[android] Updating the list view when the adapter data changes

When the data associated with array adapter is changed, invalidating the listview is sufficient to show the updated values? Following piece of code is not working, did i misunderstood something here.?

public class ZeroItemListActivity extends Activity {
    private ArrayList<String> listItems=new ArrayList<String>();
    private ListView mMyListView;
    /** Called when the activity is first created. */
    @Override
    public void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.main);
        mMyListView=(ListView) findViewById(R.id.MyListView);
        mMyListView.setAdapter(new ArrayAdapter<String>(this, android.R.layout.simple_list_item_1,listItems));
    }
    public void addItem(View v){
        listItems.add("list Item");
        mMyListView.invalidate();
    }
}

Layout used :

<?xml version="1.0" encoding="utf-8"?>
<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
    android:orientation="vertical" android:layout_width="fill_parent"
    android:layout_height="fill_parent">
    <TextView android:layout_width="fill_parent"
        android:layout_height="wrap_content" android:text="@string/hello" />
    <ListView android:layout_width="wrap_content"
        android:layout_height="wrap_content" android:id="@+id/MyListView"></ListView>
    <Button android:layout_width="wrap_content"
        android:layout_height="wrap_content" android:id="@+id/AddItemsButton"
        android:text="Add Items" android:onClick="addItem"></Button>
</LinearLayout>

I found a solution that is more efficient than currently accepted answer, because current answer forces all list elements to be refreshed. My solution will refresh only one element (that was touched) by calling adapters getView and recycling current view which adds even more efficiency.

mListView.setOnItemClickListener(new AdapterView.OnItemClickListener() {
    @Override
    public void onItemClick(AdapterView<?> parent, View view, int position, long id) {
      // Edit object data that is represented in Viewat at list's "position"
      view = mAdapter.getView(position, view, parent);
    }
});

Change this line:

mMyListView.setAdapter(new ArrayAdapter<String>(this, 
                           android.R.layout.simple_list_item_1, 
                           listItems));

to:

ArrayAdapter<String> adapter = new ArrayAdapter<String>(this,
                                   android.R.layout.simple_list_item_1, 
                                   listItems)
mMyListView.setAdapter(adapter);

and after updating the value of a list item, call:

adapter.notifyDataSetChanged();

invalidate(); calls the list view to invalidate itself (ie. background color)
invalidateViews(); calls all of its children to be invalidated. allowing you to update the children views

I assume its some type of efficiency thing preventing all of the items to constantly have to be redraw if not necessary.