jquery get checked checkboxes

You need to use the filter() function:

    var obj = $(this).closest('li').find(':checkbox');

    var childCount = obj.size();
    var checkedCount =  obj.filter(':checked').length;

filter
Reduce the set of matched elements to those that match the selector or pass the function's test.

Also, you don't need to wrap obj with $(), because it's already a jQuery object.

to get checked checkboxes length :

$('input[name^="complete"]:checked').length;

to get unchecked checkboxes length :

$('input[name^="complete"]:unchecked').length;

where "complete" is a name attribute.

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