In editing science papers, I routinely come across the phrase "Altogether, these results suggest that..." I have changed it to "All together" because it seems to me that the phrase is referring to considering all of the results together. But I have seen "Altogether" so many times that I decided to look it up again, and now I am unsure. Perhaps the meaning is "All in all, these results suggest that..."
The examples I have seen in Garner's and Grammar Girl don't really match this situation. For example, "Altogether, I have too many socks" vs "My socks are all together in my dresser."
I am still leaning toward "All together" because it is modifying "these results" whereas in the example of "altogether" above, it is modifying "I have".
Or perhaps because it is ambiguous, I should leave it as is?