How statistics can mislead you?

misleading statistics

Mankind has used statistics for thousands of years. The Roman Empire gathered statistics by conducting census.

Statistics sound impressive. They seem so solid, so specific and irrefutable. Figures don’t lie, we are told.

But be on guard. Honestly used, they can be very informative and useful. However, statistics can also be presented in a way that misleads you.

How figures can mislead you?

Percentages, averages, charts and proportions—statistics may be delivered in a host of ways."

And, either by accident or by design, people may use essentially accurate figures to present a biased or distorted picture.

For example, the percentage sign has a comfortable, persuasive air of respectability and finality.

But percentages are not always used fairly. Consider the production figures of two home-building companies:

                                     2012     2013      Increase      Increase in percentage                                        
Northlakes Bldg. Co.    30        60              30                     100%

Cottage Const. Ltd.      208      312            104                    50%

The use of the percentage figure alone would give a wrong impression—that the Northlakes Building Company was the more successful of the two. 

In fact, the increase in production by Cottage Constructions was more than three times that of Northlakes.

Beguiling also may be the sense of proportion.

Although an advertisement may proudly proclaim: “Nine doctors out of every ten prefer this method,” we may reasonably wonder what the other thousand doctors in the country think who were not asked to give an opinion.

And if it is true that “leading dentists recommend this brand of toothpaste,” it may also be true that they recommend most, if not all, the brands of toothpaste available today.

Just as the summary of a book on its jacket cannot possibly tell the whole story, such proportional presentations of figures cannot give a totally unambiguous report.

Consider also the statement: “More people die in bed than anywhere else.” 

That is possibly true, but does it mean that it is dangerous to spend time in bed?

Well, look a little closer and you will probably find that this is largely because people who are very sick and likely to die are put in bed.

Suppose, too, that statistics told you that the outback town of Alice Springs, Australia, has less illiteracy than the major city of Sydney.

Would you conclude from this that the country teachers in the outback are more capable than the city teachers in Sydney?

It may sound like that, but there are just more people living in Sydney. Alice Springs also has less literacy than does Sydney!

Additionally, the actual presentation of statistics can be a "means of persuasion."

An unassuming 35 percent, for example, can be made to sound either good or bad, depending on how it is presented.

To assert, “There were at least 35 percent present” is far more flattering than to mutter, “There were only 35 percent present.” 

Yet, when you think about it, both statements are saying essentially the same thing.

Bad understanding of averages

Most people think they understand averages, until they start to use them.

There are many kinds of averages, and each is intended for a different problem.

You may do a good job of sewing with a needle and a thread, but a needle used for making potato sacks would have limited value in surgery.

Similarly, to use the wrong kind of average in a calculation will lead to confusion.

Consider Sam Jones the greengrocer. He was selling two grades of tomatoes, one slightly better than the other. Grade A was sold at 2 kilograms for $3.

He sold 60 kilograms of these and received $90.

Grade B sold at 3 kilograms for $3. He also sold 60 kilograms of these, netting $60, making a total of $150 for 120 kilograms of tomatoes.

The next week, Sam decided to combine grades A and B and sell them for seemingly the same amount, pricing them at 5 kilograms for $6.

He sold the same quantity as before, 120 kilograms. But, adding up his receipts Sam found that this week there was only $144 in his till, whereas last week there had been $150. What had gone wrong?

Sam did not calculate the true average, or mean. He should have calculated the price per kilogram and then taken the average of that. Thus:

2 kilograms at $3.00 = $1.50 per kilogram

3 kilograms at $3.00 = $1.00 per kilogram

Average = $1.25 per kilogram

In this way, 5 kilograms should have sold for $6.25. Sam lost money because he did not understand averages.

Good use of statistics

When handled carefully and in a professional manner, statistics are valuable. And the misuse of them by some does not detract from their value when used properly.

Statistics gathered on road accidents help authorities to determine which weekends and seasons will necessitate a greater policing of driving habits.

It is because of accident statistics that some lands have introduced the compulsory wearing of seat belts in auto-mobiles and the testing of drivers’ breath for alcohol content.

When statistics reveal that there is a big increase in crimes such as fraud, forgery and false pretenses this helps the authorities to decide how best to deploy available police forces.

Reports of a 10-percent rise in motor-vehicle thefts, or in the suicide rate, also help in their decision making.

Should we build more hospitals? If so, where? Which age group is involved in most car accidents and thus needs special attention?

What diseases and ailments are the most widespread and thus need the most attention to handle and prevent?

How successful has this or that advertising campaign been? Statistics that have been professionally gathered and honestly presented are invaluable in making decisions in areas such as these.

Handled sensibly, such statistics can help you make wise decisions. But be on guard.

They can also be handled deceitfully to mislead you.

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