There's a key difference between a null array and an empty array. This is a test for null.

int arr[] = null;
if (arr == null) {
  System.out.println("array is null");
}

"Empty" here has no official meaning. I'm choosing to define empty as having 0 elements:

arr = new int[0];
if (arr.length == 0) {
  System.out.println("array is empty");
}

An alternative definition of "empty" is if all the elements are null:

Object arr[] = new Object[10];
boolean empty = true;
for (int i=0; i<arr.length; i++) {
  if (arr[i] != null) {
    empty = false;
    break;
  }
}

or

Object arr[] = new Object[10];
boolean empty = true;
for (Object ob : arr) {
  if (ob != null) {
    empty = false;
    break;
  }
}

Technically speaking, there's no such thing as a null array; but since arrays are objects, array types are reference types (that is: array variables just hold references to arrays), and this means that an array variable can be null rather than actually pointing to an array:

int[] notAnArray = null;

An empty array is an array of length zero; it has no elements:

int[] emptyArray = new int[0];

(and can never have elements, because an array's length never changes after it's created).

When you create a non-empty array without specifying values for its elements, they default to zero-like values — 0 for an integer array, null for an array of an object type, etc.; so, this:

int[] arrayOfThreeZeroes = new int[3];

is the same as this:

int[] arrayOfThreeZeroes = { 0, 0, 0 };

(though these values can be re-assigned afterward; the array's length cannot change, but its elements can change).

Because .size() is method, its implementation is hidden. And you can't be sure that this method optimized (there's a possibility, that some collections, for example, enumerate items every time you call .size() method). That is why computing the .size() of collection could be expensive. In the same time, .isEmpty() can checks just is there at least one item in collection, and return result.

But .length is just a field. It does nothing, just returns a value. There are no calculations. This field just stores the length of array with fixed size.

I believe that .size() and .length are totally different things and in this case they can not be compared, as well as collections and arrays.

You're trying to call the isEmpty() method on a null reference (as List test = null;). This will surely throw a NullPointerException. You should do if(test!=null) instead (checking for null first).

The method isEmpty() returns true, if an ArrayList object contains no elements; false otherwise (for that the List must first be instantiated that is in your case is null).

You may want to see this question.