What do you think is meant by something causing something else?

Thinking About Causation

What is ‘Causation’?

In everyday life, we very often make claims about what we think caused a state of affairs to come about. Although claims about causes might seem straightforward, it actually turns out that thinking about causation can be tricky, and this often results in faulty reasoning.

What do you think is meant by something causing something else?

You flipped a switch and caused the light to turn on. You turned the key and caused the engine to start. Hatfield shot McCoy through the heart and caused McCoy’s death. The drought caused the failure of the corn crop. Those are perfectly reasonable and legitimate causal claims. But determining what caused what is not always so easy. In fact, causal reasoning is subject to a variety of pitfalls and problems.


Thinking About Causation


Arthur, Bert, and Carl are all members of the French Foreign Legion, stationed far out in the desert. Both Bert and Carl hate Arthur, and separately they plot his murder. When Arthur is ordered to go alone on a long mission across the hot, dry desert, both men see their opportunity. Shortly before Arthur leaves, Bert puts a deadly poison in his canteen. A few minutes later, Carl, not knowing about the poison, pours all the (poisoned) water out of Arthur’s canteen, and replaces the water with sand. Arthur goes on his journey, and dies of thirst. Now obviously both Bert and Carl are evil men who plotted murder and attempted to murder Arthur. But the question is this: Who was the actual murderer? That is, who caused Arthur’s murder?

This is a tricky question! It all depends on how we understand the concept of ‘cause’.


What is ‘a’ Cause?


A cause of an event E, is, roughly, any condition or event which helps to bring about E.

But how much does this understanding help us? Consider some examples:

0 Uncle Bruce’s daily heavy smoking was a cause of his contracting lung cancer.

0 Uncle Bruce’s waking up every day was also a cause of his contracting lung cancer.

0 Maybe the Big Bang is also a cause of Uncle Bruce’s contracting lung cancer.


Consider – The Butterfly Effect


What is ‘a’ Cause?

Definition (Amended)

A cause of a kind K of event: roughly, any condition or event which helps to bring about an event of kind K at least sometimes and which under normal circumstances, significantly raises the probability that an event of kind K will occur.


What is ‘a’ Cause?

‘Smoking Causes Lung Cancer’

Smoking causes lung cancer.

This doesn’t mean:

Smoking is sufficient for contracting lung cancer.

And we don’t mean:

Smoking is necessary for contracting lung cancer.

All we mean is that:

Given the lives that most people live, smoking significantly raises the probability that the average person will contract lung cancer.


‘The’ Cause of Something


The cause of an event E or of a kind K of event: roughly, the abnormal condition or event C which combines with normal circumstances in the bringing about of event E or an event of kind K. What counts as abnormal depends on the context in which the event occurs and your reasons for being interested in the event.

Even given this definition, it seems there are at least four different things that people might mean in talking about ‘the’ cause of something.


‘The’ Cause of Something: Interpretation #1

The special condition which, given the laws of nature and standard background circumstances, brings about a type of event.


0 Why do we have rainbows?

0 What causes gas explosions?


‘The’ Cause of Something: Interpretation #2

The condition whose presence enables a suitably placed, suitably resourced person to bring about an event of a particular type (a tractable sufficient condition).


0 How can you make a fire using chemicals?

0 How can you make a Van de Graaff Generator?


‘The’ Cause of Something: Interpretation #3

The condition which a normal observer could remove from a situation in order to prevent an event of a certain type (a tractable necessary condition).


0 How do we prevent certain objects from rusting?

0 How do we prevent kitchen fires?


‘The’ Cause of Something: Interpretation #4

The condition in virtue of which we hold somebody responsible for the occurrence of an event.


0 Who is to be blamed for the 9/11 attacks?

0 Who is accountable for the government shutdown?


Causation and Problems with Equivocation

A lot of fallacious reasoning involving appeals to causes occurs because people equivocate on the meaning of the word cause.


The fallacy of equivocation occurs when a word or phrase is used ambiguously, shifting into different meanings during the course of an argument.

Are we talking about guns being ‘a’ cause of people being killed or ‘the’ cause?


Causation and Problems with Equivocation

Consider the following argument:

P1. People are the (ultimate) cause of other people being killed by guns.


C. Guns don’t kill people (?)

If C is interpreted to mean that guns are not the ultimate cause of other people being killed by guns, then C does follow from P1 but it is not a claim that anyone seriously debates.

