Makes Sense to Me (Production, Products, and Probability)

Ha! I notice that everyone was more than willing to explain what was wrong in my first post on this subject. But, as soon as the problem becomes more counter-intuitive, everyone runs away. 

Almost everyone — Zack Estes explained it perfectly. 

Let’s look at some numbers using the example from my second post and show that, while we might not like his motives, the Left Coast hating auditor is correct. Department #1 will be Customer Service and Department #2 will be Customer Complaints.

Department #1 Number of Transactions Number of Errors Error Rate
San Francisco 5 20%
New York 8 2 25%
New York has a higher error rate.   

                  

Department #2 Number of Transactions Number of Errors Error Rate
San Francisco  8 6 75%
New York 5 80%
New York has a higher error rate.

                                                                                                             

Departments Combined Number of Transactions Number of Errors Error Rate
San Francisco  13 7 54%
New York 13 46%
The overall error rate for San Francisco is higher.

 

As with the payment center example, the devil is in the details. And just to prove that this concept of understanding the underlying numbers is not purely an academic exercise, I am currently working with auditors looking at sales promotions. In one instance, management has indicated that there is a 6 percent increase in sales for those using a certain program versus a 0.5 percent increase for those not using it. We had just been discussing these blog entries when we started asking ourselves, “What really is beneath those numbers?” This has led to some stratification analysis and some interesting discoveries about what is actually occurring. At the end of the day, we may prove the success of the program. But it is a much more rigorous (and valuable) proof than the customer previously had available.

Now, let’s get away from those boring internal audit type issues and look at three (quick) logical missteps.

First, an easy one. The division had a horrible year last year and production was down 60 percent. However, last year the division turned it around and production was up 70 percent. The division is celebrating the fact that it is doing 10 percent better than last year. Why are the celebrations premature?

Second, a mathematical exercise, but very basic math nonetheless. (Nothing more than your basic algebra class.)

1. Assume a=b
2. Multiply both sides by a. a2=ab
3. Subtract b2 from both sides. a2-b2=ab-b2
4. Factor both sides of the equation (this one will really tax that algebra knowledge). 
(a+b)(a-b)=b(a-b)
5. Divide both sides by (a-b). a+b=b
6 Now assume a=1, which means (#1 above) b=1. 1+1=1 or 2=1

 

What happened/went wrong?

Third item, good old probability. A die is painted with four faces green and two red. Which of the following series of throws is most likely to occur?

  1. RGRRR
  2. GRGRRR
  3. GRRRRR

Take a stab and let us all know what you think? Answers and another exercise by the end of the week. (Not Monty Hall, but we’ll get there eventually.)

 

 

Posted on Feb 16, 2010 by Mike Jacka

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