What effect would converting the lowest denomination note to a coin be? In New Zealand our lowest denomination note is a $5 note. 

For perspective, a can of coke costs $1.50 - $2.00, a Big Mac costs around $5. 

The idea of a $5 coin is on the cards. 

The question is - what effect does turning a note in to a coin have? 

I imagine there would more of a piggybank effect (coins being lost, stuck in collection jars). 

Are there any studies on what's happened when notes have been replaced by coins?
The usual rationale for replacing notes with coins is that small-denomination notes and coins circulate heavily, and notes need to be replaced much more often than coins. However, as an example, the costs of transitioning to a dollar coin (think vending machines, etc.) in the U.S. would be significant enough to make the change not worthwhile, according to a FRB staff working paper. See "Costs and Benefits of Replacing the \$1 Federal Reserve Note with a $1 U.S. Coin" for details on their approach, which covers the issues pretty well.