select based on sum of rows compared to another field value
This is an UNPIVOT problem.To get the sum of credit items and the sum of debit items you can use a SUM of a CASE statement. To show that, we need a table first:

SQL Fiddle

MySQL 5.5.32 Schema Setup:

CREATE TABLE invoice_items
    (`invoice_item_id` int, `invoice_set_id` varchar(3), `credit_debit` varchar(6), `amount` int)
;

INSERT INTO invoice_items
    (`invoice_item_id`, `invoice_set_id`, `credit_debit`, `amount`)
VALUES
    (62, 'a22', 'debit', 15.00),
    (63, 'a22', 'debit', 8.00),
    (64, 'a22', 'credit', 23.00),
    (65, 'b23', 'debit', 44.00),
    (66, 'c55', 'debit', 15.00),
    (67, 'c55', 'debit', 2.00),
    (67, 'c55', 'credit', 8.00)
;


Now you can combine SUM and CASE like this:
Query 1:

SELECT invoice_set_id,
       SUM(CASE WHEN credit_debit = 'debit' THEN amount END) AS debit_amount,
       SUM(CASE WHEN credit_debit = 'credit' THEN amount END) AS credit_amount
  FROM invoice_items
 GROUP BY invoice_set_id;


Results:

| INVOICE_SET_ID | DEBIT_AMOUNT | CREDIT_AMOUNT |
|----------------|--------------|---------------|
|            a22 |           23 |            23 |
|            b23 |           44 |        (null) |
|            c55 |           17 |             8 |


From here it is fairly simple to filter out the unwanted rows. We just need to wrap the two sums in COALESCE statements to turn NULL into 0:

Query 2:

SELECT invoice_set_id
  FROM(
    SELECT invoice_set_id,
           SUM(CASE WHEN credit_debit = 'debit' THEN amount END) AS debit_amount,
           SUM(CASE WHEN credit_debit = 'credit' THEN amount END) AS credit_amount
      FROM invoice_items
     GROUP BY invoice_set_id
  )X
WHERE COALESCE(debit_amount,0) &gt; COALESCE(credit_amount,0);


Results:

| INVOICE_SET_ID |
|----------------|
|            b23 |
|            c55 |


If your actual problem is as simple as your example and you do not need the intermediate values for anything else, you can get the result also by just changing the sign of the amount based on the credit_debit value before calculating the sum. That would look like this:

Query 3:

SELECT invoice_set_id
  FROM invoice_items
 GROUP BY invoice_set_id
HAVING SUM(CASE WHEN credit_debit = 'debit' THEN amount ELSE -amount END)&gt;0;


Results:

| INVOICE_SET_ID |
|----------------|
|            b23 |
|            c55 |