some's comments are correct... this has nothing to do with variable scoping, and everything to do with the fact that the inner function (the 'onreadystatechange' function) setting the value of MyVariable will not have been executed by the time that the alert() happens... so the alert will always be empty.
The inner function doesn't get executed synchronously (ie, right away), but is deferred and executed later, when the request returns, which is long after the alert() has been executed. The only solution to this is to defer the alert until after the request finishes.
But regardless of all this, the inner function can set variables outside its scope, as the other posts mention. But your problem is more about execution order than it is about variable scope.
