Spurious Relationships: POSSpring 0W58
Aug 20, a number of examples in ecology and public health to remind of the danger of have and proposed a general rule of judging whether spurious correlation .. sediment supply, land use/cover types of uplands, and watershed. lem's verbal content (e.g., its cover or contextualizing story) and a strategy for . Einstellung demonstrated, however, reliance on correlational structure, in general, same token, if confirmatory examples contain a spurious correlation between. Nov 21, We won't cover everything about determinism. (For example, my vote is one independent variable in an explanation of who wins the election.) . It turned out, of course, that this was a spurious correlation, since the problem was . looking at is what factors cause voter turnout for elections taken in general.
As it turned out, almost everybody in those circles had lice most of the time. It was, you might say, the normal condition of man. When, however' anyone took a fever quite possibly carried to him by those same lice and his body became too hot for comfortable habitation, the lice left. There you have cause and effect altogether confusingly distorted, reversed, and intermingled. He illustrates widespread innumeracy in newspapers. Studies have shown repeatedly, for example, that children with longer arms reason better than those with shorter arms, but there is no causal connection here.
Consider a headline that invites us to infer a causal connection: Without further evidence, this invitation should be refused, since affluent parents are more likely both to drink bottled water and to have healthy children; they have the stability and wherewithal to offer good food, clothing, shelter, and amenities.
Families that own cappuccino makers are more likely to have healthy babies for the same reason.
Spurious Correlation Explained With Examples
Making a practice of questioning correlations when reading about "links" between this practice and that condition is good statistical hygiene. However, learning new words does not make the feet get bigger. Instead, there is a third factor involved - age. As children get older, they learn to read better and they outgrow their shoes.
In the statistical jargon of chapter 2, age is a confounding factor. In the example, the confounder was easy to spot. Often, this is not so easy. And the arithmetic of the correlation coefficient does not protect you against third factors. But association is not the same as causation.
Fat in the diet and cancer. In countries where people eat lots of fat like the United States rates of breast cancer and colon cancer are high. See figure 8 next page. This correlation is often used to argue that fat in the diet causes cancer.
How good is the evidence? If fat in the diet causes cancer, then the points in the diagram should slope up, other things being equal.
So the diagram is some evidence for the theory. But the evidence is quite weak, because other things aren't equal.
For example, the countries with lots of fat in the diet also have lots of sugar.
A plot of colon cancer rates against sugar consumption would look just like figure 8, and nobody thinks that sugar causes colon cancer. As it turns out, fat and sugar are relatively expensive. In rich countries, people can afford to eat fat and sugar rather than starchier grain products.
Some aspects of the diet in these countries, or other factors in the life-style, probably do cause certain kinds of cancer and protect against other kinds.
So far, epidemiologists can identify only a few of these factors with any real confidence. Fat is not among them. Abelson is highly respected and widely honored "We have seen that the category of methodological artifacts is a broad one. Here we discuss three general categories that come up repeatedly: Cases involving third variables typically apply to correlational studies, procedural bias to experimental studies, and impurities to both types of studies.
Third Variables We go back to basics and begin our discussion by considering an elementary claim from a correlational study that two variables are related as cause and effect. We saw in chapter 1, in our discussion of the purported longevity of conductors, how misleading such claims can be.
With what should the mean age at their deaths, With the general public? All of the conductors studied were men, and almost all of them lived in the United States though born in Europe.
The author used the mean life expectancy of males in the U. Since the study appeared, others have seized upon it and even elaborated reasons for a causal connection e. The calculation of average life expectancy includes infant deaths along with those of adults who survive for many years.
Because no infant has ever conducted an orchestra, the data from infant mortalities should be excluded from the comparison standard. Well, then, what about teenagers? They also are much too young to take over a major orchestra, so their deaths should also be excluded from the general average.
Carroll argued that an appropriate cutoff age for the comparison group is at least 32 years old, an estimate of the average age of appointment to a first orchestral conducting post. On the contrary, when they prepare in a quiet environment, like the library, they tend to concentrate better, and so, they write their paper better.
No such connection exists; the size of the hands depend on genes. The assumption here is that longer the hair, higher the scores. However, the lurking factor here may be that female students got better, may be because they worked harder and more sincerely than the guys.
Spurious Correlation Explained With Examples
Or perhaps, they were seniors who already had some experience due to which they fared better. People assume that the more they read, they outgrow their shoes, or their shoes don't fit them as they read better. How wrong, how wrong. The very obvious factor here is age.
As they grow bigger, they tend to develop their reading ability. Along with mental skills, their bodies undergo a change as well, and their feet grow bigger, which is why they outgrow their shoes.
Truth be told, it is the fact that eating excessively causes them to be lethargic and lazy, which is why they are not into sports and other activities, which makes them clumsy and obese. But to help in ruling out the presence of a confounding variable, another culture is subjected to conditions that are as nearly identical as possible to those facing the first-mentioned culture, but the second culture is not subjected to the drug.
If there is an unseen confounding factor in those conditions, this control culture will die as well, so that no conclusion of efficacy of the drug can be drawn from the results of the first culture. On the other hand, if the control culture does not die, then the researcher cannot reject the hypothesis that the drug is efficacious. Non-experimental statistical analyses[ edit ] Disciplines whose data are mostly non-experimental, such as economicsusually employ observational data to establish causal relationships.
The body of statistical techniques used in economics is called econometrics. The main statistical method in econometrics is multivariable regression analysis.
Typically a linear relationship such as y.