## How to Conduct a Simple Hypothesis Test in Six Sigma

I was teaching a Six Sigma Green Belt course in Washington, DC and was asked to simplify the basic road map in Hypothesis Testing.

In the example below, we are testing whether or not there is a correlation between two continuous variables.

Example:

1. What is the practical question?

– Does an increase in tire pressure cause an increase in tread wear?

2. What is the X? (Input being Controlled)

– Tire Pressure

3. What is the Y? (What is being Measured)

– Tread Wear

4. Gather Data, Run the Analysis and determine the Pearson Correlation Co-efficient and P-Value

5. Run a Correlation Analysis (selecting Pearson method). In this example the Pearson value ( r ) = 0.554 with a P-value = 0.0228

6. The results indicate that there is a medium correlation of the two factors and that the data set is significant at an Alpha riskAlpha risk (α) is the risk of incorrectly deciding to rejec... Learn More... levelThe value of an input in an experimental run. of .0228.

A guideline of R Values:

- between -0.2 and +0.2 is random chance of a relationship
- between -0.8 and -1.0 or +0.8 and +1.0 is a strong relationship
- the remaining levels / values indicate there is a weak to moderate relationship

Remember that correlation is not causation. It is only a test of the strength of the linear relationship of two continuous factors; so the R Value indicates the strength of the relationship and the P Value indicates the Alpha Level the relationship can be stated to be significant.

We hope this simplifies the concept. Using Six Sigma and Hypothesis Testing, what problems (or opportunities) would you apply this to in your organization?

Pearson sample correlation coefficient is a measure of the strength of a linear relationship. We must always create a scatter plot to check the form of the relationship to assure that r will be an appropriate metric. For example, a second order (parabolic) relationship may have an r value close to zero which would lead an analyst to erroneously conclude there is no relationship between the variables.