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Correlation And Causation Homework Chart

Correlation is a measure of how two different things change together.

Causality is the actual relationship between causes and effects.

If they change together very closely, they have a positive correlation

If one thing goes up while the other goes down then we have a negative correlation.

Here are three examples of correlations:

(a) As someone owns more properties (during the recession) increases, the amount of foreclosures increases.

(b) People with lower education have a higher unemployment rate, and people with higher educations have a lower rate.

(c) There is no relationship between one’s education, and whether or not one owns pets.

{ from Correlation, http://www.mathsisfun.com/data/correlation.html }

{ from http://resources.esri.com/help/9.3/arcgisdesktop/com/gp_toolref/spatial_statistics_toolbox/regression_analysis_basics.htm }

When two different things change like this, does that prove that they are related? Does it prove that one thing causes another? Nope, not at all.

Sure, sometimes when two things change together, there is a reason for it. The correlation has a real cause!

But other times they may appear to change together out of dumb blind like; this is called a coincidence.

Just because two things are correlated (change together) doesn’t mean there is causation (one thing causes the other.)

So how can we tell if it is a coincidence, or if one thing really does cause the other?

If one thing causes something else to happen, there must be a way this happens – a causal mechanism

If you can show a realistic causal mechanism, then maybe the correlation does mean that A causes B.

Do pirates cause global warming? Look at this graph.

As time goes by, what happens to the number of pirates in the world? It goes way down!

And what happens to the world’s average temperature? It goes up.

In fact, the temperature goes up just as the number of pirates goes down.

These numbers are correlated.

But does that imply causation? (Does the decreasing # of pirates cause the increasing temperature?  No.)

One way we know this is that there is no causal mechanism:

whether or not one chooses to be a pirate doesn’t affect temperature.
So why are these two different things correlated? Random chance (a coincidence.)

Millions of different things correlate with each other, with no reason.

Always be careful when someone says that A causes B.

Does A really cause B? If so, they must be able to show you a reason why it would happen.

{ from http://www.venganza.org/ }

Does organic food cause autism? Look at this graph.

As time goes by, what happens to the amount of organic food grown, sold and eaten? It goes up. And what happens to the number of people diagnosed as having autism? It goes up also.

These numbers are correlated. But does that imply causation? No.

One way we know this is that there is no causal mechanism. If someone wanted to prove that organic food caused autism, they would have to show how this happens.

Does using Microsoft Internet Explorer as your web browser causer murder?
Obviously IE use rates are correlated with murder rates.
But is there causation? (Does using one kind of web browser really drive people to commit murder?) No.
Again, we see correlation without causation.
The correlation, again, is a coincidence.

Does the choice of words in a National Spelling Bee correlates with the number of people killed by venomous spiders?
Obviously these two different things are correlated.
But is there causation? (Do judges choosing words in spelling bees, somehow affect the number of venomous spiders? No.)
Again, we see correlation without causation.
The correlation, again, is a coincidence.


This image comes from the amazing website of Tyler Vigen. He created his website as a fun way to look at correlations and to think about data.
http://tylervigen.com/view_correlation?id=2941
So correlation doesn’t mean anything without causation
{ from http://fjhsalgebra1.blogspot.com/2013/11/correlation-vs-causation.html }

Many people assume that correlation equals causation, and that’s not only wrong, but dangerous.
It causes people make bad decisions, because they can get the chain of events wrong.
It also makes people expect that they will get some desired result, when really the result has nothing to do with the action.
Consider this fact: Many studies show that married people are more likely to be happy than unmarried people.
Does this mean that if you marry someone, that you will suddenly become a happy person?
Or is it exactly the other way around? Are happy people more likely to develop stable relationships and thus get married?

When can correlation equal causation?

Learning Standards

2016 Massachusetts Science and Technology/Engineering Curriculum Framework

Analyze data to identify relationships among seasonal patterns of change; use observations to describe patterns and/or relationships in the natural world and to answer scientific questions.

Science and engineering practices: Construct, analyze, and/or interpret graphical displays of data and/or large data sets to identify linear and nonlinear relationships.
• Use graphical displays (e.g., maps, charts, graphs, and/or tables) of large data sets to identify temporal and spatial relationships.
• Distinguish between causal and correlational relationships in data.
• Analyze and interpret data to provide evidence for phenomena.

Statistics Definitions > Causation

What is Causation?

According to Merriam-Webster, causation is “the act or process of causing something to happen or exist.” In other words, causation means one event is 100 percent certain to cause something else. If you paint, you’ll make a painting. If you stand in the rain, you’ll get wet.

On the other hand, Merriam-Webster states that correlation is “the relationship between things that happen or change together.” Correlation means there’s a relationship, but not a hundred percent. If you paint, you might sell a painting. If you stand in the rain, you might get hit by lightning.

Correlation vs. Causation

“…correlation does not imply causation, but it sure as hell provides a hint.”Slate.com

In real life it’s sometimes hard to pinpoint causation. For example, take the statement “if you commit a felony, you’ll go to jail.” The reality is that you might go to jail….if you get caught. And even if you get caught, you might get yourself an excellent attorney who will get you probation and community service. So you can’t say for sure that committing a felony will cause you to go to jail. But there is a definite link in that if you commit a felony you are highly likely to go to jail (a lot more likely than someone who commits a minor crime or who doesn’t commit crimes at all). That link is what is called correlation; you can say there is a correlation between committing a felony and going to jail.

Causation in Statistics

In statistics, correlation can be quantified and given a number where zero is “no correlation” and 1 is “perfect correlation.” Perfect correlation exists and it is pretty much indistinguishable from causation. You’ll rarely (if ever) use the term “causation” and instead you’ll be talking about various types of correlation coefficients and whether your results are statistically significant.

Causation can be extremely hard to prove, as what you’re trying to prove is 100 percent correlation (which rarely happens). Take the case of cigarette smoking. For decades, activists, trade groups, and scientists debated about whether tobacco smoke caused lung cancer and if so, how strong was the link. Many other reasons were suggested for the link between lung cancer and smoking, including sleep deprivation or alcoholism. In layman’s terms, it’s now known that smoking causes lung cancer. But in scientific (or statistical) terms, you can’t really say “cause” as that would mean every single person who smoked even just one cigarette would get lung cancer. As statisticians, we say that there is a very strong correlation between smoking and lung cancer.

For some true, funny, examples of how correlation doesn’t always imply causation (like eating margarine and marriages in Kentucky), check out this guy’s site.

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If you prefer an online interactive environment to learn R and statistics, this free R Tutorial by Datacamp is a great way to get started. If you're are somewhat comfortable with R and are interested in going deeper into Statistics, try this Statistics with R track.

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