimate for the project is based on a similar project.
Parametric estimates are based on an algorithm/ formula and generally require a bit finer breakdown of the project tasks(at least, compared to an analogous estimate) in order to arrive at the estimate. For example, "This project entails the creation of 10 new reports for the customer. 4 are of low complexity, 5 are of medium complexity and 1 is highly complex." Experience has shown that the effort can be estimated as 10 hours per low complexity report, 20 hours per medium complexity reports and 30 hours for highly complex reports. Thus, the estimate for this project would be 4*10 + 5 * 20 + 1*30 = 170 hours.
In the parametric example, you can see that more work had to take place in order to get an estimate, since the work had to be more defined than in the analogous estimate.
I hope this helps!
Best regards,
Tracy