Hypothesis testing is a powerful way to analyze data. But to make the most progress, a Six Sigma team must not only be able to perform a hypothesis test, it must also be aware of the test’s limits of practical significance. Two groups of stakeholders are involved with the results of statistical analysis. The team’s need for understanding is obvious, but the team’s customer also must be able to understand the results and their significance.

By following a consistent reporting format, a Six Sigma team and its customers can better understand and explain hypothesis test results and conclusions. A good format allows reviewers to know exactly where to look for information, which will increase their confidence in the results.

Provided here is a description of the four parts to include in a reporting format for the results of a hypothesis test. An example from an inbound call center is used to illustrate the format. In the example, a company’s Six Sigma team investigates the contract compliance of an embedded service provider. The team gathered cycle time data (in units of seconds) and wants to know if the vender is complying with the guaranteed 5-minute (300-second) cycle time terms of their agreement. Based on continuous data collected over three days by the call center’s call management system, and the team’s desire to know if the embedded service provider is in compliance, the single population t-Test was used.

### Practical Problem

The *practical problem* is a statement that describes the practical question to be answered by the test. It is written in process owner or customer language and states what is being asked. It is phrased as a question.

### Statistical Problem

The *statistical problem* is a statement that describes the specific hypothesis test that will be used along with a definition of the “null” and “alternate” hypotheses for the test. The statement is written in the specific statistical terms required by the hypothesis test being used.

### Statistical Solution

The *statistical solution* is a statement that describes the solution to the statistical problem. It too is written in the specific statistical terms required by the hypothesis test used.

### Practical Definition of the Statistical Solution

The *practical definition* is a statement that describes the statistical solution in practical terms. It is written as a statement and answers the practical problem question in the first step. Process owner or customer language is used. No elaboration is allowed, just the specific answer to the specific question posed in the practical problem statement.

### Practical Limits of Hypothesis Testing

Hypothesis testing does not establish the why or how. Other process knowledge will help answer those questions. Note that the way the test is set up in the example, it does not indicate whether the actual average service time is greater than or less than 5 minutes. The test can be restructured to look at one side of the data’s distribution, or other process information can be used to determine which direction from 5 minutes the distribution’s actual mean is. This is typical of the practical limits of what a hypothesis test can tell you.

You didn’t mention that on answering the practical question you should look at the confidence intervals and state how far above or below from 5 the process had exhibited. A properly done hypothesis test WILL show you which side of 5 the data is centered.

I love hypothesis testing. It is an amazingly simple tool to test all the different assertions that come up in problem solving teams. No messing around with opinion you simple set up a test that is more often than not done without interupting the process and you have data and an answer.

To Mike’s point. I never take a side on a debate as to what an answer may be to a problem. Get everyone to put it into hypothesis terms and do the study. Case closed!