By following a consistent format the Six Sigma team and its customers can better understand and explain hypothesis test results and conclusions. Reviewers know exactly where to look for information, which will increase their confidence in the results. This is an example format to use.

Practical Problem

This 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

This 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

This 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

This is a statement that describes the statistical solution in practical terms.  It is written as a statement and answers the practical problem question in step one. Process owner or customer language is used. No elaboration is allowed.  Just the specific answer to the specific question posed in step one.

Example:

Practical Problem:

The vender promised service in an average of 5 minutes. Is this a true statement?

Statistical Problem:

Single population t-Test with H₀: m = 5.

H_a: Service time does not average 5 minutes. Confidence interval equals 95%

Statistical Solution:

P = 0.0000, H₀ is rejected because P < 0.05.

Practical Definition of Statistical Solution:

The service time does not average five minutes.

Hypothesis testing does not establish the why or how. Other process knowledge will help answer these questions. Note that the way the test is set up, 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 the direction from 5 minutes the distribution’s actual mean really is.