How to validiate form onsubmit when form is submitted via a link instead of a button

I've got the following simple test to validate the input on the form when it is submitted by clicking the "submit" link. Unfortunately, it doesn't validate the form.

<form id="testform" action = "?blah" onsubmit="return validateForm()">
  <input type="text" name="testinput" >
  <a href="#" onclick="document.getElementById('testform').submit();">Submit</a>
</form>

<script>
function validateForm() {
    var x = document.forms["testform"]["testinput"].value;
    if (x == null || x == "") {
        alert("Field must be filled out");
        return false;
    }
}
</script>

If I replace submitting with a button instead of a link then it validates the form properly. But how can I ensure it validates when I am using a link to submit as in the above example?