# Correlation CAN Imply Causation! | Statistics Misconceptions

This video is about how causal models (which use causal networks) allow us to infer causation from correlation, proving the common refrain not entirely accurate: statistics CAN be used to prove causality! Including: Reichenbach’s principle, common causes, feedback, entanglement, EPR paradox, and so on.

# Coincidences: Remarkable or Random?

Most improbable coincidences likely result from play of random events. The very nature of randomness assures that combing random data will yield some pattern.

By Bruce Martin via The Committee for Skeptical Inquiry – CSI

“You don’t believe in telepathy?” My friend, a sober professional, looked askance. “Do you?” I replied. “Of course. So many times I’ve been out for the evening and suddenly became worried about the kids. Upon calling home, I’ve learned one is sick, hurt himself, or having nightmares. How else can you explain it?”

Such episodes have happened to us all and it’s common to hear the words, “It couldn’t be just coincidence.” Today the explanation many people reach for involves mental telepathy or psychic stirrings. But should we leap so readily into the arms of a mystic realm? Could such events result from coincidence after all?

There are two features of coincidences not well known among the public. First, we tend to overlook the powerful reinforcement of coincidences, both waking and in dreams, in our memories. Non-coincidental events do not register in our memories with nearly the same intensity. Second, we fail to realize the extent to which highly improbable events occur daily to everyone. It is not possible to estimate all the probabilities of many paired events that occur in our daily lives. We often tend to assign coincidences a lesser probability than they deserve.

However, it is possible to calculate the probabilities of some seemingly improbable events with precision. These examples provide clues as to how our expectations fail to agree with reality.

## Coincident Birthdates

In a random selection of twenty-three persons there is a 50 percent chance that at least two of them celebrate the same birthdate. Who has not been surprised at learning this for the first time? The calculation is straightforward. First find the probability that everyone in a group of people have different birthdates (X) and then subtract this fraction from one to obtain the probability of at least one common birthdate in the group (P), P = 1 – X. Probabilities range from 0 to 1, or may be expressed as 0 to 100%. For no coincident birthdates a second person has a choice of 364 days, a third person 363 days, and the nth person 366 – n days. So the probability for all different birthdates becomes:

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# Understanding Coincidence

By Kyle Hill via randi.org

Many people have a legitimate fear of numbers, equations, and probability. This “math anxiety” keeps much of the lay public from ever willfully learning about mathematics; indeed, ignorance in this regard is often touted. Commonly used phrases like “I’m not a numbers person” and “I hate math” betray that fact that a good portion of society does not understand math and consciously avoids it.

Comprehending this deficit and doing something about it should be taken up within our school system; we should engage students with math early, often, and more rigorously.

But mathematical illiteracy plays a role in perpetuating not just equation ignorance, but pseudoscience. Not understanding just how much of your life is governed by randomness generates many a fallacious belief about the way that the world works. It should be clearly understood that randomness creates coincidence. That is to say, if there were no coincidences in life, we could speculate that some outside force is controlling the events in our lives. However, with true randomness comes the expectation that coincidences will happen: there will be cancer clusters, your friend will call you just when you were thinking about them, and last night’s dream will have somehow “predicted” the events of the following day. It is with the last example, predictive dreams, which I would like to press on with. With a short lesson in randomness and probability, we can see that so-called predictive dreams (and any other event “too amazing to be a coincidence”) are nothing more than random happenings. You don’t have ESP, it’s not fate, and it’s not magic.

“I Dreamt This Would Happen!”

The purpose of this example is to show that many pseudoscientific ideas about the way the universe works are driven by a misunderstanding of randomness and probability. While predictive dreams are harmless, I would suspect that this belief characterizes the kind of thinking that underlies pseudosciences like astrology, ESP, and parapsychology.

Let’s overcome our math anxiety with a dreaded word problem. Let’s stipulate that the chance of a dream to some extent matching the events of the following day is 1 in 10,000. This means that out of 10,000 dreams, the vast majority, 9,999, will not match any future events. Let’s also assume that having a non-matching dream one night will not affect the dream of the next night, so each night is independent from one another. So given these stipulations, the odds of having a dream that does not match any real life event is 9,999/10,000. When people speak about predictive dreams, it is not as though they have them every night. If this were happening, we might consider it to be more than coincidence. However, anyone who has experienced this phenomenon (myself included) will probably tell you that they do not hit a homerun every night. It is this fact, that an amazingly serendipitous event only happens once in a while, that alludes to chance as the rational explanation.

Remembering the odds above, the chance of having a dream that does not match any real life event for two nights in a row will follow the multiplication principle of probabilities, meaning that the probability is (9,999/10,000)*(9,999/10,000). Likewise, the probability that you will have a dream that does not predict anything for three nights in a row is (9,999/10,000)*(9,999/10,000)*(9,999/10,000). Following this principle, the chance that you will have successive dreams that do not match reality can be expressed as (9,999/10,000)N, where N is the number of nights. As I said above, I don’t think that anyone would say that these predictions are a common occurrence, so let’s consider a time period of one year. The probability that you will have successive dreams every night for a year that do not predict anything would be (9,999/10,0009)365, with N equal to the number of days in a year. This results in a 96.4 percent chance that people who dream every night of a year with not have any predictive dreams. This of course means that over a period of one year, 3.6% of people who dream every night will have at least one dream that matches reality in some way. Consider that for a moment. Even though coincidences like these can drive people to believe in fate, precognition, ESP, etc., using our definition here we can say that these probabilities in large population would produce literally millions of predictive dreams each year! Even if we relax our standards and make a predictive dream a one-in-a-million event, it would still produce thousands upon thousands of predictive dreams each year by chance alone.

It’s not magic, it’s not fate, it’s not a spiritual connection with someone else; if there’s a likelihood that something will happen, however small, it is explained by chance alone that it is bound to happen to some people at some time. Look at what happened with the supposedly prophetic Nostradamus. He threw out a claim that had to do with two towers coming down and . . .

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