An interesting post from Elliot compared the number of searches in a month on Google versus the number of visitors received on type in traffic domains. He used the Google Keyword Tool and looked at the traffic of domains to compare the two. The results showed that longer domains received less type in traffic as a ratio to Google searches relative to short domains.
The best way to show you what this means is to look at some of the results. I will post two of several of his results here:
Google exact search volume for: torah: 49,000 Type-in traffic for Torah.com:1,052 uniques (50% total site traffic – keep in mind other extensions are developed websites)
Google exact search volume for: tropical birds: 5,400 Type-in traffic for TropicalBirds.com: 215 uniques (4% total site traffic)
Looking at more of the results can give you some insight. I have not seen a study published on this yet and I would love to see some domainers compile such data, even if they anonymize the domains.
Related Topics: SEO: General
I think you are missing the awareness factor in these findings. The existence for Torah.com might be more well known then tropicalbirds.com. Moreover, the Torah is a specific thing, whereas Tropical Birds can be so broad and ambiguous to mean anything. Do a Google search and you will see how variable it is.