Causal reasoning relates to establishing the presence of causal relationships among events.  When causal relationships exist, there is good reason to believe that events of one type (the causes) are systematically related to events of another type (the effects).

I.  Introduction of causal reasoning

Causal reasoning relates to establishing the presence of causal relationships among events.  When causal relationships exist, we have good reason to believe that events of one type (the causes) are systematically related to events of another type (the effects).  It may become possible for us to alter our environment by producing (or by preventing) events if we can identify the causes.

Most studies of student ability to coordinate theory and evidence focus on what is best described as inductive causal inference (i.e., given a pattern of evidence, what inferences can be drawn?).

If there is a causal relationship between variables x and y, there can be several kinds of causes:

Necessary causes:  If x is a necessary cause of y, then the presence of y necessarily implies the presence of x with a probability of 100%.  The presence of x, however, does not imply that y will occur.

Sufficient causes:  If x is a sufficient cause of y, then the presence of x necessarily implies the presence of y with the probability of 100%.  However, another cause z may alternatively cause y.  Thus the presence of y does not imply the presence of x.  For example, if it is sunny outside, then it is daytime.  It being sunny is a sufficient cause for one to conclude that it is daytime.  But just because it is daytime does not necessarily mean it is sunny outside.

Contributory causes:  If x is a contributory cause of y, it means the presence of x makes possible the presence of y, but not with the probability of 100%.  In other words, a contributory cause may be neither necessary nor sufficient but it must be contributory.  For example, stubbing my toe causes pain.  Stubbing my toe is a contributory cause to being in pain because I could be in pain from a headache or sore throat instead.

II. The most common logic fallacy:  correlation implies causation

The thinking model is as follows:  A occurs in correlation with B; therefore, A causes B.  This is a logical fallacy because there are at least five possibilities for the correlation between A and B:

1. A may be the cause of B

2. B may be the cause of A

Consider the following statement:  the more firemen fighting a fire, the larger the fire.  If B is the cause of A, then firemen cause fire.  The strong correlation between the number of firemen at a scene and the size of the fire that is present does not imply that the firemen cause the fire.  Firemen are sent according to the severity of the fire and if there is a large fire, a greater number of firemen are sent; therefore it is fire that causes firemen to arrive at the scene.

3. Some unknown third factor C may actually be the cause of both A and B

In a widely-studied example, numerous studies showed that women who were taking combined hormone replacement therapy (HRT) also had a lower-than-average incidence of coronary heart disease (CHD), leading doctors to propose that HRT was protective against CHD.  Just because there is a correlation between HRT and CHD does not mean there is any causal relationship between the two.  If we want to prove a causal relationship, we need select a sample of people who could represent the whole population and randomly separate then into two groups.  The first group would be treated with HRT while the second group gets a placebo.  Only if the incidence of CHD in first group is lower than in the second group, we can conclude that HRT was protective against CHD.

In reality, randomized controlled trials showed that HRT caused a small but statistically significant increase in risk of CHD.  Re-analysis of the data from the initial studies showed that women undertaking HRT were more likely to be from higher socio-economic groupswith better than average diet and exercise regimes.  The use of HRT and decreased incidence of CHD were coincident effects of a common cause (the benefits associated with a higher socioeconomic status), rather than the cause and effect relationship that had been supposed.

4. There may be a combination of the above three relationships

One way this can occur is that B causes of A, and, at the same time, A causes B.  This describes a self-reinforcing system and is called bidirectional causation.  An example is the relationship between pressure and temperature.  The ideal gas law, PV = nRT, describes the direct relationship between pressure and temperature (along with other factors) to show that there is a direct correlation between the two properties.  For a fixed volume, an increase in temperature will cause an increase in pressure; likewise, increased pressure will cause an increase in temperature. The two are directly proportional to each other and not independent functions.

5. The "relationship" is a coincidence, or it is so complex or indirect that it is more appropriately called a coincidence

This could mean that two events occurring at the same time have no direct relationship to each other besides the fact that they are occurring at the same time. A larger sample size helps reduce the chance of a coincidence, unless there is a systematic error in the experiment.  One example is as follows.  Since the 1950s, both the atmospheric CO2 level and the crime level have increased sharply.  A conclusion of atmospheric CO2 causes crime doesn’t make sense.  The two are simply a coincidence.

III.  Sample question of correlation-causation

Question ID: 20200100100

A zoologist travels to Africa to study the natural breeding environment of giraffes. While there, he notices a type of tall tree that produces a special fruit that only grows at the top of the tree. He also notices that giraffes that frequently eat this fruit appear to be stronger and taller than those who cannot reach the fruit. He concludes that the fruit contains rich nutrients which make the giraffes that eat the fruit grow stronger and taller. Which one of the following statements do you agree with?

1. When a giraffe frequently eats this special fruit, it grows stronger and taller.
2. The nutrients in the fruit can help the giraffe grow stronger and taller.
3. Both A and B are correct.
4. The result is not sufficient to demonstrate that eating the fruit causes a giraffe to grow stronger and taller.
5. None of the above statements is reasonable.

