Causal Arguments

Having examined analogical arguments and generalizations, we now turn to the final type of argument we will study this semester, causal arguments. Causal arguments, like analogical arguments and generalizations, will always be invalid, that is, the truth of the premises do not guarantee the truth of the conclusion. Rather, causal arguments have varying degrees of strength, that is, the truth of their premises provides a conclusion that is true with some degree of probability or likelihood.

(Please note the spelling of "causal." For some reason, students tend to spell "causal" as "casual.)

Causal Claims and Arguments

A causal claim is one that asserts that there is a relationship between two events such that one is the effect of the other. A causal claim takes the form of "x causes y," with x referring to the cause and y referring to the effect. A causal argument provides the premises to support a conclusion about a cause and effect relationship.

Please note that causal claims take a variety of forms, many of which do not use the term "cause." For example, we see that a friend has seemed less talkative recently, and we wonder why. Is she physically sick? Is she troubled emotionally? Is there some combination of the two? We might hypothesize that she is having financial problems, her child is sick. In other words, these things are possible causes of her behavior. If you go to a party instead of studying for an exam, you might say that going to the party caused you to perform badly on the exam. An airplane crashes and teams of experts study all the wreckage and other evidence to determine the cause of the crash.

Note that we do not always use the term "cause" even when we mean it. If we say the ice on the road led to the accident, "led to" has the same meaning as "cause" in this claim. If your doctor says that the vaccine will prevent you from getting the flu, she means that the vaccine will cause you NOT to get the flu. If the highway patrolman says that wearing a seat belt reduces your risk of dying in an automobile accident, he means that the seat belt will cause you not to be killed. If your instructor admonishes you to attend class regularly because it will help you get better grades, he is saying that going to class regularly causes good performance. If a friend says that too much caffeine keeps him awake, he means that caffeine causes him to stay awake.

Please think of a causal claim that either you have made recently or that someone has made to you. (Do not repeat one I have just given.)

Again, essential to a causal claim is a relationship between two events such that one is the effect of the other.

Types of Causes

It should be evident even from the few examples above that when we say "x causes y," we may mean the term in one of several ways. (Recall our discussion of necessary and sufficient conditions.) When we say "x causes y," we may mean that x is a necessary condition for y. For example, the presence of oxygen made it possible for human life to develop on earth, so that without oxygen, human life would not have developed. "X causes y" might also mean that x is a sufficient condition for y, as when we say that a temperature of below 32 degrees Fahrenheit caused the rain to turn into snow. At other times, and probably most frequently, when we say x causes y, we mean that x contributed to y, though it may not be a necessary or sufficient condition. If all of my relatives are New York Yankees fans, they may be a contributing factor to me being a Yankees fan as well, though certainly we do not mean that these relatives being fans ais either a necessary or sufficient condition for me being a Yankees fan.

The concept of contributing factor helps us to see that for any given event or occurrence there is normally a variety of conditions and causes. A man is killed in an automobile accident when his brakes fail when he is driving in the mountains. The official report may say the cause of the accident was the failure of the brakes. Yet, a friend might point out that the brake failure was caused by the negligence of a mechanic who was supposed to have repaired the brakes. Someone else might say that the man would not have been driving in the mountains if his girlfriend had not gone to visit relatives there, so the girlfriend feels guilty because her going to see her relatives caused her boyfriend to be killed.

Some writers refer to the series of events that collectively cause an event as a "causal chain," that is that x causes y, y causes z and so forth. In the example above, the shoddy repair job caused the brakes to be weak, and the excessive strain put on the brakes by driving in the mountain caused them to fail, and the failure of the brakes caused the car to plunge off of the mountain, which caused the driver to be killed. In this example, causes and effects are envisioned as links in a chain.

Other writers think that the image of a "causal web" is more appropriate, that events are bound to one another in several different ways, and depending on our interests we look at different aspects of the causal web. For example, the policeman reporting on the accident described above would probably most concerned to show that the failure of the brakes caused the argument. The lawyer for the family of the deceased man would be more interested in proving in a lawsuit that the negligent mechanic caused the accident. The girlfriend whom the man was coming to see when he was killed is probably very emotionally distraught because she may feel that she caused her boyfriend to be killed. Again, depending on your interest, you will look at different aspects of the causal web.

