PHP Variables are server-side variables. You can not change server side variables from client side directly.
Common approaches are: (Although both do same in background)
Using GET to send your data
Using AJAX to dynamically send, fetch and change DOM (Maybe preferred in our case)
On selecting the item on the Drop Down menu, you need to call a method which sends a data to your PHP page and you can change variables.
Your PHP page should handle a GET request change the variable to $test
$test = $_GET["sent_variable"]
While on AJAX, you need to something like:
$.ajax({
url: "your-php-page.php",
type: "POST",
data: { sent_variable: selectedVar}
}).done(function() {
//Something here after doing
});
Read more about AJAX here.
Note: You have to trigger AJAX on selecting drop-down menu. Read about that here.