Many teams are trying to generate unusually powerful and varied sets of software tests by using Design of Experiments-based methods to generate many or most of their tests. The two most popular software test design methods are orthogonal array testing and pairwise testing. This article describes how these two approaches are similar but different and suggests that in most cases, pairwise testing is preferable.

Before advancing, it may be worth pointing out that Orthogonal Array Testing is also known as OA or OATS. Similarly, pairwise testing is sometimes referred to as all pairs testing, allpairs testing, pair testing, pair-wise testing, or simply 2-way testing. The difference between these two very similar approaches of pairwise vs. orthogonal array is that orthogonal array-based solutions require the same coverage goal that pairwise solutions do (e.g., that every pair of inputs is tested at least once) plus an additional hurdle/characteristic, that there be a uniform distribution throughout the domain.

I have studied the question of how can software testing inputs be combined most efficiently and effectively pretty steadily for the last 7 years. I started by searching the web for "Design of Experiments" and "software testing" and found references to Dr. Madhav Phadke (who, by coincidence, turns out was a former student of my father).

• I discovered that Dr. Phadke had designed RDExpert which, although it had been primarily created to help with Research & Design projects in manufacturing settings, could also be used to select small sets of powerful test sets in software testing projects, using the Orthogonal Array-based test selection criteria.

• I used RDExpert to create test sets (and compared those test sets against sets of tests that had been selected manually by software testers)

• I gathered results by asking one tester to execute the manually selected tests and another tester to execute the the Orthogonal Array-based tests; the OA-based tests dramatically outperformed the manually-selected ones in terms of defects found per tester hour and defexts found overall.

So, in short, I had confirmed to my satisfaction that an OA-based test data combination strategy was far more effective than manually selecting combinations for the kinds of projects I was working on, but I was curious if other techniques worked better.

 

After more study I have concluded that:

• Pairwise is more efficient and effective than orthogonal arrays for software testing.

• Orthogonal Arrays are more efficient and effective for manufacturing, and agriculture, and advertising, and many other settings.

 

And we have built Hexawise as a software tool to help software producers test their software, based on what I have learned from my experience. We take full advantage of the greatly increased efficiency and effectiveness of letting testers to determine what needs to be tested and software algorithms to quickly create comprehensive test plans that provide more coverage with dramatically fewer tests.

But we also go well beyond this to create a software as a service solution that aids the software testing team with many huge advantages such as: automatically generating Expected Results in test scripts, automated importing of data from Excel or mind maps, exporting tests into other tools, preventing impossible to test for values from appearing together, and much more.

 

Why is a pairwise testing strategy better than an orthogonal array strategy?

• Pairwise testing almost always requires fewer tests than orthogonal array-based solutions (it is possible, in some situations, for them to have an equal number of tests).

• Remember, the reason that orthogonal array-based solutions require more tests than a pairwise solution to reach the coverage goal of testing all pairs of test conditions together in at least one test is the additional hurdle/characteristic that orthogonal array testing has, e.g., that there be a uniform distribution throughout the domain.

• The "cost" of the extra tests (AKA experiments) is worth paying in many settings outside of the software testing industry because the results are non-binary in those tests. Someone seeking a desired darkness and gloss and luminosity and luster for a particular shade of green in the processing of film, for example, would benefit from with the information obtained from the added information gathered from orthogonal arrays.

• In software testing, however, the added costs imposed by the the extra tests are not worth it. You're generally not seeking some ideal point in a continuum; you're looking to see what two specific pieces of data will trigger a defect when they appear in the same transaction. To identify that binary approach most efficiently and effectively, what you want is a pairwise solution (with fewer tests), not a longer list of orthogonal array-based tests.

 

Let me also add these points.

• First, unlike some of my other views on combinatorial test design, my opinion on this narrow subject is not based on multiple empirical studies; it is based on (a) the reasoning I laid out above, and (b) a dozen or so conversations I've had with PhD's who specialize in the intersection of "Design of Experiments" and software test design, and (c) anecdotal evidence from using both methods.

• Secondly, to my knowledge,very few, if any, studies have gathered empirical data showing benefits of pairwise solutions vs. orthogonal array-based solutions in software testing scenarios.

• Thirdly, I strongly suspect that if you asked Dr. Phadke, he would give you his reasons for why orthogonal array-based solutions are appropriate (and even preferable) to pairwise test case selection methods for certain kinds of software projects. I have a huge amount of respect for both him and his son.

 

Time doesn't allow me to get into this last point much now, but "mixed strength" tests are another even more powerful test design approach for you to be aware of as well. With mixed strength testing solutions, the test designer is able to select a default coverage strength for the entire plan (e.g., pairwise / AKA 2-way coverage) and, in the same set of tests, select certain high priority values to receive higher coverage strength (e.g., 4-way coverage strength selected for each "Credit Rating" and "Income" and "Loan Amount" and "Loan to Value Ratio" would give you a palm that achieved pairwise coverage for everything in the plan plus comprehensive coverage for every imaginable combination of values from those four high priority parameters. This approach allows you to focus on risk-based testing considerations.

 

Sorry if I got a bit long-winded. It's a topic I'm passionate about.

Originally posted on Stack Exchange, Additional note added after the first 3 comments were submitted:

@Hannibal, @Peter K., and @MichaelF, Thanks for your comments! If you'd like to read more about this stuff, I recommend the multiple links available through this "bundle of links" about pairwise testing and combinatorial testing. In particular, Michael Bolton's article on pairwise testing is directly relevant and very clearly written. It is one of the few introductory articles around that accurately describes the difference between orthogonal array-based solutions and pairwise solutions. If I remember correctly though, the example Michael uses is a rare exception to the rule; the OA solution has the same number of tests as an optimal pairwise solution does.

Related: The Empirical Evidence for Using Pairwise and Combinatorial Software Testing - 3 Strategies to Maximize Effectiveness of Your Tests - Hexawise TV

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