Alpha and Beta Errors with a Simple Example

Lean Six Sigma embraces DMAIC and DMADV (DFSS) as two strong methodologies in driving projects and successfully completing these projects with a business benefit.

In the journey of DMAIC/DMADV; Y=f(x) is a concept that drives us completely through-out the project.

• “Y” is the CTQ (Critical to Quality). It is the Metric on which we are driving the complete project; whereas
• “X” are the potential causes that are impacting the Project Y.

The story of identifying potential causes and/or potential x’s start in the Measure phase, Fishbone Diagram and/or Ishikawa Diagram and/or Cause and Effect Diagram is a Lean Tool we utilize in the Measure phase to identify all the potential causes by doing a Brainstorming Session. 

Once the potential causes have been identified in the respective project, the project leader needs to collect the data for all the potential causes identified with the help of DCP (Data Collection Plan).

Now we have the data of the “Y” Metric and with the Help of the DCP (Data Collection Plan), we have collected the data for X’s as well.

We now move to the Analyze Phase where a Project Leader needs to preform Hypothesis Testing for all the potential causes / potential X's identified. This is a very critical step as we need to provide, prove with the help of data evidence if the potential causes identified are really significant causes / vital causes.

The complete Hypothesis Testing happens with the help of Data. Project Leaders can either use Minitab or JMP for their statistical analysis.

In the journey of testing all the potential causes in the Analyze Phase, a Project Leader can either go correct or make a human error while in the journey of identifying the critical x's and/or significant x's and/or vital x's, in the case when a human error takes place, the project leader can land up making a Alpha Error or a Beta Error.

Let me explain this with the help of the below picture:

With the above simple example, while doing a Hypothesis Testing, a project leader can fail to understand the significance of the P-Value and therefor e make an error in either making an Alpha Error or a Beta Error.

• Alpha error is when a project reject the Null Hypothesis when it is true.
• Beta Error is when we accept Null Hypothesis when it is false.

While the above pictorial diagram is self-explanatory, let me also take up the Example of COVID-19. The most critical situation that the world is presently undergoing and very badly experiencing. Hence let me take up the example of COVID-19 which will make everyone's thoughts easy:

In the above diagram; let us take the example of the patients / people who are suffering from COVID-19 (Corona Virus). We all understand how dangerous and deadly this Corona Virus is to the world and how this is impacting.

In the above diagram, we have four situations and two opportunities where the doctors can absolutely go right. The two opportunity where the Doctors / Reality can be absolutely right are:

• Situation 1 where the Doctors can be right:
  • When the Medical Report of the Patient says that the Patient is Negative and is not infected with Covid-19 (Corona Virus)
  • The Truth also is that the Patient is not infected with Covid-19 (Corona Virus).
• In any of the above scenario's the Patient is also safe as the patient is not infected with Covid-19 (Corona Virus) and at the same time the Society (World) is also safe as the infection of Covid-19 (Corona Virus) will not spread.

• Situation 2 where the Doctors can be right:
  • When the Medical report of the Patient is Positive on Covid-19 (Corona Virus)
  • The Truth also is that the Patient is infected with Covid-19 (Corona Virus)
• In any of the above scenarios the Patient will be immediately admitted in the Hospital and appropriate treatments will be given the Patient.
• This is another Scenario where Patient is also SAFE and the Society (World) around us also safe as nobody is getting infected with Covid-19 (Corona Virus).

The Two Opportunities where the Doctors / Facts can be WRONG:

• Situation 1 where the doctors can be wrong:
  • When the Medical report of the Patient says that the Patient is Positive from Covid-19 (Corona Virus)
  • The Truth also is that the Patient is not infected with Covid-19 (Corona Virus)
• In this case while the Truth of the matter is that the Patient is not infected and NOT POSITIVE in Covid-19 (Corona Virus), the patient is this case is getting impacted.
• A good healthy person is forcibly getting admitted in the Hospital and will experience all the torture and/or would also get infected in the hospital as many of the Covid-19 (Corona Virus) positive cases would be available in the Hospital.
  • This is an Error committed by the Doctors and the Patient would be suffering for some-time or for lifetime.
  • This is a situation when we call “ALPHA α Error or Type I Error”
    • A Good Example that I can quote is from a Movie “TERE NAAM” – Salman Khan in this movie is absolutely fit and fine however at the end of the movie, he is again been taken away in the Hospital Ambulance and he undergoes big amount of torture which will continue for this entire life.
    • In this case only one person is getting impacted however the person life is getting ruined. This in simple words is called “ALPHA α Error or Type I Error”

• Situation 2 where the doctors can be wrong:
  • When the Medical report of the Patient says that the Patient is Negative from Covid-19 (Corona Virus) and/or the patient has not examined on any medical test and assumes that he is perfect
  • The Truth unfortunately is that the Patient is infected with Covid-19 (Corona Virus POSITIVE)
• In this case the TRUTH of the matter is that the Patient is actually infected with Covid-19 (Corona Virus) and is Corona Positive who is freely moving in Society meeting various people.
• In this case the Society (World) is at very high risk. The simple reason is that the Patient who is Covid-19 (Corona Virus) Positive, is freely moving around the society, meeting and enjoying with his people in the Society. 
• The patient and the Society in this case are at completely high risk.
  • This is an Error committed by the Doctors or by the Patient himself.
  • This is a situation when we call “Type II Error / Beta β Error”
    • Examples - Covid-19 (Corona Virus) with “Type II Error / Beta β Error”
      • Example 1: Kanika Kapoor while she was COVID-19 (Corona Virus) positive, she continued meeting up with people in various meetings, parties. This was a major threat to her family and the society she was moving and meeting around with.
      • Example 2: A Big Group of about 2000 members were gathered in Nizammudin (Tabligi Jamat). Many from this group were already COVID-19 (Corona Virus) positive however due to their negligence, they did not get themselves medically checked and after repeated protocols from the legal bodies, the group of about 2000 continued with their meeting. Today the entire world is at threat because of the negligence due to these guys.
      • Example 3: A Group was again identified at Ajmer, Rajasthan. The group again had a gathering which was against the LOCK DOWN regularities. The world is at THREAT because of the negligence done by a group of about 200 in Ajmer Rajasthan.

I hope with the above examples that I have quoted, you should you able to understand the significance of “ALPHA α Error or Type I Error” and “Type II Error / Beta β Error”

Many assume and perceive that Lean Six Sigma is only applicable in their WORKLIFE. Lean Six Sigma is a day-in and day-out activity that we can practice every single day. Lean Six Sigma is one very important and very impactful philosophy that can impact Corporate’s , Working Professionals and the Clients / Customers in every business. I highly encourage all working professionals and corporates to implement, use the Lean Six Sigma methodology for gaining maximum business benefits.

Should you still have any Queries, please be at liberty to reach out to me. GenGyan is a World’s Leading Training and Certification body conducting Quality based Training’s in India and International Location.