![]() ![]() ![]() ![]() Over millions of years, we got pretty good at adding together whole numbers. We’re never chased by 1.7 mountain lions or must have 2.5 children to carry on the species. “Whole number dominance” makes sense from an evolutionary standpoint: things in nature really only come in whole numbers. One theory that explains why we are bad at percentages - as well as fractions and decimals - is that humans evolved math skills only dealing with whole numbers. While this was only a single study, the prevalence of double discounts in stores is strong evidence marketers had already figured out and were using this cognitive shortcoming.Ī basic principle is when we refuse to do the math ourselves, we will be fooled by someone who has done it. Not surprisingly, the double discount generated more purchases, more revenue, and more profit than the equivalent single discount. One of the studies in the paper “When Two Plus Two” looked at the effect of in a retail setting of presenting a discount as a single decrease or two percentage discounts. Multiple percentage changes are only one example of framing, which has a profound impact on our choices (read about framing in “The Framing of Decisions” by Tversky and Kahnemann). Any piece of data can be presented in multiple ways - for example, a medication can be described as having 10% chance of causing a side effect or as having a 90% chance of causing no side effects (the framing here is positive versus negative). What the salesperson would be doing in these situations is framing: presenting information in a context to get us to make a decision in her favor. Instead of presenting these increases separately - where adding gets you to 50% - the seller would be better off presenting them as one number, 56%, which is the actual increase. Or consider a computer with a display that has 20% more pixels than the last model which had 30% more than the previous. The salesperson wants you to add the percentages and conclude the discount is 75% instead of the more modest 62.5% discount for the actual value. This occurs often in retail where you can take an extra 25% off an item on sale for 50% off. )įor example, look at the “double discount”. For more on this, read Influence by Robert Cialdini. (It’s a good rule of thumb that errors in human logic are discovered first in marketing and only later are they published in academic journals. As with most other human errors, there are people already taking advantage of it for their benefit. Knowingly or not, we deal with multiple percentage changes all the time and when we don’t realize this, it’s usually to our detriment. Why Does this matter?Īll of the above were hypothetical examples of very real situations. Students were worse than 2 years previous not better, and their parents were still math illiterate (but not you anymore!). Not to be a downer, but the total overall change - wait, work this one out yourself - was a 31% decrease in test scores. Had you made the common error, you would have ended up on the wrong side of 0! A similar error occurred when standardized test scores in California decreased by 60% one year and increased by 72% the next, resulting in praise for the raising of student scores from the baseline. In the last case, adding the two percentages gets you a 20% increase in what was actually a 4% decrease. Our primary resource is the paper: “When Two Plus Two Is Not Equal to Four: Errors in Processing Multiple Percentage Changes” ( link). In this article, we’ll discuss what the error is, how to avoid it, why this matter, and why people make it. Yet, despite the ubiquity of the error and the ramifications for us personally and as a nation, we are incapable of teaching people how to correctly stack percentages. We thus have another entry in the long list of things people aren’t very good at, combining multiple percentage changes.įar from being an abstract, theoretical idea, finding a total change from a sequence of percentage moves has implications in our daily lives from the price of consumer goods to national budgets to our retirement account value, to the battery life on our newest laptop. The common error is taking the percentages at face value and adding them together to get the overall percentage change. Not only did the majority of college students get this question wrong, they did not even get the correct direction, with over half guessing this was an increase. The answer, of course, is C, an overall decrease of 4%. What is the total percentage change in the following situation?ĭecrease of 40% followed by an increase of 60%. Incredibly, after 16 years of schooling, the majority of American college students get this question wrong: Solving a Common Math Problem with Everyday Applications ![]()
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