Plotly Blog - Spurious Correlations
A “correlation means causation” argument needs to pass further testing, Spurious Correlations, a “ridiculous book of charts” involving bizarre correlations. . Line chart, costs vs revenues: “Line graphs are used to track. Additive Relationship: Line Graph. 9. Figure 2. Preference for equality in the US and Canada controlling for gender, % (fictional data). Example. Check out the book! Spurious charts; Fascinating factoids; Commentary in the footnotes Discover a correlation: find new correlations. Go to the next page of.
The heat wave is an example of a hidden or unseen variable, also known as a confounding variable. Another commonly noted example is a series of Dutch statistics showing a positive correlation between the number of storks nesting in a series of springs and the number of human babies born at that time.
Of course there was no causal connection; they were correlated with each other only because they were correlated with the weather nine months before the observations. Here the spurious correlation in the sample resulted from random selection of a sample that did not reflect the true properties of the underlying population.
Because of this, experimentally identified correlations do not represent causal relationships unless spurious relationships can be ruled out. Experiments[ edit ] In experiments, spurious relationships can often be identified by controlling for other factors, including those that have been theoretically identified as possible confounding factors.
For example, consider a researcher trying to determine whether a new drug kills bacteria; when the researcher applies the drug to a bacterial culture, the bacteria die. Simplification of the formula for r X, Y The fact that d X, Y [see section 1] is a raw rather than tranformed, artificially skewed number, and thus likely to be more compatible and blendable with c X, Y.
This is obvious when you check the summary statistics in the spreadsheet and set a to 1. Technically, all the simulated Y's are uniform, random, independent variables, so it is amazing to see so many high weak correlations - there are indeed all spurious correlations.
Generalization It is possible to integrate auto-correlations of lag 1, 2, and up to n-2, but we then risk to over-fit, except if we put decaying weights on the various lags. This approach has certainly been investigated by other scientists can you provide references?
It would be great to do this analysis on actual data, not just simulated random noise. Or even on non-random simulated data, using for instance the artificially correlated data with correlations injected into the data described in my article Jackknife Regression. Asymptotic properties, additional research I haven't done research in that direction yet.
I have a few questions: Is the choice of a test variable X I mean, the values as in the first raw of my spreadheet has an impact on the summary statistics, in my spreadsheet?
Could we estimate the proportions of genuine, real correlations that are missed by the strong correlation false negatives What proportions of spurious correlations are avoided with strong correlations, depending on n and a? About synthetic metrics and our research lab The strong correlation is a synthetic metric, and belongs to the family of synthetic metrics that we created over the last few years.
Synthetic metrics are designed to efficiently solve a problem, rather than being crafted for their beauty, elegancy and mathematical properties: Lice make a man healthy. Everybody should have them.
More sophisticated observers finally got things straightened out in the New Hebrides. As it turned out, almost everybody in those circles had lice most of the time.
Tutorial: How to detect spurious correlations, and how to find the real ones - Data Science Central
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. 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.Optimized Excel Line Charts: Prevent drop to zero & dynamic Legend positioning
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.
Tutorial: How to detect spurious correlations, and how to find the real ones
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.