"There are three kinds of lies: lies, damned lies and stastics."

Remember the last idea you pitched at work? Chances are, you came up with the concept, fleshed out the details, and then found a ton of numbers to substantiate your claim. More often than not, business is an outright numbers game, and statistics are vital if you want to play. Qualitative data doesn’t suffice when it comes to getting hard evidence. But the sad fact is that statistics are ridiculously easy to manipulate, and because we rely on numbers to tell the truth, the results can be particularly misleading.

The Law of Averages
When we’re presenting a group of numbers, we often simplify our data to an average figure. For example, the average cost of placing an advertisement is $5,000, or the average number of microwaves sold in July is 325. And while that average may be statistically true, it could actually be highly inaccurate. For example, you might read something like "executives at XYZ Corporation make an average annual salary of $250,000." But if you looked at the raw data, you might find that the CEO made $3,000,000 while the other executives made less than $80,000. In this instance, the median (or middle) value would represent a far more accurate picture.

Incomplete Statistics
Statistics are often used to substantiate comparative claims – for example, "88% of those surveyed prefer QRS brand potato chips." But this statistic fails to mention the sample size. Think about it – we all know that there’s a 50% chance that a tossed coin will come up heads. But if you flip a coin six times in a row you might get one head and five tails. Does this mean that the original statistic is wrong and in fact, a coin will come up heads 16% of the time? Of course not – it’s just that we didn’t conduct the experiment with a large enough sample size. If we don’t know what the sample size is, we have no way of evaluating the accuracy of the statement. So maybe 8 out of 9 people questioned preferred QRS chips, but is this really the kind of information on which you want to base an investment decision?

Another example of an incomplete statistic is a claim such as "ABC ink jet printers use 22% less ink." Is that 22% less ink than other ink jet printers, other printers in general, or printers developed 10 years ago? Without a basis of comparison, this claim is essentially worthless.

Picture Perfect
The most popular way to present statistical data is with a graph. Technically, a graph should be more accurate than a statement, since it represents all of the variables of your data. But graphs can be just as misleading when you’re depicting statistics.

Consider the following annual sales report:
 
The results show slow but steady growth. However, if we take the same graph but cut the bottom off, the figures are still the same, but sales growth looks far more impressive.

 

Now, if we really wanted to manipulate the data to show dramatic results, we could alter the scale used. 

1Benjamin Disraeli (1804-81), English statesman, author. Quoted in: Mark Twain, Autobiography, ch. 29 (ed. by Charles Neider, 1959). 

The exact same data now shows exponential sales growth for the period. So remember, if you’re using a graph to interpret results, make sure you check the scale. Manipulating the scale is a simple way of dramatically altering the visual impact of a set of data.

Percentages or Percentage Points?
One final point – be aware of the difference between percentages and percentage points. A percentage point is a unit of measurement that is calculated as a portion of 100. A percentage is a portion of the whole (where the whole isn’t necessarily 100). Consider the following example. A manufacturer sold 52 stereos in April and 33 of them (or 63%) had a faulty component. The industry average for faulty parts is 35%. Manufacturer A claimed that its incidence of faulty parts was only 28% higher than the industry average. Actually, it was 28 percentage points higher than the national average – but 80% higher. This is because the base figure here is 35, not 100. So in order to calculate the percentage difference, you have to divide 28 by 35, and multiply by 100.

"People are unpredictable by nature, and although you can take a nation's pulse, you can't be sure that the nation hasn't just run up a flight of stairs"

These few points are really just the tip of the iceberg – there are literally hundreds of ways to manipulate statistics. Despite the assertion that "the numbers don’t lie," it’s easy to see that numbers are just as easy to manipulate as words. So the next time you’re looking at graphs and statistics, make sure you consider the story behind the figures, and not just the numbers that you see in front of you!  

Reference:
Darrell Huff. How to Lie with Statistics.
New York: W.W Norton & Company, 1954.

1. H.G. Wells


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