The checked() method, called without any parameters, will return the current checked state of a SplitButton element.
The checked(bool) method is used to update a SplitButton's checked/unchecked state. Passing true will check the element.
This method is only applicable when the toggle property of the SplitButton widget is enabled.

<button id="but1">Click me</button>

<script type="text/javascript">
     $(function () {
            toggle: true

    $("#but1").swidget().checked(); // return false
    $("#but1").swidget().checked(true) // check the button
    $("#but1").swidget().checked(); // return true