Illusory correlations¶
Alena DeVaughn & Jason Ah Chuen
Imagine you are at a children’s birthday party, and everyone is having a good time. There are decorations, toys, and sweets everywhere. After the children eat their cake, open their goodie bags, and enjoy their spoils from the piñata, the gaggle of children seem to have a second wind of energy and are running and playing so quickly and loudly that they seem to be bouncing off of the walls. What is your first impression on the cause of their behavior? In this instance, many parents attending the party would remark, “All this sugar sure is making them hyper,” or something along those lines. Enough Americans hold this conception that candy and sugar is correlated to high-energy boosts in children that for most it feels like common knowledge. However, contrary to this extremely popular belief, multiple studies spanning years of research all conclude that there is no scientific evidence that the two are related (Wolraich et al., 1995). So how do people come to that conclusion that children + candy = hyperactivity?
An illusory correlation is the mistaken belief that two unconnected variables have a strong relationship (Chapman, 1967). This can happen for a variety of reasons, but generally occurs when a person sees an association between two events but falsely infers that there is a correlation there which doesn’t actually exist in reality. As a result, they then make incorrect judgments concerning the existence of that correlation. This error in observation may be because an individual is paying too much attention to irrelevant information, like events that statistically only happen quite infrequently, or it may be due to a person’s preconceived notions about the information they are being presented with. People build up illusory correlations over time because of observations they’ve made across many situations, but it’s also possible to create an illusory correlation in an instant, when a person sees something strange and immediately makes assumptions about what they’ve seen from then on. Either way there is a tendency for people to create predictions like these and then use those beliefs to make judgments in the future, meaning that our illusory correlations affect the way we view the world and the way we behave as a result.
Initial Research¶
Chapman originated this term and the research on its topic in 1967. He hypothesized that stimuli that are either distinctive or associated with each other in the person’s mind lead a person to perceive correlations between events that are not correlated at all.
To test this, Chapman showed students word-pairs that had varying levels of association with each other, i.e. door-head, door-knife, and fork-knife. 36 word-pairs in total were repeatedly shown to each participant, in 3 successive testings and split in 3 different groups of words. 6 of the pairs had strong semantic associations with each other (such as fork-knife). Importantly, each pair was shown equally often.
Participants were then instructed to report in a questionnaire; they were shown one of the primary words (door, in the above example) and all its possible coinciding words (head, knife, and magazine), and asked what percentage of the occurrences of the left word was shown with the right word. In support of his hypothesis, students reported the co-occurrences were higher for word-pairs that have stronger semantic associations between their meanings. In other words, though each word-pair was repeated the same amount of times, students reported that pairs like “fork-knife” or “lion-tiger” occurred together more often than pairs like “hat-tiger” and “boat-egg”. This opened the door to show how associations can lead us to erroneously overestimate an occurrence’s importance and frequency. Chapman proposed after his study that the results reflect real-life situations.
Distinctiveness-based Correlations¶
Chapman’s initial research on this topic also showed how distinctiveness is also effective at creating an illusory correlation (1967). In the same study, students reported, similarly to associated word-pairs, that distinctive word-pairs occurred more often than non-distinct and non-associated pairs. Chapman did this by including exceedingly long words as a marker for “distinctiveness”. Of the 30 non-associative word-pairs, 3 of the pairs were arbitrarily and unusually long. These, similar in length to “envelope-sidewalk,” were included at the same frequency as all other pairs. However, once again participants reported that these occurred a higher percentage of the time– showing that participants believed the distinct stimuli occurred more frequently. The results from this portion of the study were also concluded to be representative of a person’s experience in a real-life scenario.
Distinctiveness-based correlations happen when a person focuses too closely on strange or noticeable information and overestimates how significant it is in the explanation of a relationship. Subconsciously honing in on a variable that stands out creates a bias so that it appears as though we are more likely to unwittingly determine that unique and unusual information is explanatory of a connection between two events (Hamilton & Gifford, 1976). When a person sees something weird, different, or distinct, we naturally and often subtly pay extra close attention to it, making us prone to using these more “easily available” observations when trying to explain other incoming stimuli. This explains why Chapman’s 1967 study found that people were more likely to assume that the distinctive long word-pairs were more common than the typical short word-pairs.