If, however, C is interpreted to mean that guns are not an intermediate or proximate cause of people being killed by guns, then it does not follow from P1; in fact, on this interpretation, P1 is irrelevant to C.


Causation and Problems with Equivocation

“Bazookas don’t kill people! People kill people!”


Causation and Problems with Equivocation

“Weapons of Mass Destruction don’t kill people! People kill people!”


Distinguishing Causation from Correlation

Even we when understand what is meant by ‘cause’ in a particular context, there is another problem that needs to be dealt with – How do we distinguish genuine causal factors from incidental associations?


When two sets of phenomena are strongly correlated, that indicates that there may be a causal relationship between the two. The correlation alone is not enough to establish a causal link. Further inquiry is necessary.


Distinguishing Causation from Correlation


Distinguishing Causation from Correlation


Distinguishing Causation from Correlation


Accounting For Two Events Being Correlated

1. Events of Type A cause Events of Type B


Whenever you push the light switch, the light comes on.


Accounting For Two Events Being Correlated

2. Events of Type B cause Events of Type A


Whenever the street lights come on, the sun goes down.


Accounting For Two Events Being Correlated

3. Events of Type A and Type B are causally linked to Events of Type C


Whenever sales of ice cream go up, so does crime.


Accounting For Two Events Being Correlated

4. Events of Type A and Events of Type B are merely (accidentally) correlated without any causal connections; Co-incidence


When I wore my good luck charm, I survived that horrible car crash.


The Fallacy of The Questionable Cause


An unjustified causal claim commits the questionable cause fallacy.


Cum Hoc, Ergo Propter Hoc

Cum Hoc, Ergo Propter Hoc (Latin: “With this, therefore because of this”)

This fallacy occurs when one reasons as follows: (1) Events C and E both happened at the same time; (2) therefore, C caused E.


Whenever the rooster crows the sun is rising. Therefore, the rooster causes the sun to come up.


Post Hoc, Ergo Propter Hoc

Post Hoc, Ergo Propter Hoc (Latin: “After this, therefore because of this”).

This fallacy occurs when one reasons as follows: (1) Event C happened immediately prior to event E; (2) therefore, C caused E.


My son was vaccinated just before he started developing autism. Therefore, the vaccine caused autism.


Testing for Causation – The Methods of Science


The Randomized Controlled Experiment (or Trial) is a scientific method used to isolate a cause of a kind of phenomenon.

It is used when you want to test a causal hypothesis as it may pertain to a target population, but you cannot test every member of that population.


Testing for Causation – The Methods of Science


Testing for Causation – The Methods of Science


Suppose we want to test the following causal hypothesis:

Protein supplements cause greater muscle growth among people beginning weight-training (than those who do not use such supplements).


Divide the sample into 2 groups: (i) experimental; and (ii) control.

Random Sample (People about to begin weight-

training )

Experimental Control

Protein Supplement Placebo


Testing for Causation – The Methods of Science


A placebo is a harmless substance or procedure that is prescribed more for the psychological benefit to the patient than for any physiological effect.

The Placebo Effect

The placebo effect is any effect that seems to be a consequence of administering a placebo (and is not attributable to any sort of effective treatment).


Testing for Causation – The Methods of Science




Greater Muscle Growth



Protein Supplements raise the probability of

greater muscle growth


Prospective Studies

Randomized scientific experimentation is the ideal, but it is not always possible (for instance, if there are ethical problems – consider the example of wanting to investigate the effects of smoking on teenagers).


A prospective (or epidemiological) study requires searching out people with the right conditions, instead of creating those conditions. But, a prospective study can be influenced by factors outside of the experiment.


Dealing With Statistics

“There are three kinds of lies: lies, damned lies, and statistics”

– attributed to Benjamin Disraeli and popularized in

the U.S by Mark Twain.


Dealing With Statistics

Statistical reasoning is vitally important. Without statistical reasoning, we wouldn’t know (just to take one example) whether a new medicine that doctors are working on is effective.

Although statistical reasoning is important, there is also a lot of potential for faulty reasoning involving statistics.

Unfortunately, many people, particularly politicians and advertisers, lean on statistics the way a drunk leans on a streetlamp: for support rather than illumination. Often we must sift out the chaff before finding the valuable grain of truth in statistical reasoning.


