Makes Sense to Me (The Beginning)
It is amazing what our minds do to us. And we are never quite so obstinately unintelligent as when we think — nay, we know — that our conclusions based on numbers and statistics are absolutely true.
Those numbers lie.
I started thinking about this when I had cause to revisit the book Inevitable Illusions: How Mistakes of Reason Rule Our Mind by Massimo Piattelli-Palmarini. This is an excellent book about people’s tendency to go down mental tunnels — logical journeys to erroneous facts — and I would advise anyone to pick it up. In addition, some co-workers and I also recently were talking about the “Monty Hall Problem.” (We will revisit that one later.)
To explore this, I’m going to use my next few posts to pose some questions and provide real-life examples of how our logic and common sense can so easily mislead us. Let’s start with an easy one — ripped from the pages of actual audit work.
An auditor is evaluating the depositing practices of a payment processing center and wants to determine if it is meeting its goal (90 percent of all collections deposited the same day they are received in the department). For the two-week period under review, he obtains the following percentages.
Week 1 | Week 2 | |
Mon | 80% | 85% |
Tue | 95% | 95% |
Wed | 95% | 95% |
Thu | 99% | 98% |
Fri | 100% | 100% |
By adding the percentages and dividing by 10, he determines that 94 percent of payments are processed the same day as received. Since the department’s objective is 90 percent, he concludes that they are effectively meeting their objective.
The Auditor-in-charge knows this isn't right, but can't quite put his finger on why. Where is the fallacy in the auditor's thinking and why might the department not be meeting that objective?
Go ahead and post your thoughts below. The answer and the next problem in a couple of days.
Posted on Feb 8, 2010 by Mike Jacka
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The auditor in incorrect in his thinking because he is assuming that the department recieves around the same number of payments each day. If the department happens to received most of the payments on Monday then the department would be out of compliance. For example, on Mondays they recieve 100 payments and 80 are compliant and on Tues, Wed, Thur, and Friday they only receive 10 to 15 payments thier overall compliance would be less than 90%.