Search FRED for ophnfb -- output per hour, non-farm business -- a measure of labor productivity. Three series turn up: OPHNFB, PRS85006092, and PRS85006091. But only sometimes. Sometimes you get a list with only one item on it: OPHNFB. For some reason they design software these days to give inconsistent responses. Maybe the reason is some kind of corner-cutting to save money. But it seems to me the reason is just pure stupidity.
Well that's out of the way. I hope it's not my stupidity!
It took me fifteen minutes to duplicate the list with three results so I could write this post. When you're old as I am, 15 minutes is a big chunk of Time Remaining.
The three series offer the data as an index (2009=100), as Percent Change at Annual Rate, and as Percent Change From Quarter One Year Ago. If I start with the index, I can get "Percent Change From Quarter One Year Ago" easily. I can also get "Percent Change" (though not at an annual rate). Usually I just use the index in whatever form I need, without a thought.
Today for some reason, there was a thought: I can compare the "Percent Change at Annual Rate" series to the index in its "Percent Change" form. And I can see whether they just multiply by four or if they do something more complicated to get the "at Annual Rate" thing.
So I divided the "Percent Change at Annual Rate" series by the "Percent Change" form of the index:
Of course, it's close to four. It would have to be. And maybe you could multiply by four and no one would ever know the difference, but it wouldn't be right.
Okay. The Dallas Fed has a page that shows the calculation: Annualizing Data.
I printed the Dallas Fed page as a PDF file (two pages) and made it available for download.