A few years ago, the American Statistical Association carried out research on the history of statistics, tracing their use throughout the course of human society’s development. The results of the study are displayed in the form of a chart called the Timeline of statistics, available on the association’s website.

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The chart shows that the first use of statistical data took place 450 years before Christ, when Hippias of Elis, a Greek sophist and Socrates’ contemporary, deduced the date of the first Olympic Games. He calculated the average length of the kings’ reigns known up until that time, and extrapolated from there, thus establishing the approximate date of the first Olympic Games, 300 years before the realisation of this study.

Another example of the use of statistics is King Rutuparna, presented in the Indian epic  poem Mahabharata, who estimated the number of fruits and leaves on two boughs of a vibhitaka tree by counting the fruits and leaves on a single twig. He multiplied the result with the number of similar twigs and this helped him conclude that 2095 fruits and 50 million leaves were on the tree. This estimation proved to be pretty close to the real number.

The Bible also contains references to the use of statistics from the period in which Israel was enslaved in Egypt. We find numerous passages in which the people of Israel are “counted”—meaning a census was taken. We also find an example from the New Testament in Luke 2:1-3: “In those days Caesar Augustus issued a decree that a census should be taken of the entire Roman world. (This was the first census that took place while Quirinius was governor of Syria.) And everyone went to their own town to register.”

Everyday statistics

Looking back, we may notice the particularisation of statistics. In the beginning, only rulers and their administrators had access to any records of people, territories, and goods. Later on, different institutions started to specialise and focus on very particular branches of statistics, in order to discover unique insights and form innovative solutions to problems.

Nowadays, statistics are used in many different fields, from medicine, advertising campaigns and marketing strategies to the economy, politics and religion. They influence popular beliefs and the daily choices most of us make.

When they are the result of meticulous scientific studies—methodologically correct, transparent and conceived to provide objective information—statistics are beneficial.

But at what point can statistics become harmful?

Biased statistics

If altered, through various methodological errors and not faithfully reflecting the bigger picture it analyses, a statistic can be used for manipulative purposes. In such cases, we are  most likely being confronted with biased statistics, which are the result of a subjective, partial, and biased study.

Taking statistics out of context

An error which is frequently made is using statistics outside of their proper context. Often, fragments from statistics are being presented, which are disconnected from their source and the real purpose for which they have been gathered. In such cases, not all of the relevant information about the study is being presented, and the tendency is to extract only those pieces of information which are necessary for leading the public towards a certain conclusion.

For example, there was a toothpaste advertisement which claimed that 80% of dentists recommend the advertised brand. In Great Britain, this slogan was  eventually banned after the case was looked at more closely: From the ad, consumers could draw the conclusion that 80% of dentists recommend that particular toothpaste only, while the other 20% recommend other products. In reality, the dentists who were interviewed had recommended several products, not just the advertised brand.

Therefore, the brand presented in the ad was just one of a number recommended products, but this was not mentioned in the commercial, precisely in order to make it seem as though the advertised product was special, and to stimulate sales of that particular brand. This misleading piece of advertising was banned in Great Britain by the Advertising Standards Authority.

The strategy of the herd effect

An efficient strategy, often used to distort the true meaning of statistics, is that of using overwhelming figures in favour of a certain product and leaving out information regarding counter indications, side effects of the product, or even information regarding the context of the analysis. For instance, one may use large but vague numbers to convince people to buy a certain hair product, based on other people’s convictions: “500 000 beauty parlours from around the world have ordered product X. Half a million salons cannot be wrong.”1

Believe, and do not doubt

There are cases in which statistics are fabricated and presented to the general public by an  apparent authority in a certain field, which is why challenging this data seems almost impossible, or at least hard to accomplish (usually, only via an approved authority). For the everyday person, the fact that this or that authority or brand claims certain data based on particular statistics is a sufficient criterion to accept the presented claims without further analysis.

In the years 2009 and 2010, a sports clothing and footwear company made the following statements about their products: “Lab tests showed that these sport shoes help develop the calves and hamstrings of up to 11% [of wearers] and, at the same time, by simply wearing them, they tone the thighs of up to 28%, compared to regular sport shoes”. This data proved to be completely false, and the Federal Trade Commission fined the company 25 million dollars for misleading advertising.

When a point goes down in history

While some biased statistics are intentional, there are also cases in which the results of certain studies may contain errors due to other reasons.

In 1870, the German chemist, Erich von Wolf, analysed the level of iron in spinach, among other studied plants. When he registered the results, he mistakenly placed the decimal point in the wrong place. While 100 grams of spinach contains just 3.5 milligrams of iron, the German chemist’s transcripts mention 35 milligrams—about the same as a small fragment of a paperclip. In 1930, German researchers rectified the mistake and publicly admitted that a mistake had been made. However, the discovery of the fact that spinach is a valuable source of iron proved to be a useful piece of propaganda during the Second World War, when the population lacked sufficient food variety. The statue of the spinach-gobbling Popeye in Crystal City, Texas, is a monument to how this cartoon character managed to raise spinach consumption by 33%.

Where is our faith headed?

An article published by BBC Future analyses religious convictions and their development through the ages. The article presents a few examples of old beliefs in a range divinities, which, in time, were replaced or mythologised. Based on these examples, it is concluded that, at a certain point, depending on certain data, religion may disappear. Noticing that the statistical data regarding Christianity shows a decrease in the number of worldwide adherents, the article suggests by analogy that, at some point, this religion will disappear too. This is actually an example of biased statistics and an incomplete analogy, which does not take into account Judaism, a religion which appeared long before Christianity yet still exists to this day. Additionally, the article fails to describe, in some historical situations, the sociopolitical context with its specific implications.

False truth

This oxymoron represents the state of affairs generated by distortions of reality at a social level. A society accepts a syllogism as a generally valid truth only for this to proved false after some time. If there was a time when tobacco was recommended by doctors as a remedy against coughing, now its harmful effect on the body, especially the lungs, has been proved. Yesterday’s truth has become false today, in the presence of new arguments. The belief accepted by Galileo Galilei’s seventeenth-century society, namely the flat Earth theory, was not acceptable to him. He was executed for taking a contrary position to that of the church authorities of that time, leaving behind the famous words: “And yet it moves”.

What is accepted by the majority is not automatically the truth.

Short prescription

To avoid the pitfall of false or incomplete statistics, it is necessary to identify the characteristics of the information presented. In which context were the statistics gathered? Is it the result of rigorous, scientific effort? Is the methodology correct? Is the source credible? Who paid for the study? What is the duration of its development? What is the sample, and how was the sample designed? Is there a degree of subjectivity involved? Are the data inconsistent? Are certain aspects left out, or veiled?

Critical thinking develops one’s capacity to distinguish reasoning errors when making an argument or a presentation. It helps identify the context, an idea’s implications and certain justifications, which enable us to understand the reality behind what we are presented with on a daily basis. Advertising campaigns, marketing strategies, or statistical data can be mistakenly or willfully distorted. Helping individuals to be more rational and critical thinkers may seem a small step for humanity, but, in the present context, it may represent the path to reform for a society which is ill with ignorance.

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1.
Marius Dobre, «Teoria sofismelor în abordări contemporane de gândire critică», in the Philosophy Magazine, volume LXI, no. 2, 2014, p. 143.