Claims involving The ‘Average’

One area where there is potential for statistical confusion is where averages are appealed to.

What do we mean by the average?

Typically, when we speak of the average of a set of values, we are referring to the arithmetic mean (or just the mean). The mean is calculated by adding up all the values together, and then dividing by the number of values.

So, for example, the mean of the values 3, 4 and 5 is 4.


Claims involving The ‘Average’

But there are other meanings some people use when talking about the average. One of these is the median. The median refers to the value in the middle of the set of values. For instance, the median of 2, 4 and 7 is 4.

When there is an even number of numbers, the median is the mean of the two middle numbers. Thus, the median of the numbers 2, 4, 7 and 12 is (4 + 7) / 2 = 5.5


Claims involving The ‘Average’

A third possible interpretation of ‘average’ is the mode. The mode is the most frequently occurring value in a set of values. For example, in the set of numbers 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, the mode is 3.

The reason these different interpretations of averages are important is because sometimes people might try to take advantage of ambiguous references to the average.


Claims involving The ‘Average’


Claims involving The ‘Average’

Example 1

Consider the following situation where the following seven students have amounts outstanding on their student loans:

$10,000, $20,000, $25,000, $30,000, $100,000, $5,000 and $5,000.

What is the average outstanding amount on a student loan?


Claims involving The ‘Average’

MEAN: ($5000+$5000+$10000+$20000+$25000+$45000+$100000)/7 = $30, 000.

MEDIAN: $5000, $5000, $10000, $20000, $25000, $45000, $100000 = $20, 000.

MODE: $5, 000.

Clearly, the way you interpret ‘average’ will have an effect on your assessment of the situation.


Claims involving The ‘Average’

Student loans aren’t that much of a problem; the average student only owes $5,000 (mode).

Student loans are a problem – the average student owes $20,000 (median).

Student loans are a terrible problem – the average student owes $30,000 (mean)!


Claims involving The ‘Average’

Example 2

Imagine a company with nine employees, who have the following salaries: 900,000; 850,000; 800,000; 750,000; 50,000; 15,000; 12,000; 12,000; 12,000.

Median: 50, 000.

Mode: 12, 000.

“Our average salary is 50, 000” (median) – our workers receive good, modest incomes.

“Our average salary is 12, 000” (mode) – so if you are earning 15,000, you are earning above average for this company.


Claims involving The ‘Average’

“Reports of averages may be informative, but they can also cover deceptive ambiguity, since “average” may indicate mean, median, or mode; and depending on which measure is selected, the results can easily be manipulated.”


Empty Claims

Certain statistical assertions can be meaningful assertions after you sort things out (e.g. trying to figure out what exactly someone means when she speaks of the ‘average income’ in a certain company).

Other statistical claims, however, are devoid of any real meaning (we often find such claims in advertising); these are empty claims.


Empty Claims


Empty Claims


Empty Claims


Empty Claims


Empty Claims


Empty Claims


Empty Claims


Empty Claims


Empty Claims

There are two problems here (the second is the major problem):

(1) How do we quantify (measure) claims about things that are, for instance, 43% ‘cleaner’?

(2) There is no base comparison: 50% more than what? 50% cleaner than what? Without base comparisons, such statistical claims are meaningless or empty.


The Context of Statistical Claims

Another sort of statistical claim to watch out for is one that is statistically accurate but is nevertheless misleading because of considerations regarding context.


Suppose that an assault victim reports that her assailant was wearing a Cleveland Browns stocking cap. The police spot Jones wearing a Cleveland Browns stocking cap. Does this make him a reasonable suspect? Suppose it is true, according to statistical reports, that 0.01% (less than 10, 000) of all the men in the world wear Cleveland Browns stocking caps.

If the crime took place in Cairo or Baghdad, then this might be a good basis on which to take Jones in for questioning. But if the crime took place in Cleveland, then probably not.


The Context of Statistical Claims

[Searching the island for Sarah]

Dr. Ian Malcolm: Sarah! Sarah!

Nick Van Owen: Sarah Harding!

Dr. Ian Malcolm: How many Sarahs you think are on this island? Sarah!


Problematic Base Rate Comparisons

Even in statistical claims where the base comparison is specified, there is still potential for deception.

