Statistical Language - Correlation and Causation
A correlation between two variables does not imply causation. On the other hand, if there is a causal relationship between two variables, they must be correlated. the meanings of statistical terms like correlation, association, and causality. the other (relationship trouble); or they can be negative, which would mean that. The four approaches to causality include neo-Humean regularity, Taken together the evidence for a relationship between smoking and lung cancer now.
Rothman contends that the Bradford - Hill criteria fail to deliver on the hope of clearly distinguishing causal from non-causal relations. For example, the first criterion 'strength of association' does not take into account that not every component cause will have a strong association with the disease that it produces and that strength of association depends on the prevalence of other factors.
In terms of the third criterion, 'specificity', which suggests that a relationship is more likely to be causal if the exposure is related to a single outcome, Rothman argues that this criterion is misleading as a cause may have many effects, for example smoking. The fifth criterion, biological gradient, suggests that a causal association is increased if a biological gradient or dose-response curve can be demonstrated.
However, such relationships may result from confounding or other biases. According to Rothman, the only criterion that is truly a causal criterion is 'temporality', that is, that the cause preceded the effect. Note that it may be difficult, however, to ascertain the time sequence for cause and effect. The process of causal inference is complex, and arriving at a tentative inference of a causal or non-causal nature of an association is a subjective process.
For a comprehensive discussion on causality refer to Rothman. Bull World Health Organ, Oct.
What’s the difference between Causality and Correlation?
Hill, AB, The environment and disease; association or causation? Why are observational data not conclusive? We can never conclude individual cause-effect pair. There are multiple reason you might be asked to work on observational data instead of experiment data to establish causality. First is, the cost involved to do these experiments. For instance, if your hypothesis is giving free I-phone to customers, this activity will have an incremental gain on sales of Mac.
Causality - Wikipedia
Doing this experiment without knowing anything on causality can be an expensive proposal. Second is, not all experiments are allowed ethically. For instance, if you want to know whether smoking contributes to stress, you need to make normal people smoke, which is ethically not possible. In that case, how do we establish causality using observational data?
There has been good amount of research done on this particular issue. The entire objective of these methodologies is to eliminate the effect of any unobserved variable.
In this section, I will introduce you to some of these well known techniques: Panel Model Ordinary regression: This method comes in very handy if the unobserved dimension is invariant along at least one dimension. For instance, if the unobserved dimension is invariant over time, we can try building a panel model which can segregate out the bias coming from unobserved dimension. But, because the unobserved dimension is invariant over time, we can simplify the equation as follows: We can now eliminate the unobserved factor by differencing over time Now, it becomes to find the actual coefficient of causality relationship between college and salary.
And then compare the response of this treatment among look alikes. This is the most common method implemented currently in the industry. The look alike can be found using nearest neighbor algorithm, k-d tree or any other algorithm.The Geometry of Causality - Space Time
One of them starts smoking and another does not. Now the stress level can be compared over a period of time given no other condition changes among them. This is actually a topic for a different article in future. This is probably the hardest one which I find to implement.
Correlation does not imply causation
Following are the steps to implement this technique: Find the cause — effect pair. Find an attribute which is related to cause but is independent of the error which we get by regressing cause-effect pair.
This variable is known as Instrumental Variable. Example 1 Sleeping with one's shoes on is strongly correlated with waking up with a headache. Therefore, sleeping with one's shoes on causes headache.
The above example commits the correlation-implies-causation fallacy, as it prematurely concludes that sleeping with one's shoes on causes headache. A more plausible explanation is that both are caused by a third factor, in this case going to bed drunkwhich thereby gives rise to a correlation. So the conclusion is false.
Example 2 Young children who sleep with the light on are much more likely to develop myopia in later life. Therefore, sleeping with the light on causes myopia. This is a scientific example that resulted from a study at the University of Pennsylvania Medical Center.
Published in the May 13, issue of Nature the study received much coverage at the time in the popular press. It did find a strong link between parental myopia and the development of child myopia, also noting that myopic parents were more likely to leave a light on in their children's bedroom.
Example 3 As ice cream sales increase, the rate of drowning deaths increases sharply. Therefore, ice cream consumption causes drowning. This example fails to recognize the importance of time of year and temperature to ice cream sales.
Ice cream is sold during the hot summer months at a much greater rate than during colder times, and it is during these hot summer months that people are more likely to engage in activities involving water, such as swimming. The increased drowning deaths are simply caused by more exposure to water-based activities, not ice cream.
The stated conclusion is false. This suggests a possible "third variable" problem, however, when three such closely related measures are found, it further suggests that each may have bidirectional tendencies see " bidirectional variable ", abovebeing a cluster of correlated values each influencing one another to some extent.
Therefore, the simple conclusion above may be false. Example 5 Since the s, both the atmospheric CO2 level and obesity levels have increased sharply. Hence, atmospheric CO2 causes obesity.
Richer populations tend to eat more food and produce more CO2. Example 6 HDL "good" cholesterol is negatively correlated with incidence of heart attack. Therefore, taking medication to raise HDL decreases the chance of having a heart attack.