# Testing is Sampling

It seems it is about this time of year that I need to detach a bit from the world to reflect back on the past year and reevaluate my personal and professional goals moving forward. Perhaps I am just getting older or perhaps just a bit wiser (that is synonymous with 'sapient' for the C-D crowd), but I find it refreshing to break away this time of year to tend to my gardens, work on my boat, read some novels, and contemplate life's joys. Now, the major work projects are (almost) finished on my boat, the garden is planted and we are harvesting the early produce, and I reset both personal and professional development objectives for the next year and beyond. So, let me get back to sharing some of my ideas about testing.

Many of you who read this blog also know of my website Testing Mentor where I post a few job aids and random test data generation tools I've created. I am a big proponent of random test data using an approach I refer to as * probabilistic stochastic test data*. In May I was in Dusseldorf, Germany at the Software & Systems Quality Conference to present a talk on my approach. I especially enjoy these SQS conferences (now igniteQ) because the attendees are a mix of industry experts and academia, and I was looking for feedback on my approach. I call my approach probabilistic stochastic test generation because the process is a bit more complex than simple random data generation. Similar to random data generation we cannot absolutely predict a

*probabilistic*system, but we can control the feasibility of specified behaviors. And the adjective

*stochastic*simply means "pertaining to a process involving a randomly determined sequence of observations each of which is considered as a sample of one element from a probability distribution." In a nutshell, my approach involves segregating the population into equivalence partitions, then randomly selects elements from specified parameterized equivalence partitions (which is how we know the probability of specific behaviors), finally the data may be mutated until the test data satisfies the defined fitness criteria. By combining equivalence partitioning and basic evolutionary computation (EA) concepts it is possible to generate large amounts of random test data that is representative from a virtually infinite population of possible data.

One of the questions that came up during the presentation was how many random samples are required for confidence in any given test case; in other words how to we determine the number of tests using randomly generated test data? This is not an easy question to answer because the sample size of any given population depends on several factors such as:

- variability of data
- precision of measurement
- population size
- risk factors
- allowable sampling error
- purpose of experiment or test
- probability of selecting "bad" or uninteresting data

**Using sampling for equivalence class partition testing**

But, the question also brought to mind a parallel discussion regarding how we go about selecting elements from equivalence class partition subsets. I am adamantly opposed to hard-coding test data in a test case (automated or manual), but a colleague challenged me and said that since any element in an equivalent partition is representative of all elements in that partition then why can't we simple choose a few values from that equivalence subset. I realize this approach is done all the time by many testers; which is perhaps why we sometimes miss problems. But, hard-coding some small subset of values from a relatively large population of possible values is rarely a good idea, and is generally not the most effective approach for robust test design. One problem with hard-coding a variable is that the hard-coded value becomes static, and we know that static test data loses its effectiveness over time in subsequent tests using the same exact test data. Also, by hard-coding specific values in range of values means that we have absolutely 0% probability of including any other values in that range that are not specified. Another problem with hard-coded values stems from the selection criteria used to choose the values from a set of possible values. Typically we select values from a set based on based historical failure indicators, customer data, and our own biased judgment or intuition of ‘interesting’ values.

However, the problem is that any equivalence class partition is a hypothesis that all elements are equal. Of course, the only way to validate or affirm that hypothesis is to test the entire population of the given equivalence class partition. Using customer-like values, or values based on failure indicators, and especially values we select based on our intuition are biased samples of the population, and may only represent a small portion of the entire population. Also, the number of values selected from any given equivalence partition set is usually fewer than the number required for some reasonable level of statistical confidence. So, while we definitely want to include values representative of our customers, values derived from historical failure indicators, and even our own intuition, we should also apply scientific sampling methods and include unbiased, randomly sampled values or elements from our set of values or population to help reduce uncertainty and increase confidence.

For example, lets say that we are testing font size in Microsoft Word. Most font sizes range from 1pt through 1638pt and include half-sized fonts as well within that range. That is a population size of 3273 possible values. If we suspected that any value in the population had an equal probability of causing an error the standard deviation would be 50%. In this example, we would need a sample size of 343 statistically unbiased randomly selected values from the population to assert a 95% confidence level with a sampling error or precision of ±5%. Even in this situation, the number of values may appear to be quite large if the tests are manually executed which is perhaps one reason why extremely small subsets of hard-coded values fail to find problems that are exposed by other values within that equivalent partition (all too often after the software is released). Fortunately, statistical sampling is much easier and less costly with automated test cases and probabilistic random test data generation.

**Testing is Sampling**

Statistical sampling is commonly used for experimentation in natural sciences as well as studies in social sciences (where I first learned it while studying sociology an anthropology). And, if we really stop to think about it; any testing effort is simply a sample of tests of the virtually impossible infinite population of possible tests. Of course, there is always the probability that sampling misses or overlooks something interesting. But, this is true of any approach to testing and explained by B. Beizer's Pesticide Paradox. The question we must ask ourselves is will statistical sampling of values in equivalence partitions or other test data help improve my confidence when used in conjunction with customer representative data, historical data, and data we intuit based on experience and knowledge? Will scientifically quantified empirical evidence help increase the confidence of the decision makers?

In my opinion anything that helps improve confidence and provides empirical evidence is valuable, and statistical sampling is a tool we should understand put into our professional testing toolbox. There are several well established formulas for calculating sample size that can help us establish a baseline for a desired confidence level. But, rather than belabor you with formulas, I decided to whip together a Statistical Sample Size Calculator that I posted to CodePlex and also on my Testing Mentor site to help testers determine the minimum number of samples of statistically unbiased randomly generated test data from a given equivalence partition to use in a test case to help establish a statistically reliable level of confidence.

**Cockamamie chaos causes confusion; controlled chaos cultivates confidence!**