Permutations and Combinations

Permutation: It is an ordered arrangement of objects from a group without repetitions.

For example, there are two ways to order the boxes 12 without repeating a sequence. The two permutations are 12 and 21.

In general, the number of permutation of n items chosen k at a time is:

nPk = n!
(n − k)!




Why these are important?

If there are only two possible outcomes then permutations can be used to calculate the probability of an event in that experiment.

Combination: A selection of objects from a group, when the order of the selection does not matter. For example, the combinations of the number 123 taken two at a time are 12, 13, and 23.

The subgroups 12 and 21 are considered the same combination, because order does not matter.

In general, the number of combinations of n things taken k at a time is:

_nC_k  =           n!            

            (n − k)! k!

Why these are important?

In statistics, this expression is used in the formula to calculate the probability of observing k events (successes) in n trials in an experiment with only two outcomes (a binomial experiment).

Types of Errors

There are two types of errors one can make in their decision -  to reject or fail to reject the null hypothesis (Ho ).

If you reject the null hypothesis when it is true, you make a Type I error. 

If you fail to reject the null hypothesis when it is false, you make a Type II error.

Consider a researcher interested in comparing the effectiveness of two drugs. The null and alternative hypotheses are:

Null hypothesis  (Ho ): d1 = d2

Alternative hypothesis (H1 ): d1 is not = d2

If someone commits a Type I error, they reject the null hypothesis by concluding that the two drugs are different when they are not. 

If the drugs are the same in effectiveness, they may not consider this error as too serious because patients are receiving the same level of effectiveness.

If someone commits a Type II error, they fail to reject the null hypothesis when you should have rejected it. 

That is, when someone concludes that the drugs are the same when, in fact, they are different.  

The probability of making a Type I error is a, which is the level of significance you set for your hypothesis test. An a of 0.05 indicates that you are willing to accept a 5 percent chance that you are wrong when you reject the null hypothesis. 

The probability of making a Type II error is b, which is a value that you typically cannot know. However, you can lessen your risk of committing a Type II error by making sure your test has enough power. You can do this by making sure you sample size is large enough to detect a difference when one truly exists. 

ASQ - Question

Some notable comments on developing organizational culture

Jeffrey Liker - the author of Toyota Under Fire made many remarkable comments in his book about how to develop the organization's culture. Below are some really important and notable comments made by him.

• Process and procedures are never enough to ensure excellence.
• Acheiving consistent excellenace is extraordinarily difficult and rare.
• Excellence, where it does occur is a result of culture rather than just processes.
• Yesterday's solutions no longer apply to today's context.

Below is diagram describing Toyota's culture house.

Jeffrey Liker on Toyota Culture




John Shook on Toyota Culture

What is an elevator speech?

An elevator speech is a change management tool, which can be used effectively to get "Buy-in" from very Senrior Stakeholders whithin your organization. The idea here is that if you happen to catch your CEO or VP in an elevator, how could you maximize your chances for the success of your project.

Typical elevator speech is between 20 seconds to 6o seconds.

Typical structure of elevator speech:

1. The project or solution
2. The need for change
3. The vision of the desired state you are working towards
4. What you would like from the person or their staff

Video Guide


As per the above video following are the components of the 3 minute elevator speech.

1. Introduction - 30 sec
2. Body - three interesting ideas - 90 sec
3. Conclusion - 30 sec
4. Close with specific call to action - 30 sec

Video Guide


As per the above video the elevator speech must pass 4 key test

1. Succinct
2. Easy to understand
3. Greed inducing / adrressing "What's in it for me"
4. Irefutable

Example Elevator Pitch

I am the Risk Coordinator for the SCA. I am leading the SCA's Unusual Occurrence Management Project. I am responsible for putting together the focus group to understand the needs of the organization with regards to its occurrence reporting process. I have established the methods which are primarily focused on making the frontline staff reporting process simple and easy. I am people oriented and have recognized  the needs of various stakeholders within the organization. I am a lean six sigma practitioner developing a standard reporting method which will be the key in driving this project a success. Our goal is to have this project live by early August.



Video Guide:Ted Talk

















Additional Reading & Tools

How to Craft an Effective Elevator Speech
http://www.creativekeys.net/powerfulpresentations/article1024.html

Harvard Business School - Elevator Speech Builder
http://www.alumni.hbs.edu/careers/pitch/

http://www.change-management.com/Prosci-Elevator-Speech-Webinar-Slides.pdf

What is organizational change management?

How to Change Your Culture: Organizational Culture Change

 

http://humanresources.about.com/od/organizationalculture/a/culture_change_2.htm

 

Online Book - Overview of Elementary Concepts in Statistics.

http://www.statsoft.com/textbook/

Chapters

What are variables? Correlational vs. experimental research Dependent vs. independent variables Measurement scales Relations between variables Why relations between variables are important Two basic features of every relation between variables What is "statistical significance" (p-value) How to determine that a result is "really" significant Statistical significance and the number of analyses performed Strength vs. reliability of a relation between variables Why stronger relations between variables are more significant

Why significance of a relation between variables depends on the size of the sample Example: "Baby boys to baby girls ratio" Why small relations can be proven significant only in large samples Can "no relation" be a significant result? How to measure the magnitude (strength) of relations between variables Common "general format" of most statistical tests How the "level of statistical significance" is calculated Why the "Normal distribution" is important Illustration of how the normal distribution is used in statistical reasoning (induction) Are all test statistics normally distributed? How do we know the consequences of violating the normality assumption?

Online Book - Engineering Statistics

http://www.itl.nist.gov/div898/handbook/



Chapters

1. Exploratory Data Analysis (5.4 Mb)
2. Measurement Process Characterization (3.1 Mb)
3. Production Process Characterization (1.1 Mb)
4. Process Modeling (3.1 Mb)
5. Process Improvement (3.7 Mb)
6. Process or Product Monitoring and Control (2.1 Mb)
7. Product and Process Comparisons (1.2 Mb)
8. Assessing Product Reliability (1.9 Mb)

Change Management Tips

Enterprise Change Management:

• The psychology of change: understanding the guiding principles of effective change management
• Principle 1 - the disconnect between senders and receivers
• Principle 2 - Understanding resistance
• Principle 3 - Authority for change, the role of leadership during change
• Principle 4 - Value systems: change management and culture
• Principle 5 - Incremental vs radical change: scaling your efforts
• Principle 6 - The right answer is not enough
• Principle 7 - Change is a process
• Five tips for: Succeeding in change management

Five levers of change management:

• The What, Why and How of change management - The "harder" side of change
• Five change management levers
• Positioning change management
• Examining the definition of change management - the three clauses
• Five tips for: Succeeding in change management
• Communications: with and without change management
• Five tips for: Better communications 
• Five tips for: Managing resistance

 
The sponsors of change:

• Role and importance of sponsors
• Neutralizing threat #1 - the missing sponsor
• Five Bs of Executive Buy-in
• Principle 3 - Authority for change, the role of leadership during change