Correlation with Causation

Experimental (random) error Confusing correlation with causation 

Employing a study design that is complex, when a simpler one would be as good 

Random variability—experimental error—is produced by a multitude of uncontrolled factors that tend to obscure the conclusions one can draw from an experiment based on a small sample size. This is a very critical consideration in research where small sample sizes are the mle, because it is more difficult to detect significant treatment effects when they truly exist, a type 11 error. 

One or two wild data points (outliers) in a small sample can distort the mean and hugely inflate the variance, making it nearly impossible to make inferences—at least meaningful ones. Therefore, before experimenters become heavily invested in a research project, they should have an approximation of what the variability of the data is and establish the tolerable limits for both the alpha (a) and beta Q3) errors, so that the appropriate sample size is tested. 

Although, traditionally, type 1 (a) error is considered more serious than type 11 Q3) error, this is not always the case. In research and development (R D) studies, type 11 error can be very serious. Eor example, if one is evaluating several compounds, using a small sample size pilot study, there is a real problem of concluding statistically that the compounds are not different from each other, when actually they are. Here, type 11 Q3) error can cause a researcher to reject a promising compound. One way around this is to increase the a level to reduce j3 error that is, use an a of 0.10 or 0.15, instead of 0.05 or 0.01. In addition, using more powerful statistical procedures can immensely reduce the probability of committing j3 error. 

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The two problems we have just discussed add up to a weakness in the best-known theory of scientific explanation, that proposed by Carl Hempel. He argues that explanation amounts to logical deduction of the event to be explained, with general laws and statements of initial conditions as the premises. One objection is that the general laws might reflect correlation, not causation. Another is that the laws, even if genuinely causal,... 

Finally, even when HC composition and cuticular transpiration are correlated, causation cannot be assumed. For example, higher cuticular water-loss rates in the desert ant, Pogonomyrmex barbatus, are correlated with a decrease in abundance of an n-alkane and an increase in a methylalkane (Figure 6.2 Johnson and Gibbs, 2004). This is exactly what one would expect if lipid melting points affect cuticular permeability, but this increase is also accompanied by a change in mating status. Mated, de-alate queens that have founded... 

Humphrey I want to come back to the question of correlation and causation. It s tempting of course to assume that a relation between two variables is causal when we can see how it would work, but to assume it s a mere correlation when we can t see it. So, when we find that IQ correlates with brain size or head size, we think that s probably because large brains do indeed cause high IQ. But when we find IQ... 

Kim raises another worry about dependence that is related to the common cause objection. He argues that causal dependence cannot distinguish the situation in which mental events are genuine causes from the view in which they are mere epiphenomena that are nomologically correlated with brain events that are the genuine causes. Kim pictures the situation involving mental causation as follows ... 

For this reason, other techniques are required to provide unequivocal evidence for the effect of a food or a food component in the causation or prevention of disease. One important techniqne is epidemiology, in which factors such as serum levels, adipose tissue levels, or dietary intake of a component can be correlated with the incidence of, or death from, major diseases such as cancer and coronary heart disease. Serum and adipose tissue levels of a component such as CLA can be measured accurately however, they indicate only recent intake and may not be indicative of intake in previous years or at a time close to the initiation of the disease. Although subject to assessment error, dietary intake at various periods can overcome these difficulties. Final proof of efficacy for a component in disease prevention is provided by the randomized, double-blinded, clinical intervention study. 

How well can causation be inferred from correlation The problem is akin to inferring the design of a microprocessor based on the readout of its transistors in response to a variety of inputs. The task is impossible in a strict mathematical sense, in that the microprocessor layout could be arbitrarily complicated, but is likely to prove at least somewhat tractable in a more constrained biological setting, especially when combined with ways to cut specific wires in biological circuits using antisense and related techniques. 

An ethological view, then, keeps us focused on behavior and its adaptive value. It leads to the realization that human motives, or emotions, raise fitness by serving tissue needs in quite direct ways, more directly than do learning and cognition. This may seem obvious to ethologists, but this functional perspective is virtually absent from most mainstream approaches to emotion and motivation. The proximate causation of emotions and their visceral and expressional correlates is described in detail, but with little consideration of the adaptive value of the behavior or its correlates. 

A concern about the above correlates is that they do not imply causation. Because covaries with other purported causal determinants of social outcomes, for example SES, the causal antecedents of its correlates are equivocal. In Terman s (1925— 1959) famous longitudinal study of intellectually gifted participants, for example, subjects were appreciably above the norm on several educational and vocational criteria. On various indices of physical and psychological health, they were also significantly better off than normative base rate expectations would lead one to... 

A difficulty with conclusions based on observations is that correlation of changes does not prove causation. As Gillbricht (1988) pointed out for the Helgoland... 

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