Writing array in Firebase android

The .setValue() method needs a List rather than an Array.

The native types accepted by this method for the value correspond to the JSON types: Boolean, Long, Double, Map, String, Object, List, Object...

Firebase ref = new Firebase("<my-firebase-app>/names"):
String[] names = {"John","Tim","Sam","Ben"};
List nameList = new ArrayList<String>(Arrays.asList(names));
// Now set value with new nameList
ref.setValue(nameList);  

But, I recommend using a Map instead of a List. Rather than having an index based key (1,2,3...), you could use the name as the key so it's easier to retrieve.

Firebase ref = new Firebase("<my-firebase-app>/names"):
HashMap<String, String> names = new HashMap()<String, String>;
names.put("John", "John");
names.put("Tim", "Tim");
names.put("Sam", "Sam");
names.put("Ben", "Ben");
ref.setValue(names);

And now if you want to retrieve the data, you just need to know the name.

Firebase ref = new Firebase("<my-firebase-app>/names"):
Firebase johnRef = ref.child("john");
johnRef.addValueEventListener(new ValueEventListener() {
    @Override
    public void onDataChange(DataSnapshot snapshot) {
       System.out.println(snapshot.value); // the String "John"
    }
    @Override
    public void onCancelled(FirebaseError firebaseError) {

    }
});

Read the Firebase docs for more information.