Yes. A statistical result that is visible when classified data disappears or reverses when a combination of the same data is done. This is called Simpson’s Paradox. Edward Simpson was a statistician who also worked as a cryptanalyst at his former University, Bletchley Park. He described this statistical phenomenon that later took up his name in a technical paper done in the 1950s. Thus, Simpson Paradox argues on the favourite things concerning data: the need to have a good intuition regarding the natural world and how data in a larger dimension is complex (Sowey & Petocz, 2017). Simpson encourages people to see beyond data to master its art of science. This means that academicians need to use and develop tools that generate ideas of what the hidden reality looks or feel like. His paradox also highlights the significance of scepticism and how data can be interpreted in the real world. It is dangerous to oversimplify a complicated truth by viewing the whole scenario from a single point of view. Hence, this essay will explain how the paradox can lead to confusion and misinformation and critically avoid becoming a victim.
Simpson Paradox is a situation that happens when the result that appears in the dataset that is separate either reverses or disappears when the data is aggregate (Merikoski, 2017). Two examples will be highlighted to assist in the understanding of how the paradox can lead to misinformation. The first example of the Simpson Paradox is the famous scenario of gender- bias that happened at his institution, UC Berkeley. In 1973, the institution was beginning its academic year. As a result, it admitted almost 44% of the male students and 35% of the female counterparts. The story is that the institution was later sued for gender discrimination, although this was not true. Since the school feared the lawsuit, they engaged a statistician, Peter Bickel, to investigate the data. What he gathered was interesting. Statistically speaking, the gender bias favoured females for 4 out of six departments, with no gender bias for the remaining 2. Bickels and his team found that female applicants applied to departments that had a small percentage of the overall applicants, and the hidden variable impacted the marginal values of accepted applicants. Essentially, the conclusion of this lawsuit changed when Bickels team used departments to account for the total admission to the school. As a result, this changed the whole data-viewpoint.
The second example is of two friends trying to choose between two restaurants. Assume that these two friends, Alex and Anna, are looking for the best restaurant to have a pleasant and sumptuous meal. Since finding the best restaurant can lead to many hours of arguments, they both decide to use the standard oracle of life: online platforms. By doing so, Alex choice, X Restaurant, has high reviews than Annas choice selection, Y Restaurant. However, since it is straightforward, X Restaurant triumphantly takes the lead; Anna refutes their claims and state that Y Restaurant is more recommended as it has a higher percentage of all users. So who is lying at this point? Are the reviews at the site miscalculated? While both of them may be right, they have unknowingly entered the Simpsons paradox.
Based on the two examples above, Simpsons paradox can be misleading and make it hard to make decisions (Li, 2020). People can regroup, resample and even scrutinize data to their best ability, but if there are many conclusions drawn from the various categories, selecting a group to have a final insight and develop a decision is difficult. Thus, the hidden variable must be understood, and a person has to choose a data-viewpoint that gives a fair share of the truth. Mark Liddell also argues on Simpson’s paradox by stating that in as much as statistics are persuasive; they can lurk inside, which can turn the whole results upside down (Liddell, 2016). Hence, to avoid two opposite conclusions, people need to choose how to segregate data together or in groups. While it seems so simple to do so, how can the same conclusion be achieved? Think casually about how the data was obtained, and based on this, find out the factors that influence the results. Unfortunately, these factors are not always shown in the data.
Take another simple example in a business setting. Please assume that the sales department in a soft drinks company is trying to choose between two new flavours they have produced. The team has decided to sample public opinions on the two flavours. Two sampling stalls are set up for each taste on a busy highway, and they ask about 1000 people at each booth if they enjoyed the new flavours. 85% of the participants enjoy the “sour strawberries”, and only 75% want the “sweet peach”. In this case, the sour strawberries take the lead on the most preferred flavour. Now suppose that the sales team collected other information while doing the sampling criteria, for instance, the sex of the participants sampling the drink. What might happen if the data is divided up by gender? This would mean that 85% of men and 42% of women liked the sour strawberry. On the other hand, 86% of men and 45% of women liked sweet peach. The results may be a little strange for anyone who pauses to think how the same was arrived at. Indeed, that effect is the Simpsons Paradox!
Anyones intuition will tell them that the most preferred flavour by both males or females should also be preferred when sex is unknown. And it is even more confusing to discover that that is not true- which becomes the heart of the paradox. Hence, the hidden variable in the paradox is the lurking variable, and they are not easily identified. However, this might not be the case in the soft care drink example. The sales team should be quick to see that using the sex of the participants inevitably impacts their opinion. A straightforward way the paradox can be explained is to consider the lurking variable- sex, and some bit of probability theory.
X (Preferred Strawberry) = X (Preferred Strawberry | Male) X(Male) + X (Preferred Strawberry | Female) P(Female)
850/1000 = (740/900) (900/1000) + (42/100) (100/1000)
X (Preferred Peach) = X (Preferred Peach | Male) X (Male) + X (Preferred Peach | Female) X (Female)
750/1000 = (600/700) (700/1000) + (150/300) (300/1000)
In the probability theory above, the marginal probabilities of gender (X (Male) and X (Female) as indicated in the case of “sour strawberry” makes the total probability shift towards the male side. While there is a hidden male bias in the “sweet peach” sample, it is not quite strong, and therefore a more significant proportion of the female opinion is taken into account. As a result, there is a lower marginal probability for the entire population sample to like this flavour, despite each gender liking it when the sample is separated.
However, before making any decision, it has to be noted that not the same people will like the same flavour. When participants are divided into sex, then the results can be very different. So how can one avoid becoming a symptom of Simpson’s paradox? The paradox can be resolved by understanding data, which entails exploring how it was generated and establishing the lurking variable (Pearl, 2014). Hence, this cannot be regarded as a randomized controlled experiment but an observation of how people decide. In the examples above, it is clear that people prefer Sour Strawberries to Sweet Peach and both men and women have a preference for each.
In all the above examples, the weighting of the sample can be a result of a minor error in the sampling methods. For instance, in the soft care drink scenario, the act of generating data was inherently flawed. Hence, it is essential to know if the presented data is poorly sampled or an actual case of a paradox. Also, from a business perspective of promoting a product, the sampling technique of a product will be attractive to particular demographics, and this may present a lurking variable. This was the same case with the UC Berkley experiment, where women were more likely to choose specific departments. While it is correct to analyze data by gender, the results do not reflect an accurate picture of the overall population. Therefore, it is essential to carefully examine the actual situations from the statistics and identify a lurking variable present. Otherwise, we can be vulnerable to those people who use the same data to manipulate us while promoting their agendas.
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