Statistics is more complex than our minds want us to believe. We are inclined to think in very different ways, often leading to errors of judgement. For example, when an event occurs more often than expected in a certain period of time, we tend to believe that it will occur less frequently in the next period. This reasoning is wrong and unfounded. The reason why this happens is that people, who make decisions about the future, rely on sequences of past outcomes, and are influenced by a non-existent correlation and an information misuse.
The impulsive aspect of our minds make it is easy to identify cause/effect relationships between events even when the connection is minimal or non-existent. We tend to not accept fate, so we process data in order to force meaning upon it. We interpret this too small sample of events as if it was adequately representative of the entire population and the result is a distorted interpretation of these data.
This is what is called inductive statistics: to determine a rule about a population of reference by observing a reasonable size sample and representativeness, in order to have a small margin of error in the result. When the sample is numerically small, inferential statistics leads to important misleading situations. The problem is that the ‘law of small numbers’ is used by many people in everyday context to assess situations and to obtain answers that otherwise could only be explained by chance.
Two common errors arise in this context: the gambler’s fallacy and the hot-hand fallacy. The term fallacy is defined as an argument that is credible but logically flawed by hidden errors in the reasoning that consequently make it false.
The ‘gambler’s fallacy’ is a logical error concerning the misconception that past events have influence on the future ones, when in reality these situations happen by chance. Usually, these fallacies are related to the law of small numbers explained above. When faced with unusual events, the brain looks for a solution to the problem and hypothesises a way to interrupt the observed trend in order to re-establish a classical pattern.
For example, if we consider a coin toss, we have the same 50% probability to get head or tail. Moreover, each toss result will be independent: if head comes up five times in a row, we will be mentally led to think that tail will come up in the next toss. In reality there will always be a 50% chance regardless of the history of the previous five tosses. The outcome is random and even the head or tail streaks occur by chance. Therefore, the misperception of random processes leads to prediction errors.
In contrast, the ‘hot-hand fallacy’ predicts that independent outcomes are positively correlated. This tendency leads people to predict that a series of equal outcomes will continue in the future, despite the absence of scientific evidence, and each event is independent to the other.
Both fallacies are two sides of the same coin: when evaluating different situations to make future decisions, people often rely on past results and look for a pattern in time series that have no influence on what will happen in the future. In fact, the idea that a series of events has predictive power is an illusion and people who are affected by the gambler’s fallacy, or the hot-hand fallacy misinterpret random sequences.
In general, the characteristics that make subjects more likely to commit these types of errors of judgement occur when:
- there is a presence of long series of the same result,
- the two situations occur close together,
- the incentives are low,
- the decision-maker has little experience.
The two fallacies occur in many fields or sectors and stem from the propensity of individuals to apply the law of large numbers to small sample sizes, expecting the few observations to be perfectly representative of the distribution of infinite observations.
People sometimes make mistakes when they have to make decisions and, if they are contextualised in the financial market, they can lead to significant financial losses.
In conclusion, understanding the hot-hand fallacy and the gambler’s fallacy provides insight into how individuals rely on a variety of past data to make decisions about the future. These two phenomena indicate the propensity of individuals to believe that two independent events are actually autocorrelated and that it is possible to predict the future by analysing past data.
Written by Riccardo Pandini.
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