In an explanation of how this can occur, Hamilton and Gifford posited that a person is more likely to mentally associate two variables with each other because that extra attention on the unique event actually leads to greater encoding (1976). They attempted to delve deeper in order to test their hypothesis that these judgments can be created “on the basis of purely cognitive, information-processing mechanisms”(p 392). In order to achieve this without including the role of previous associations, the researchers had to create novel stimuli that the participants had never encountered before, so they invented two groups of people: Group A and Group B. By creating new groups instead of testing participants on existing groups that are differentiated by race or gender or class etc., the researchers could be sure that the results wouldn’t be skewed due to the participants’ pre-conceived beliefs and associations connected to each group. Group A and Group B were assigned actions that were coded as “desirable” or “undesirable”. Hamilton and Gifford showed each group multiple times to the participants, and every time each group was assigned four descriptive actions. Group A was shown more often than Group B, and desirable actions were shown more often than undesirable ones. Researchers therefore measure both Group B and undesirable behaviors as “distinctive”. At the end of the study, participants had to report how many of the statements reflected the behavior of each group, and how many of the statements were undesirable. Hamilton and Gifford’s hypothesis predicted that participants would overestimate how often the two distinctive events occurred together. This happened - participants reported that the undesirable actions were attributed to Group B, the smaller group, much more often than they actually had. Their bias in estimating the occurrence of undesirable vs desirable behaviors as it relates to occurrence of each group led them to perceive each group differently. This has important implications for the formation of stereotyping in real world scenarios, as we will touch on later.
Expectancy-based Correlations¶
Expectancy-based correlations happen when people have pre-existing expectations of relationships. Hamilton and Rose were among the first to study the phenomenon in an experiment in 1980, wherein participants read trait-descriptive sentences about different groups of people and the traits were either aligned with (that is, stereotypical) or just neutral with the expectancies for people in each group. Two stimulus sets of people were created, one using male names and traditionally male occupations, and the other using female names and traditionally female occupations. For male stimuli the stereotypical traits chosen were “accountants (perfectionist, timid), doctors (thoughtful, wealthy), and salesmen (enthusiastic, talkative)” and the chosen neutral traits were “courteous” and “boring”. For female people, the stereotypical traits chosen were “librarians (productive, serious), stewardesses (attractive, comforting), and waitresses (busy, loud)”, while their neutral traits were “clever” and “demanding”. The neutral and stereotypical traits were paired the same number of times for each group. The dependent variable being measured for this experiment was the frequency at which the subjects estimated that each trait adjective was used to describe members of each occupational group. The participants used in the study were a group of 20 males and 16 females. The results showed that the participants overestimated the frequency of stereotype-congruent traits that were used to describe the groups, although there were no correlations between the traits and occupations in the stimulus sets created. This means that the participants perceived relationships that would be expected on the basis of their stereotypic expectancies. A similar second experiment was conducted but in which neutral traits were paired more frequently with the group as compared to the stereotypical traits. The results for this second experiment showed that the stereotypical traits were still more frequently associated with their groups, which would mean that relationships mentioned are perceived as stronger if they confirm a stereotype even though they might actually appear as often in the evidence.
One way of interpreting the results is through the availability heuristic (Tversky & Kahneman, 1973). The latter is a “judgmental heuristic in which a person evaluates the frequency of classes or the probability of events by availability, i.e., by the ease with which relevant instances come to mind.” This can lead to systematic biases and illusory correlations. In fact, their paper also talks about illusory correlations and shows that traits that are associated with each other are more easily retrieved from memory and thus their frequencies are overestimated, just like in the two experiments mentioned above.
Another way that Hamilton and Rose explained their findings above is through the schema theory (Rumelhart & Ortony, 1977). A schema describes a pattern of thought or behavior that organizes categories of information and the relationships among them. The schema theory itself is that information in our brain is organized into those schemas, and the latter are thus used to select and organize any new information and integrate it into our existing knowledge. Information can also be retrieved from those schemas whenever we need it. The way it explains illusory expectancy-based correlations is that information is more easily stored and retrieved if it belongs to an existing schema. Hence, when traits are stereotypical or expected for a particular group, they are both encoded and retrieved more effectively from memory.
