In Part One of this article, I set up a fictitious example using Google to demonstrate how you would measure trust within a Lean Six Sigma project. More specifically, this is part of our FUSE© methodology. For those of you who have not read Part 1 of this article, we presented a series of data collected from a fictitious Google example through a survey and the following results were compiled:

- The survey was sent to 10,000 people in 10 different countries for a total of 100,000 people.
- The survey was sent to 8,000 employees in each country and 1,000 managers, 1,000 partners;
- We received 6,000 employee, 800 managers and 700 partner responses back from each country;
- The founder of the company believes that 90% of all employees and managers share the same interpretation of the vision that he has;
- 70% of the employees and 88% of managers select the explanation of the vision which was the same as founder across all countries. In order to keep the math simple, we have assumed that there are no differences in results across the countries.
- 75% of the employees, 80% of managers and 60% of partners selected the interpretation of the values, which were the same as the founder. Again, we are trying to keep the math simple so we assume no differences across countries as well as across values.

So now, we want to use this data to set up some hypotheses tests that will help us understand if there are trust issues for this fictitious example I have provided.

**Hypotheses Test #1 – To Identify if Trust Issues Exist from employees and from managers**

Here is the first question we may want to answer:

- Do managers and employees (individually) share the same interpretation of the vision as the founder?

To answer the question, we will conduct the following hypothesis testing.

We will need to set up our null (H_{o}) and alternative (H_{a}) hypothesis and test our assumptions (assume that we want a confident of 95% or a level of significance of 5%). The null hypothesis is the opposite of the claim so in our case that less than 95% of Google employees have the same interpretation as the founder. Now let’s also assume that we want to be more confident of our results 19 times out of 20 (or 95% of the time), this means our confidence level is 95% and level of significance is 5% (or 100% minus 95%). The null and the alternative are stated below.

- Ho
_{1}:The percentage of employees with an interpretation of Google’s vision that is same as its founder is less than 90% or P<90% (P being the percentage) - Ha
_{1}: The percentage of employees with an interpretation of Google’s vision that is same as its founder equal to greater than 90% or P≥90%

- Ho
_{2}:The percentage of managers with an interpretation of Google’s vision that is same as its founder is less than 90% or P<90% - Ha
_{2}: The percentage of managers with an interpretation of Google’s vision that is same as its founder equal to greater than 90% or P≥90%

The rule for our test is if the Z_{score}, which I will show you how to calculate in a moment, is greater than -1.65 than we reject the null hypothesis otherwise we accept the null as true.

To calculate the Z_{score} we use the following formula:

Z_{score }= (P1-P_{0})/sqrt[(P_{0})(1- P_{0})/sample size]

Putting the numbers into the formula

Z_{score} _{employees }= 70%-90%/0.0039

Z_{score} _{employees} = -51.64

Z_{score managers} = 88%-90%/0.0107

Z_{score} _{managers }= -1.89

Since the Z_{ score} for employees is much less than -1.65, then we accept the null and accept the statement that less than 90% of Google employees have the same interpretation of its vision as the founder. On the contrary, we reject the null for managers and say that 90% or more of Google managers share the same vision as its founder.

**Hypothesis Test #2 – To Test if Trust Issues Exist for employees and managers collectively**

Here is another question we may want to answer:

- Do managers and employees collectively share the same interpretation of the vision as the founder of Google?

We probably suspect the answer to be no but we will go ahead and show you how to conduct that test. To answer the question, we will conduct the following hypothesis testing.

In this instance what we are saying is that P_{1}=P_{2} or P_{1}-P_{2}=0 (P1=percentage of employees and P2=percentage of managers). In order to conduct this test we also need to know the percentage of all employees and managers that share the same interpretation as the founder at Google and it is approximately 72%. This is denoted as P_{3}.

We set up our null and alternative hypothesis as follows:

- Ho
_{1 }= H_{02}(There is no difference in the percentage of employees and managers that share same interpretation of Google’s vision as its founder.) - Ho
_{1 }≠ H_{02 }(There is a difference in the percentage of employees and managers that share same interpretation of Google’s vision as its founder.)

We use the following equation and calculate our Z_{score}

Z_{score} = P_{1}-P_{2}/sqrt [P_{3}*(1-P_{3})*(1/n_{1}+1/n_{2})]

(n_{1}=sample size for employees, n_{2}=sample size for managers)

Z_{score }=0.70-0.88/0.017

Z_{score} =-51.3

Note that this is a two tales test, the rule is that if the Z_{score} >1.96 or <-1.96, we reject the null hypothesis; otherwise, we accept it.

In this instance, since the Z_{score} of -51.4 (which is <-1.96), we reject the null and we say that there is a difference in the percentage of employees and managers that share the same interpretation of Google’s vision as its founder.

We will not go through the remainder of the calculations’ however, what we can see from this example is that there appears to be a difference in a unified vision; and thus, trust issues likely exist and should be examined further as we implement the FUSE methodology.

**Concluding Thoughts**

This article (Part 1 and 2) show hypothesis testing can be used to determine if there is a misalignment in vision and values between employees, managers and its founders/leaders. Many leaders and its employees may have their own assumptions; it is only when these statistical tests are conducted to have substantive proof that trust issues exist, which may hinder any change effort.

So what are your thoughts about measuring the level of trust within an organization using statistical methods?

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**About the Author**

Kyle Toppazzini is the president of Toppazzini and Lee (T&L) Consulting, and an international leader and consultant in lean Six Sigma. He publishes blogs and articles in Bloomberg Business Week, Digital Journal, Quality Digest Magazine and Social Media and is the author of the CFO Scorecard published in Exchange Magazine. (A global magazine produced by the Association of Financial Professionals). Kyle is currently working on a book that will bring new innovations in Lean Six Sigma and Quality Management. Kyle is a six sigma master black belt and lean six sigma black belt receiving his training from the University of Notre Dame’s Mendoza College, a certified Balanced Scorecard Trainer, and a member of the Palladium Executive Group founded by David Norton founder of the Balanced Scorecard. Kyle has conducted more than 30 performance and process improvement projects across the public and private organizations in government and health care yielding millions of dollars in cost savings and 80% improvement in performance. |

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