What is "All Pairs"?

"All Pairs" is a method of testing several variables together. The test cases include all the pairs of values for every variable. The main role of "All Pairs" is that every value is paired with another value at least once.

Here are some examples of testing several variables:

• A window with several fields.
• A search screen with several search criteria.
• Configuration options of software.
• Configuration options of hardware.
• Environment configuration of software (operation system, SQL, networking, RAM, ROM…).

"All Pairs" drastically reduces the number of test cases required to test software and it can help you find most errors with the smallest number of test cases.

How to use "All Pairs"?

Let say, for example, that we have a screen with 3 fields: A1, A2 and A3.

• A1 can get as values the numbers '1' and '2'.
• A2 can get as values the chars 's' and 't'.
• A3 can get as values the chars 'z' and 'y'.

In other words: Let A1, A2, A3 be 3 variables.

• A1 has '1','2' as values.
• A2 has 's', 't' as values.
• A3 has 'z', 'y' as values.

Step 1 - calculate all combinations using "All Singles" method:

The Cartesian product will be:

A1 X A2 X A3 = {1, 2} X {s, t} X {z, y}

Now let's write in a table the test cases using "All Singles" method which means writing all the combinations:

* This table is just a reminder to the "All Singles" method.

Step 2 – base table

Now, let's create a table that each column represents a variable and each row represents a test case combination:

Step 3 - pick the last row (mark in red):

Step 4 – If all pairs exist in other rows – delete the last row and go up, if not keep the row and go up to the next row:

We can see that the pair (2, t) exists in test case 7, the pair (2, z) exists in test case 6 and the pair (t, z) exists in test case 4. Because all pairs in test case 8 (the last row) exists in above rows, we can delete test case 8. The new table will be:

 Now, let's move one row up to test case 7:

We don’t have the couple (2, t) so we keep the line (test case 7) and move up to the next row up to test case 6:

We don’t have the couple (2, z) so we keep the line (test case 6) and move up to the next row up to test case 5.

We can see that the pair (2, s) exists in test case 6, the pair (2, y) exists in test case 7 and the pair (s, y) exists in test case 1. Because all pairs in test case 5 (the current row) exists in other rows, we can delete test case 5.

Now, let's move one row up to test case 4.

We don’t have the couple (t, z) so we keep the line (test case 4) and move up to the next row up to test case 3:

We can see that the pair (1, y) exists in test case 1, the pair (1, t) exists in test case 4 and the pair (t, y) exists in test case 7. Because all pairs in test case 3 (the current row) exists in other rows, we can delete test case 3.

Now, let's move one row up to test case 2:

Now, let's move one row up to test case 1.

We don’t have the couples (1, s), (1, z), (s, z) so we keep the line.

Well, no more lines left which means that after using "All Pairs" method, we have 4 test cases to test. We reduced the number of test cases from 8 to 4 (50% less).

This was a small example that 3 variables had 2 values for each variable.

Let's say we have a screen with 3 variables, each variable can have 5 values.
The amount of test cases with "All Singles" will be: 5X5X5 = 125 test cases.
Using "All Pairs", we can reduce it to 25 test ceases, which is 80% less.

Practice 1

Using "All Pairs" you will have 13 test cases: (the result is only an example, you can get other results, it all depends on the first row you started with)

Free tools

Microsoft PICT - free tool to implement "All Pairs" method.