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An example of a spurious relationship can be found in the time-series literature, where a spurious regression is one that provides misleading statistical evidence of a linear relationship between independent non-stationary variables. In fact, the non-stationarity may be due to the presence of a unit root in both variables.
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 drunk , which thereby gives rise to a correlation.
Simpson's paradox has been used to illustrate the kind of misleading results that the misuse of statistics can generate. [7] [8] Edward H. Simpson first described this phenomenon in a technical paper in 1951, [9] but the statisticians Karl Pearson (in 1899 [10]) and Udny Yule (in 1903 [11]) had mentioned similar effects earlier.
For example, an electrical utility may produce less power on a mild day based on the correlation between electricity demand and weather. In this example, there is a causal relationship, because extreme weather causes people to use more electricity for heating or cooling.
On the other hand, the approach remains valid even in the presence of correlation among the test statistics, as long as the Poisson distribution can be shown to provide a good approximation for the number of significant results. This scenario arises, for instance, when mining significant frequent itemsets from transactional datasets.
Cum hoc ergo propter hoc (Latin for 'with this, therefore because of this'; correlation implies causation; faulty cause/effect, coincidental correlation, correlation without causation) – a faulty assumption that, because there is a correlation between two variables, one caused the other. [57]
The consequences of such misinterpretations can be quite severe. For example, in medical science, correcting a falsehood may take decades and cost lives. Misuses can be easy to fall into. Professional scientists, mathematicians and even professional statisticians, can be fooled by even some simple methods, even if they are careful to check ...
For example, by truncating the bottom of a line or bar chart so that differences seem larger than they are. Or, by representing one-dimensional quantities on a pictogram by two- or three-dimensional objects to compare their sizes so that the reader forgets that the images do not scale the same way the quantities do.