Notes:  In this question, the zoologist observes a positive correlation between the frequency of eating fruit from a tall tree and the height of the giraffes.  He then concludes that eating the fruit cause the giraffes to be taller.  This is a typical “correlation implies causation” fallacy.  It is quite possible that tall giraffes eat from the tall trees just because they are tall. We cannot make any conclusion about whether or not the fruit makes the giraffe taller.

IV. The importance of causation

1. The importance of causation in society

Causation is useful because people use such relationships to predict what will happen next, which guides their lives.

2. The importance of causation in science

Causation is useful in scientific research because scientists use such relationships to predict experimental outcomes and make possible deductions.

V. Review of research on casual reasoning

The few developmental studies that have been conducted have been used to conclude that causal inference rules emerge in childhood and remain established well into adulthood with key developmental divergences being adults’ superior abilities to differentiate between causes and enabling conditions and to consider a greater amount of information when making judgments (e.g., Harris, German, & Mills, 1996).

What constitutes adequate evidence of causation is highly debated among researchers.

1. Covariation

Hume (1988/1758) identified the covariation of perceptually salient events as one potential cue that two events are causally related. Even young children have a tendency to use the covariation of events (antecedent and outcome) as an indicator of causality (e.g., Gopnik, Sobel, Schulz, & Glymour, 2001; Inhelder & Piaget, 1958; Kelley, 1973; Schulz & Gopnik, 2004; Shultz, Fisher, Pratt, & Rulf, 1986; Shultz & Mendelson, 1975).  Although covariation between events is a necessary but not sufficient cue for inferring a causal relationship, it is one of the bases for making inductive causal inferences.

Kuhn, Amsel, and O’Loughlin (1988) were responsible for pioneering work on the development of children’s and adults’ evaluation of covariation evidence. Their primary motivation was to examine how participants reconcile prior beliefs about causal variables (but not causal mechanisms) with covariation evidence presented to them.

Cheng develop a probabilistic model of causal induction based on their covariation. (e.g., Cheng, 1997; Lien & Cheng, 2000)

2. Causal Mechanism

Koslowski questioned the assumptions about the primacy of covariation evidence. One of the main concerns in scientific research is with the discovery of causes (Koslowski & Masnick, 2002). In real scientific practice though, scientists are also concerned with causal mechanism, or the process by which a cause can bring about an effect. Koslowski noted that we live in a world full of correlations. It is through a consideration of causal mechanism that we can determine which correlations between perceptually salient events should be taken seriously and which should be viewed as spurious.

For example, it is through the identification of the e.coli bacterium that we consider a causal relationship between hamburger consumption and illness or mortality. It is through the absence of a causal mechanism that we do not consider seriously the classic pedagogical example of a correlation between ice cream consumption and violent crime rate.

In the case of theories about human or social events, Ahn, Kalish, Medin, and Gelman (1995) also presented evidence demonstrating that college students seek out and prefer information about causal mechanism over covariation when making causal attributions (e.g., determining the causes of an individual’s behavior).

A series of experiments presented by Koslowski (1996) as well as research from the conceptual development (e.g., Brewer & Samarapungavan, 1991; Murphy & Medin, 1985) and causal reasoning literatures (e.g., Cummins, 1995; Schulz & Gopnik, 2004; Shultz et al., 1986; White, 1988) support the idea that both children and adults hold rich causal theories about “everyday” and scientific phenomena that include information about covariation, theoretically relevant causal mechanisms, and possible alternative cause.

VI. References for correlation-causation

Cheng, P. W. (1997). From covariation to causation: A causal power theory. Psychological Review, 104, 367-405.

Cheng, P. W., & Novick, L. R. (1990). A probabilistic contrast model of causal induction. Journal of Personality and Social Psychology, 58, 545-567.

Cheng, P. W., & Novick, L. R. (1992). Covariation in natural causal induction. Psychological Review, 99, 365-382.

Kuhn, D. (1989). Children and adults as intuitive scientists. Psychological Review, 96, 674–689.

Schulz, L. E., & Gopnik, A. (2004). Causal learning across domains. Developmental Psychology, 40, 162–176.

Shultz, T. R., Fisher, G. W., Pratt, C. C., & Rulf, S. (1986). Selection of causal rules. Child Development, 57, 143–152.

Shultz, T. R., & Mendelson, R. (1975). The use of covariation as a principle of causal analysis. Child Development,46, 394–399.

Koslowski, B., & Masnick, A. (2002). The development of causal reasoning. In U. Goswami (Ed.), Blackwell handbookof childhood cognitive development (pp. 257–281). Oxford: Blackwell Publishing.

Koslowski, B., & Okagaki, L. (1986). Non-Humean indices of causation in problem-solving situations:Causal mechanisms, analogous eVects, and the status of rival alternative accounts. Child Development, 57,1100–1108.

Koslowski, B., Okagaki, L., Lorenz, C., & Umbach, D. (1989). When covariation is not enough: The role of causal mechanism, sampling method, and sample size in causal reasoning. Child Development, 60, 1316–1327.

Hume, D. (1988/1758). An enquiry concerning human understanding. BuValo, NY: Prometheus Books.