If the values of two observations tend to rise and fall together over time, the observations are correlated. For example, the rise of violent crime in American society in the 1960’s and 1970’s matched the rise in violence on television. That lead to speculation that violence on television caused the increase. It is fair for correlation to raise such suspicions, but the correlation falls short of proof. Measures of violence on television continued to rise in recent decades, but crime rates have fallen. Young people commit more crimes, and the baby boomer population surge reaching maturity was the more likely cause of the the rise and fall.

It may have been a pure coincidence that television became more popular as the boomers aged, but perhaps there were other factors. Early television sets were very expensive, and broadcasts were mainly available in large cities. Hence early viewers were not a random cross section of society. Perhaps viewing tastes changed as the audience broadened, and the rise in popularity of crime shows was a response to that changing audience.

Or perhaps younger viewers like programs having violence more than older viewers. If that is the case, then there was a common demographic reason behind both violence in society and violence on television.

You can see that I am spinning unproven theories to attempt to explain what happened. It would take much more work to prove or disprove any of those theories. Perhaps one could compare television viewing habits on rural versus urban audiences, or with younger versus older populations. It’s much easier to pose a theory that sounds convincing than it is to back it up with solid evidence. There is a temptation to succumb to what seems obvious.

One study showed that infants who were raised with night lights in their bedrooms grew up to have poorer eyesight than infant would did not have night lights. The conclusion was that night lights probably impair eyesight development. After the study was published, other researchers pondered the question, “Why are night lights put in infants rooms?” It is is because the parents have trouble seeing without the light. Poor vision in parents causes night lights. Parents with poor eyesight also tend to have children with poorer than average vision. So it turned out to be more nearly correct to say the poor vision caused the night lights rather than the night lights caused poor vision.

Books on statistics often cite the case of murder rates being well-correlated with ice cream sales in Chicago. Does ice cream cause murder? Does murder cause ice cream consumption? Actually, summer causes both.

Of course, correlation can be a product of pure chance. Everything in the world that rises over time will be correlated positively with every other thing that rises over time. If the variables rise and fall together, that is more convincing, but it still could be chance. Appropriations for national defense tend to rise and fall in a cycle that takes around nineteen years, which happens to correlate with the emergence of cicadas, those buzzing summer insects. We await a theory of cause and effect or of common cause for that one.

Many observations are attributed to multiple causes, and mathematical techniques are used to attempt to sort out the different causes. Unemployment statistics are seasonally adjusted to correct for the ups and downs that occur every year. Employment always tends to rise before the Christmas holiday season, when shops take on temporary workers. However, the rise may be more or less depending upon the economy in any particular year. Making a seasonal correction helps reveal the state of the economy.

Computer programs are available to help sort out multiple causes by making multiple corrections. This poses a danger, as a scientist with a pet theory to prove can try various corrections until nothing is left but what he was hoping to see. the scientist is not being malicious, he just tries various things and quits when the theory he had in mind is confirmed. If nothing he tries produces the expected result, then he gets a new theory. Good science is built up by having different studies performed on the same data, or even better, different data on the same subject.

Part of the oft-cited evidence that carbon dioxide (CO2) causes global warming is that the the complex variations of global temperature over tens of thousands of years tracks well with the amount of CO2 in the atmosphere. The graphs are often presented one above the other. The inconvenient truth, however, is if the graphs are superimposed it becomes apparent CO2 is lagging temperature. In other words, warming causes a CO2 increase. That is because most CO2 is dissolved in the oceans, and rising temperature drives it out. It is like heating a carbonated soft drink. One book author, noting the “obvious error” of CO2 lagging temperature reversed the labels so it would make sense.

When trying to prove cause and effect consider carefully which variable causes the other, whether both have a common cause, or whether it is just chance.