Type 1 - Type 2 Errors and Kalidasa
A recent post by Joshua Starmer PhD asked about the Data Science/ML terms that are generally confusing. Now for me Type 1 and Type 2 errors certainly qualify for an eternally confusing statistical pair.
As a student of MS Economics, I was lucky to have a brilliant prof of statistics in Prof K. Suresh Chandra (visiting faculty at Madras School of Economics) who simplified the terms. They have remained etched permanently in my mind since.
Prof Chandra encapsulated Type 1 and Type 2 errors in chronology of the story of Sanskrit poet and playwright Kalidasa and one of his famous play - ?Abhij?Äna?Äkuntalam. In the play, king Bharata falsely rejected his wife Shakuntala's claim that she was indeed his wife. It happened because King Bharata was cursed with selective amnesia. Now, since Kalidasa wrote this historical play it obviously preceded Kalidasa's life. And hence the error in which a true null hypothesis gets rejected is called Type 1 Error or False positive or Alpha.
On the other hand, Kalidasa's life, which definitely came into existence after ?Abhij?Äna?Äkuntalam era, had a Type 2 error. The story goes that Kalidasa was not that bright in his youth but got packaged as some one brilliant by bunch of vindictive men to take revenge on wise Vidyotama. The reality became clear only after Kalidasa and Vidyotama got married. This non-rejection of a false null hypothesis (null hypothesis being Kalidasa was intelligent) is Type 2 error or False Negative or Beta.
Power of a test
Power of a test is a related concept. It is the probability of rejecting a false null hypothesis. Using Kalidasa-Vidyotma story, the probability that Vidyotma wouldn't have married Kalidasa is Power of the Test.
Post Script-
Adding a beautiful story - commented on the original post by my ex-manager and mentor Ashish J. - of how Kalidasa, spurned initially by his wife, became one of the all time best play wright.
"That second story has an interesting end. When Kalidasa returns home as an erudite, he knocks at the door and says - "Dvaramudghatay" (open the door). Vidyottama asks, "Asti Kashchit Vagvishesham?" (Is there anything special to talk?) And Kalidasa goes on to write three different mahakavyas - Kumarsambhavam, Meghadootam and Raghuvansham - starting with these three words each (Asti, Kashchit and Vagvishesham)".
GenAI | Data Scientist | Master of Arts in Economics
2 å¹´Thanks it was really helpful!
AGM @ EIL, Data Analyst (IIM-K), AI-ML (IIT-D), PG in Data Science, LSSBB (CSSC), Project Management (IIT-D) (Oil & Gas), TQMP? (MSI), Lean Expert (AIGPE), Lead Auditor : ISO 9001, 14001 & 45001, MINITAB, Python & R
2 å¹´Good one!! One way to memorise is as follows: Type I -- Alarm sounds even when No Fire. Type II -- No Alarm even when fire breaks out. Often Type II errors cost more. Though depends on case to case.