Q:

Based on what usability research did Microsoft omit the save button on OneNote Web App? 

I've started to use the OneNote Web App, and I think Microsoft have made a very good job developing it.  I use it on the computer and on the phone with ease.  I use the keyboard shortcut ctrl + S to save and expect the document to be saved.  After using it a while, I started to browse the ribbon navigation bar and found that the save-button is omitted. 

Pressing the question "Where's the Save Button?"  gets you to a popup that does explain why its gone:

That’s interesting.  Especially since we on the User Experience Q'n'A at Stackexchenge often answer questions with conventions.  As in the famous save icon question [1] where the accepted answer referred to an idiom.  
However, I want to know which usability research Microsoft based there decision on to omit the save button.  I've searched but didn't find anything.  Not even on Microsoft official OneNote blog [2], where one would expect to find background information.  This leads me to asking: 
Based on what usability research did Microsoft omit the save button on OneNote Web App?  
[1] Save icon, is the floppy disk icon dead?  
[2] http://blogs.office.com/b/microsoft-onenote/ 

A:

According to Chris Pratley from the OneNote team:

About the Save thing.  We actually did consider putting a dummy Save button in the UI as a crutch to help people who felt they had to Save.  But in the end we couldn’t bring ourselves to waste prime UI real estate for a button that didn’t actually do anything.  We did, however, decide not to “beep” when you hit Ctrl-S :-) .  FWIW, in our tests although lots of people just dive into OneNote without being anguished over the lack of the Save button, the people who had trouble with the concept finally got up the gumption to close OneNote, then open it, and after that they were OK.  This is a one-time thing for most people.  As a fairly emotionally charged moment in ther OneNote usage, we also felt that it would help form a bond with the program – which in some ways it has.  We have people raving to their friends about how great the lack of the Save button is – would they have been so positive if they hadn’t felt a little fear at first? :-) 

Source: http://iqcontent.com/blog/2006/05/microsoft-onenote/#comments

A:

Alan Cooper has a whole chapter about Save button in his 'About Face' book. 
Main reasons why it should be avoided are:

Save your work is 99% use case while not saving it is only about 1% (that’s why Save your document?  Yes-No dialogs are ridiculous). 
Not saving your work is dangerous (your computer asking if he should save the results of your 5-hour work?  Seriously?). 
Mental model of save button is counter-intuitive.  In real world, if you take a notepad off the shelf and write something, your changes are persistent, and only one copy of the notepad exist at any point in time. 
On the other hand, in computers, there’s a copy of your document located on the disk and the copy in the RAM.  When you make changes, you make them in RAM, but they are not persistent.  This concept is very hard to understand for new-comers. 
Save button was useful when disks (hard drives or even floppy drives) were slow and saving your work could take a lot of time.  With today’s disk, it is not a problem anymore. 

A:

The use of a Save button in any application should be unnecessary in a modern GUI.   It is a learned behavior of people using the applications based upon their fear of losing their work.   This is completely backwards.   I did the work, the system should me smart enough to remember all the work I did and provide an easy way to go back in time to the previous states of the document. 
To make this work, the system needs to be architected in such a way that all incremental changes to a document can be stored.   This also means they can be undone.   Many of these ideas have been around since the beginnings of computer UI design.   One great book covering these concepts is The Humane Interface by Jef Raskin. 
OneNote to me is much more usable because of this feature.   I can count on whatever I enter in the system being there when I go back to it.   The application was originally developed to be used for in-class note taking.   I can imagine that one problem that they were trying to avoid with the design is the need to quickly close your computer and rush to the next class.   Forgetting to press save in this instance could mean the loss of all your notes.   I expect this would come out of upfront contextual inquiry or through usability testing of the product.   
OneNote is not the only application that works this way.   The settings interface on the Mac does not require an explicit save.