When a person is selling a product or an idea, it is natural to present a positive bias that reflects well on their perspective. While the best scientists, teachers, and judges may epitomize some of the exceptions to this statement, there are still enough counter-examples that we must be wary of the natural bias of our human nature. We all need to remember that rose-colored glasses are built into human reasoning and communications.
Here are a few generic examples of bias and ambiguity in the use of percentages.
- Sales grew 15% over last month. If last month’s sales were terrible, this number may paint an overly rosy picture.
- You added 15 new hires to your organization last month. If the goal was 45 new hires, 15 is not very good performance compared to plan.
- Your GPA went up 20%. If your last GPA was 2.1 and your new GPA is 2.5, this may fall short of your parents’ expectation of a B average.
- Your 401K account was up 21% over last quarter. If the rest of the markets were up 40%, your performance was relatively weak.
- Sales of product A were up 100% and product B only 10%. If product A’s sales last period were only $100,000 and product B’s were $10,000,000, these data are potentially misleading.
- The Dodgers won 6 more close games (decided by 1 run) this year than last year. This number is more significant if they won 10 close games last year than if they won 60.
- Politician X voted to cut taxes 90% of the time. If politician X voted yes 27 times on trivial tax-cutting bills and voted No on 3 significant tax-cutting bills, this measure may completely obfuscate his stance on tax cutting.
- 66.7% of doctors recommend this remedy for this affliction.
The last one is particularly interesting. With three digits of precision, you get the feeling that there must be a pretty thorough analysis behind that claim. But what if some advertising drone asked three doctors their opinions and two responded positively? That would make 66.7% an accurate but potentially misleading answer.
A more honest measure would state that two out of the three doctors asked recommended the remedy.
There are several ways to present numbers, and it is important to communicate them honestly. It is also important as an audience or a listener to be skeptical when the numbers presented fail to tell the whole story.