Reconciling expectancy-based and distinctiveness-based effects¶
The expectancy-based correlations and distinctive-based correlation effects seem to contradict each other since the subject’s prior expectancies lead to different outcomes. For expectancy-based correlations there is an overestimation of congruent effects, but in distinctiveness based correlations there is a better recall of incongruent rather than congruent effects. For example, in the Hamilton and Rose (1980) study, congruent effects would refer to the examples where traits are stereotypical or expected of the social groups, and incongruent effects would refer to examples for which the traits seem to be incompatible with the associated groups. In 1996, Garcia-Marques and Hamilton tried to explain this contradiction via the TRAP (Twofold Retrieval by Associative Pathways) model. In summary, the model proposes that retrieval processes occur through either free recall and frequency estimation, which themselves depend on different processes. Free recall initiates an exhaustive search through memory for the target object. Since there are a larger number of inter-item associations between incongruent items formed during the initial encoding phase, this exhaustive search causes more incongruent behaviors to be recalled. This means that incongruent information is processed more extensively, which thus explains distinctiveness-based illusory correlations. Conversely, frequency estimation takes a more heuristic approach whereby we try to sample items that have the target attribute. Congruent information has stronger associations with the target attribute, which speeds up the process of retrieval through frequency estimation and thus results in expectancy-based correlations. This theoretical framework model can thus explain the two seemingly incompatible types of illusory correlations.
Real-Life Implications¶
Such correlations can explain stereotype threats in humans on the negative side, and possibly halo effects which can sometimes be positive but negative at other times.
Let’s first consider stereotype threat, which is defined as the socially-premised psychological threat experienced by someone who is in a situation or doing things for which there exists a negative stereotype about that person’s social group belonging and they thus become more likely to conform to that stereotype (Steele & Aronson, 1995). It is one of the most widely studied phenomena in social psychology, especially as people from marginalized groups usually suffer from it even today. The original experiment for stereotype threat comes from that same paper, and it showed that African American subjects underperformed on a test when it was viewed as an indication of their intellectual ability but they did similarly to their White peers when it was not viewed as a indication of intellectual ability. This showed that the existence of social stereotypes can impede performance in academic fields, and possibly in many other fields too. How do those stereotypes happen in the first place?
The “paired distinctiveness” concept that came up in the Hamilton research has implications for the creation of stereotyping. As a reminder, participants viewed undesirable behavior as infrequent and unusual, and they viewed Group B as infrequent and unusual, and from there they developed an illusory correlation that the two were related. When one transfers the trends shown in the research onto real-life situations and groups of people, it seems possible that if people view a “Group B” as distinctive, and “undesirable behaviors” as distinctive, that they will then be likely to cognitively generalize and begin to associate those traits with an entire group of people. Though these types of decisions about the connection between stimuli, (such as racial groups and personality/behavioral traits), are unconsciously made and unintentionally reinforced, they end up becoming strongly held, conscious beliefs that have real effects on how we purport stereotypes onto outside groups of people and behave accordingly and intentionally.
Stereotyping can also be explained through expectancy-based correlations. Like presented in the findings of Hamilton and Rose (1980), stereotypes consist of a large number of expectancies in regard to a social group and we are more likely to recall information or traits that are in line with those expectations in contrast to expectancy-irrelevant information. Hence, this biases the processing of information as we interact with different social groups. For example, if one has the prior belief that “girls are bad at math” and they interact with a girl in a math class setting, they would be more likely to find and process cues that show that the girl is indeed bad at math, which will confirm their expectations. Unfortunately, such a mechanism would cause the perceiver to even further believe in the validity of the stereotype and reinforce their expectations for the future, which is why stereotypes usually persist for a long time, if not for all of one’s lifetime. Alas, that girl who might actually be really good at math but is aware of those stereotypes, might end up underperforming or feeling less confident of her own math abilities.
Halo effect, also known as halo error, is a type of cognitive bias whereby our perception of someone’s ability to be good at something is positively influenced by the person’s other related traits. The halo effect might be due to the fact that people extrapolate their general impression of others to attributes that they actually have no information about (Nisbett and Wilson, 1977). For example, people tend to think that attractive people are nicer and less attractive people are less nice, although there is actually no correlation between the two attributes. Several papers have made use of illusory correlations as one of the theories that can be used to explain the halo effect. For example, Chapmans’ 1969 illusory correlations study, in which illusory correlation was seen as an obstacle for clinicians to determine the sexual orientations of their clients, is discussed in the “Ubiquitous Halo” paper (Cooper, 1981) as well as in “Nature and Consequences of Halo Error: A Critical Analysis” (Murphy, Jako, Anhalt, 1993). The cognitive distortions and errors in judgement in the papers are also often referred to as “illusory halos” (which are essentially illusory correlations) as opposed to “true halos” which are actual correlations, although it has been shown that it is really hard to distinguish the two.
