Causal relationships: A causal generalization, e. Begin typing your search term above and press enter to search. Press ESC to cancel. Skip to content Home Assignment How can correlations be misused?
Ben Davis February 26, How can correlations be misused? Does correlation always signify cause and effect relationship? How are correlational and causal relationships different? Why is correlation not causation? What does a correlation not prove? What is an example of correlation but not causation?
Can correlation ever equal causation? The correlation of two variables that both have been recorded repeatedly over time can be misleading and spurious. Time trends should be removed from such data before attempting to measure correlation. To extend correlation results to a given population, the subjects under study must form a representative i.
The Pearson correlation coefficient can be very sensitive to outlying observations and all correlation coefficients are susceptible to sample selection biases. We can see that if total debt remains constant then, a fall in the equity price can increase the leverage ratio. And it is at this point where the equity price may influence credit spreads. The literature also demonstrates the highly non linear relationship between credit spreads and the equity market, particularly during times of stress 5 6 7 8.
Avramov et al. However, during tranquil periods there is no clear relation between default risk and stock returns. The second assumption listed earlier relates to constant mean and variance. In practice this means correlation either calculated numerically or via visual inspection of charts will be misleading when either or both variables exhibit long term trends i.
Such trending behaviour may also violate the third assumption of independence. In these cases, the variables may be trending up or down together over long time horizons but may move in opposite directions over shorter periods. The relationship between two series can only be assessed after the horizon of interest has been defined.
For example, Figure 3 plots two constructed series which have a long term positive trend, but which also by construction are negatively correlated over 24 month horizons. Based on this extremely high correlation and visual inspection of the chart below we might conclude that these two series always move in the same direction over all horizons.
But this is not the case. Figure 4 plots the 24 monthly returns of series two against the 24 monthly returns of series one.
There is a very strong negative linear relationship between the returns of the two series. This tells us that over any month period, if series one appreciates, series two will depreciate. Why is this happening? The series share behaviour trend over the long term, but not over the short term.
Ecologists and epidemiologists commonly use the correlation coefficient to assess spatial or temporal relationships, and in such studies observations may be either spatially or temporally autocorrelated. We look at several examples of this including a study relating solar radiation in a state to the incidence of colon cancer, a study relating abundance of the small blue butterfly in a habitat to abundance of its foodplant, and a study relating reproductive traits of fish over time to environmental characters.
In all these cases and several others the coefficient is likely to be biased towards unity giving a spurious correlation. Although most authors freely admit that their observed correlation cannot prove causality, one still gets the feeling that many feel it damn well should prove it, and that it is only the cussedness of statisticians that prevents them from claiming causality.
Yet ignoring random variation many apparent relationships could easily result from confounding factors - for example in the study relating the incidence of inflammatory bowel disease to a proxy variable for poverty. The apparent inverse relationship could just result from people in wealthier countries being more informed about the disease and being more ready to report symptoms, especially for a disease which does not automatically hospitalize or kill.
Remarkably few authors rigorously apply the generally accepted criteria for causality to the matter at hand. In one example we even see evidence of bias in selection of observations in an attempt to demonstrate a relationship which may simply not exist - the relationship between homicide rates and suicide rates is wildly unconvincing to all but the author.
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