Suppose that the sale price for a motor vehicle is $20,000. The cost price was $18,000. The difference, the mark-up, is $2,000. The salesman might claim that the mark-up was (only) 10%. After all, 2,000 is 10% of 20,000 (the sales price).

Meanwhile, the buyer might complain: mark-up is just over 11%. After all, 2,000 is just over 11% of 18,000 (the cost price).

Hence, the claim about the mark-up is ambiguous. What we think the mark-up is will depend on which base comparison we make.


Problematic Base Rate Comparisons

Here’s another example.

Suppose that you earn $50,000 a year. The company needs to cut your salary by 20%. But, they will increase your salary by 20% next year. When you lose 20% of your current salary (50,000), you will earn $40,000. Next year, 20% will be added to your salary.

Here’s the problem: 20% of what?

20% of your original salary? If so, you will be back with $50,000.

20% of your new salary? Then, you will be on $48,000.

In this context, ‘20% of your salary’ is ambiguous: it might mean ‘20% of your old salary’ or ‘20% of your new salary’.


Comparing Statistical Apples and Oranges

Consider the following argument:

Some people claim that snowmobiles are dangerous, because there have been dozens of deaths and severe injuries to people who were riding on snowmobiles. But before you jump to the conclusion that snowmobiles are dangerous, consider the thousands of people who are killed and injured in automobiles. Of course there is some danger from riding snowmobiles, but obviously not nearly so much danger as riding your automobile. In fact, when you add up the numbers, you will find that over a hundred times more people are killed in automobile crashes than in snowmobile crashes; so we have to recognize that while snowmobiles do pose some risk, they are at least a hundred times safer than cars.

What, if anything, is wrong with this argument?


Comparing Statistical Apples and Oranges

Now consider the following argument:

Ninety-eight percent of all smokers live past age 25; only 97% of the population as a whole reaches 25. So perhaps smoking actually increases your chances for avoiding an early and untimely death!

What, if anything, is wrong with this argument?


Comparing Statistical Apples and Oranges


Comparing Statistical Apples and Oranges


Comparing Statistical Apples and Oranges


Statistical Half-Truths

Sometimes, what is not stated is actually more important than the narrowly true statement being made.

A statement may be literally true but only tell half of the story.

Example: Corporate profits

A nursing home shows that its profits are too low to support a higher standard of care.

0 But the company also owns related businesses that post large profits.

0 How does that change the statistical picture?


Sample Size and “Statistical Significance”

Basically, a statistically significant result is a result that statisticians determine was very unlikely (less than one chance in 20) to occur by chance.

Medical researchers test drugs by giving them to an experimental group and not to a control group.

If enough patients live longer in the experimental group than in the control group, the result is statistically significant.


Sample Size and “Statistical Significance”

But statistical significance is not a definitive conclusion.

A larger group leads to more statistical significance, because the results are larger as well.

In that way, researchers and companies can manipulate the data on exactly what effect a certain drug or treatment is having.

The actual result may be less significant than suggested.


Manipulating Statistical Studies

When the goal is results rather than discovery of the truth, there are ways to manipulate the data.

The problem is not so much with consciously and purposefully falsified results.

Rather, the more common problem is in responding to pressures, hopes, and profits that lead one to interpret research results—or even subtly shape research results—to reach the desired conclusion.


Manipulating Statistical Studies

Cherry-picking or Data Dredging

If we study enough people for long enough, we will eventually see data that supports the positive results we want.

Dredging through all of the data and cherry-picking the positive results to support a claim is one way to manipulate statistics.

The negative data that does not support the claim is then left out of the report.



Like raw statistics, surveys can be manipulated to create a specific outcome. Some important questions to ask:

0 Is the sample sufficiently large enough to support a reliable conclusion?

0 Is the survey drawn from a representative sample?

0 Does the survey cover all genders, ethnicities, and socioeconomic classes?

0 Is the sample proportionate to the target audience?



Survey questions

How a question is phrased often affects the outcome in a survey. How can this be?


0 Should people be allowed to shoot doves?

0 Should we protect doves?

“Rigged” surveys frame the question for a certain result or are mailed out only to a segment of the population that already agrees with the survey’s premise.



Push polls

Politicians sometimes send out surveys that wholly abandon objectivity. “Push polls” are designed to sound like surveys but are actually designed to influence the people surveyed.

How does this kind of survey manipulate results?


"Is this question part of your assignment? We Can Help!"