The designers of the Fortress Programming Language did extensive reviews of scientific literature to see how operators are used and what relative precedence they have. Based on those observations, they designed operator precedence in Fortress. This is the only instance I know of where a Programming Language Designer has explicitly written down their rationale for Operator Precedence.
Operator Precedence in Fortress works a little bit different from other languages. The main difference is that there is no globally defined precedence across all operators. Instead, operators have relative precedence to other operators:
+, for example. Using two operators in the same expression without explicit parentheses that do not have a defined operator precedence, is a Syntax Error. In other words: the precedence relation is not a total ordering, it is in fact not even a partial ordering, it isn't an ordering at all because the relationship is not transitive: even if operator X is defined to be tighter than Y and Y is defined to be tighter than Z, that does not mean that X is tighter than Z and you are not allowed to mix X and Z in the same expression without parentheses because they do not have a defined relative precedence.
This neatly side-steps questions such as "should the string concatenation operator have higher or lower precedence than bitwise-XOR?" Well, neither. It doesn't make sense to mix the two in the same expression, so they don't have a defined relative precedence. And if you do mix the two, then you need to use parentheses.
In general, operators in Fortress only have a defined relative precedence, if they are commonly used together in the same expression in scientific papers and there is a general consensus in the scientific community what the precedence should be.
There is also another nice feature: the programmer can use whitespace to indicate what he thinks the precedence should be (but not override precedence). So, you can write
a×b+c, you can write
a × b + c, you can write
a×b + c, but you cannot write
a × b+c, the latter is again a Syntax Error. (And yes, Fortress uses the times symbol for multiplication, not the asterisk. It also uses ∧ and ∨ for logical-conjunction and logical-disjunction, ∪ and ∩ for union and intersection, it uses actual subscripting for array subscripting and uses superscript for exponentiation.)
A third nice feature is that Fortress has a juxtaposition operator, i.e. an operator for writing two expressions next to each other. For example, for numbers, juxtaposition is defined as multiplication, i.e. in the example above, I could have written
a b + c instead of
a × b + c. For unary functions, juxtaposition is application, so
f x are equivalent.