How to use a function that takes arguments with jQuery’s change() method?

See event.data. The data is not passed as argument to handler, but as property of the event object:

$("select#test").change({msg: "ok"},  function(event) {
    alert(event.data.msg);
});

The handler always only accepts one argument, which is the event object. This is the reason why your alert shows "[object Object]", your function is printing the event object.
If you want to use functions with custom arguments, you have to wrap them into another function:

$("select#test").change({msg: "ok"},  function(event) {
    myHandler(event.data.msg);
});

or just

$("select#test").change(function(event) {
    myHandler("ok");
});

Btw. the selector is better written as $('#test'). IDs are (should be) unique. There is no need to prepend the tag name.