How we can (try to) avoid falling for illusory correlations¶
It is very hard to avoid falling for illusory correlations. If we try to analyze the relevant data, we might want to try to recall it from our own experience, but this process and data retrieved would be biased. Instead, we can try to look at and analyze the data that people have collected through rigorous methods and perform statistical tests on it to show whether or not there is any amount of correlation, if any. For example, a contingency table is usually used in statistics to analyze relationships between categorical variables. A chi squared test can be performed on the variables to see whether a relationship does exist between them. When the variables are continuous, instead the correlation coefficient between the two variables can be calculated to determine how strong the relationship is between the two variables.
However, we note that people usually do not have such data that is needed to compute these statistics for the kinds of judgements involved in illusory correlations. This brings us back to our original point that avoiding illusory correlations is very hard!
Conclusion¶
Illusory correlations are common occurrences for the average person. Given the evolutionary need to make split-second judgments about stimuli in order to ascertain one’s safety, it makes the most sense for the human brain to make generalizations in order to speed up the process of deciding what is trustworthy and what is dangerous. This issue today comes because of the tendency of our brains to make such generalizations based on limited and irrelevant information like previous associations and infrequent events, meaning that this prioritization of speed leaves a margin of neglect when it comes to accuracy. Even though these mental connections are being formed unconsciously, they can end up manifesting as strongly held beliefs that inaccurately portray an outside individual’s traits, and in a greater sense are generalized onto large groups of people. Illusory correlations should be a factor that is kept in mind when trying to determine what kind of mistakes a person may have made in their appraisal of a situation, and where the beliefs and assumptions that led to the mistake resulted from.
References¶
Chapman L.J. (1967). Illusory correlation in observational report. Journal of Verbal Learning and Verbal Behavior, 6 (1) , pp. 151-155.
Chapman, L. J., & Chapman, J. P. (1969). Illusory correlation as an obstacle to the use of valid psychodiagnostic signs. Journal of abnormal psychology, 74(3), 271.
Cooper, W. H. (1981). Ubiquitous halo. Psychological bulletin, 90(2), 218.
Garcia-Marques L, Hamilton DL. Resolving the apparent discrepancy between the incongruency effect and the expectancy-based illusory correlation effect: the TRAP model. J Pers Soc Psychol. 1996 Nov;71(5):845-60. doi: 10.1037//0022-3514.71.5.845. PMID: 8939036.
Hamilton D.L., Gifford R.K. Illusory correlation in interpersonal perception: A cognitive basis of stereotypic judgments (1976) Journal of Experimental Social Psychology, 12 (4) , pp. 392-407.
Hamilton, D. L., & Rose, T. L. (1980). Illusory correlation and the maintenance of stereotypic beliefs. Journal of personality and social psychology, 39(5), 832.
Murphy, K. R., Jako, R. A., & Anhalt, R. L. (1993). Nature and consequences of halo error: A critical analysis. Journal of Applied psychology, 78(2), 218.
Nisbett, R. E., & Wilson, T. D. (1977). The halo effect: evidence for unconscious alteration of judgments. Journal of personality and social psychology, 35(4), 250.
Rumelhart, D.E., & Ortony, A. (1977). The representation of knowledge in memory. In R.C. Anderson, R.J. Spiro & W.E. Montague (Eds.), Schooling and the acquisition of knowledge (pp. 99-135). Hillsdale, NJ: Erlbaum
Steele, C. M., & Aronson, J. (1995). Stereotype threat and the intellectual test performance of African Americans. Journal of personality and social psychology, 69(5), 797.
Tversky, A., & Kahneman, D. (1973). Availability: A heuristic for judging frequency and probability. Cognitive psychology, 5(2), 207-232.
Wolraich, M. L., Wilson, D. B., & White, J. W. (1995). The Effect of Sugar on Behavior or Cognition in Children. JAMA, 274(20), 1617.