Independence of events, and errors in understanding it

Abstract

This article outlines errors that may occur when people predict event outcomes. The focus is on how our tendency to perceive independent events as connected, consistent with tenets of Gestalt Psychology, biases our expectations. Two well-documented phenomena that occur when people make predictions after a run of a particular outcomethe "gambler's fallacy" and the "hot hand"-are used to illustrate the issue, and research is presented that highlights the importance of misperceptions of independence. Novel implications and hypotheses are presented that are generated from use of this gestalt approach.

Secondary and university students' understanding of independence and conditional probability

“…The study confirmed students' problems with understanding the concept of independence as known from the literature (Díaz et al, 2010;Roney, 2016). In the tasks on independence (1-6), to an extent, the students could create sample spaces for two-stage experiments, which indicates that their probabilistic thinking is on the unistructural level (Mooney et al, 2014).…”

“…Two well-documented misconceptions in this area are the gambler's fallacy and the hot hand fallacy (Roney, 2016), in which the law of large numbers plays a crucial role. It posits that the ratio of the outcomes corresponding to event A and all the outcomes approaches the probability of event A.…”

“…It is based on the mistaken belief that if a random event has occurred more frequently than usual, it will occur less frequently in the future. Similarly, the hot hand fallacy (Roney, 2016) is the belief that there is a greater chance of success after a series of successful trials. Graham explains possible reasons for this misconception: People sometimes appeal to the "law of averages" to justify their faith in the gambler's fallacy.…”

“…Other perspectives on the gambler's fallacy emphasise its psychological aspects. For example, a long run of the same results motivates the participants to make certain conclusions and judgments (Roney, 2016). A long run of red numbers in roulette leads to the belief that it must be interrupted at some time.…”

“…Misconceptions and misinterpretations in the perception of the independence of random events are well documented. For example, the gambler's bias and the hot hand fallacy (Roney, 2016) are grounded in a student's belief in the internal connection between consecutive events. We often meet fallacies related to independence when looking for all possible outcomes.…”