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Query string parameters from Javascript do not make it to processing PHP  script
<div id="ListBox">
                <script type="text/javascript">
                popList("name", "categories");
            </script>
            </div>

function popList(field, table) {
    $.ajax({
        type: "GET",
        url: 'getListOfValues.php',
        data: 'field='+escape(field)+'&table='+escape(table),
        dataType: 'json',
        success: function(response) {
            var source = $.parseJSON(response);
            $("#ListBox").jqxListBox({ source: source, checkboxes: true, width: '400px', height: '150px', theme: 'summer'});
        },
        error: function() {
            alert('sources unavailable');
        }
    });
}

<?php
    require "dbinfo.php";

    // Opens a connection to a MySQL server
    $connection=mysql_connect($host, $username, $password);
    if (!$connection) {
        die('Not connected : ' . mysql_error());
    }

    // Set the active MySQL database
    $db_selected = mysql_select_db($database, $connection);
    if (!$db_selected) {
        die ('Can't use db : ' . mysql_error());
    }

    $field = $_GET["field"];
    $table = $_GET["table"];

    $field = mysql_real_escape_string($field);
    $table = mysql_real_escape_string($table);

    $qryString = "SELECT " . $field . " FROM " . $table;

    $qryResult = mysql_query($qryString) or die(mysql_error());

    $source = array();

    while ($row = mysql_fetch_array($qryResult)){
        array_push($source, $row[$field]);
    }

    mysql_close($connection);

    echo json_encode($source);
?>

ajaxRequest.onreadystatechange = processAjaxResponse;

function processAjaxResponse() {
    if (ajaxRequest.readySTate == 4) {
        var response = ajaxRequest.responseText;
        //do something with the response
        //if you want to decode the JSON returned from PHP use this line
        var arr = eval(response);
    }
}

print json_encode($listOfReturnedValues);

function popList(field,table) {
    $.ajax({
            type: "GET",
            url: 'getListofValues.php',
            data: 'field='+escape(field)+'&table='+escape(table),
            dataType: "json",
            success: function(response) {
                //the response variable here would have your array automatically decoded
            }
        });
}