Numbers don't lie?

Statistics offer us a great understanding of the world view of certain things or to lay out what history has brought us. We are made to believe that “numbers don’t lie”. Yes, it is true that with proper research, citation, and calculations, the numbers presented are accurate. But it is easy to “lie” with statistics by cherry picking data.

For instance, if I were to say that 80% of medical bodies recommend Novavax for the COVID vaccine. Does that mean that it is the best vaccine out there? Perhaps. But if we were to look at the following pictorial, it is true that 80% of medical experts recommend Novavax but 100% of them recommend Pfizer or Moderna. This is by no means a vaccine recommendation and numbers are just for illustration purposes. This is because there can be multiple recommendations! But, just based on this headline, would it be a wise decision to throw in the cash to invest in their stocks?

There’s also the concept of choosing certain numbers from a different base to represent an angle to manipulate perception. For example, if let’s say Company T with a yearly sales number of 1 million recalls 1,000 cars due to malfunction in Year 2021 and 2,000 cars in Year 2022. The data can be represented as “Company T’s cars recalled has increased by 0.1%” or “Company T’s cars recalled has increased by 100%”. The choice of our base can lead us to have a total change of perception of the company. It’s also the same as saying that a company is losing traction when its revenue is growing 40% ten years ago vs. 16% one year ago. This is because the base of the past year is immensely different. And, for this case, do check if the profits are increasing too rather than just looking at a revenue growth as costs may decline at the same time!

This example may go from a time series into two different groups. For example, if 1000 males and 100 females applied to a company. 80 males and 20 females got accepted. The outcome can be framed as “8% males and 20% females accepted” if we take the base of applicants or “80% males and 20% females accepted” based on the number of available seats. Does this mean anything about the company’s view of meritocracy or gender equality?

Correlations and probabilities may not hold constant contrary to what we may believe. In investing, we harp on the idea of portfolio theory. According to this theory, if we can find a weightage of stocks that are perfectly opposite in correlations i.e. -1 and +1, we are sure to profit. Some investors then firmly believe in this perfect winning strategy until they receive a rude awakening – a market crash. Turbulent times may result in correlations to move in tandem and bunch up and this is exactly the time where investors need a safety net but fail to have one because of the blind faith in a static correlation. Industries that were once moving in opposite directions may both see a plunge with a changed economic environment. One possible explanation could be that the whole equity market is facing withdrawals and thus stock prices fall all together and directly opposite correlations fail to hold. Stock prices are not independent any more given a new development in the markets.

A real-life incident that can explain this concept would be a famous case of Sally Clark who got falsely accused of being a child murderer for killing her 2 babies. It’s around 1 in 9,000 for a baby to die from Sudden Infant Death Syndrome (SIDS). And thus, about 1 in 81 million for both of her babies to die – assuming the events were independent. The court used probability theory to explain how she must be the killer. However, the court was wrong because genetics is the reason for why these two events are not independent of one another – and thus the court made a wrong ruling. Yet, her life was turned upside down and reputation tarnished, and she committed suicide not too long after her release.

Speaking of genetics, is this upcoming case a sheer coincidence or something related? Attention Deficit Hyperactivity Disorder is a very commonly diagnosed special need. It is said that about 10% of children have ADHD. ADHD is also known to be highly genetic – 3 out of 4 cases will have a mum or dad or relative that has ADHD. You see, given the fact that the population has a 10% chance of getting ADHD, there’s a (100% - 10%)^2 = 81% chance that both parents do not have ADHD. And that means, 19% that either parents or both parents have ADHD. Expanding this concept to a family tree of 13 people which is not difficult to achieve if we include grandparents into the mix, we can observe a (100% - 10%)^13 = 25.4% chance that all relatives do not have ADHD. Now, can we really conclude that ADHD is highly genetic? In investing, we may also think that patterns repeat itself or the movement of prices are related – yet, it may just be an illusory correlation. Don’t get me wrong – I’m not saying that ADHD isn’t genetic. But with such a high incidence rate of ADHD and how easily it is being diagnosed on almost anyone begs the question if it is truly correlated or could it be just an illusion.

With all numbers that appear in the financial world, we will need to check our sources and bases. Do verify if there is a possibility that there may be an alternative explanation to the numbers that we see. By holding back and ruminating on the facts, it gives us a better insight to the fundamentals of the claims we see about financial events. We may also be able to activate our System 2, a more pensive thought process, to remove the cognitive biases that we have when making decisions.

If you're interested to chat on this topic or to exchange ideas, please feel free to drop me a message on Telegram @elijah2212 or through email elijah.thj@gmail.com!