How to select a entry in AlertDialog with single choice checkbox android?

Using a final variable obviously won’t work (since it can only be assigned once, at declaration time). So-called “global” variables are usually a code smell (especially when they become part of an Activity class, which is usually where AlertDialogs are created).
The cleaner solution is to cast the DialogInterface object to an AlertDialog and then call getListView().getCheckedItemPosition(). Like this:

new AlertDialog.Builder(this)
        .setSingleChoiceItems(items, 0, null)
        .setPositiveButton(R.string.ok_button_label, new DialogInterface.OnClickListener() {
            public void onClick(DialogInterface dialog, int whichButton) {
                dialog.dismiss();
                int selectedPosition = ((AlertDialog)dialog).getListView().getCheckedItemPosition();
                // Do something useful withe the position of the selected radio button
            }
        })
        .show();