Causes Among Specific Events and Causation in Populations

How do we then make sense of all of this?

It is helpful to make a distinction between two very general uses of the term cause. Sometimes when we say x causes y, x and y refer to specific events. A temperature below 32 degrees Fahrenheit causes the water to freeze, just as the ice on the wings could cause the plane to crash. At other times when we say x causes y, we mean that the increase of x in a population leads to an increase in y in that population. This does not mean that every x leads to a y, but that as one increases so will the other. The claim "smoking causes cancer" is such a claim. Every person who smokes does not get cancer, but in a population, as the incidence of smoking increases so does the incidence of cancer.

We need to discuss these kinds of causes separately.

Identifying possible causes among specific events

There are two standard patterns for arguments about causes among specific events: (I am relying on Moore and Parker’s Critical Thinking here; they are relying on John Stuart Mill.) "X is the difference," and "X is the common thread."

In the first pattern, when we say x causes y, we mean that "x is the difference." We claim x causes y, because x is the only relevant difference in situations when y occurred and situations when y did not occur. For example, if I have eaten at Sloppy Joe’s Hamburger House ten times and never become sick, but then on the eleventh time that I eat, I do become sick, I would try to figure out what was different about the eleventh time. Did I eat or dring something different? Was there a different cook? Was a different spice used in the food? After considering the possibilities, I determine that the only relevant difference between the eleventh visit and the previous ten was that I had cheese on my hamburger. The cheese made me sick.

The conclusion would be, the cheese made me sick. The premises would state what had happened the previous ten times, what happened on the eleventh time, and cite the only relevant difference between the different occurrences. X is the cause because X is the difference.

In everyday life, we would probably not feel the need to test my conclusion, that is, I would probably not go back to each cheese on my hamburger just to see if it would make me sick. Yet, if I was conducting a scientific experiment, I would want to run a variety of tests to see if the results could be duplicated.

The other standard pattern for causal arguments about specific events is X is the common thread. We claim that x causes y because x is the only relevant common factor in several occurences of y. If instead of going to "Sloppy Joe’s" alone, I went with a group of friends, and the next morning three out of the six people report they became sick, we would try to identify what was common to the meals of the three sick individuals. If we discover that all three ate cheese on their hamburger, then we would conclude that the cheese was the cause of the sickness.

In evaluating causal arguments, we must determine whether we can identify any other plausible difference or common thread to the events.

Typical Errors in Causal Reasoning

There are many ways to make errors in causal reasoning. Some of the most typical are outlined here.

Post hoc ergo propter hoc - This Latin phrase literally means, "after this, therefore because of this). We are guilty of this error of reasoning when we claim that x causes y simply because x precedes y in time. Certainly a cause does preceded the effect, but that does not mean that coincidence alone establishes a causal relationship. If I notice, for example, that every day the church bells across the street chime eight times, the bus arrives and conclude that the church bell ringing causes the bus to arrive, I am guilty of post hoc ergo propter hoc or simply post hoc reasoning.

Ignoring a common cause - Sometimes we mistakenly identify one event as the cause of another without recognizing that they both may be the effect of a common cause. If I stay up watching television until one o’clock instead of studying for an exam, and then I do poorly on the exam, I might say that my fatigue caused me to do badly on the exam. In fact there, is a common cause, watching television that caused me to stay up late and to do poorly on the exam.

In my example above about post hoc reasoning, I failed to recognize a common cause for both the church bells ringing and bus arriving, namely that it is 8:00.

Another famous example of ignoring a common cause occurred when in a town many years ago, someone noted that as the number of Baptist preachers in the town increased, so too did the number of arrests for public drunkeness.  If one concluded from this correlation that Baptist preachers cause an increase in public drunkenness.   The more accurate explanation is probably that both the increase in Baptist preachers and the increase in arrests of public drunkeness had the common cause of the increased population in the town.

Assuming a common cause - We can also make errors in causal reasoning when we look too hard for a common cause. Imagine that on my way to work I receive a speeding ticket, and later in the day, I fall and sprain my ankle. When I get home I am informed that I had a check to bounce. Then I remember that I saw a black cat the day before and conclude that it must be true that they bring bad luck.

Reversed causation - Another typical error in reasoning about cause and effects is to mistake the cause for the effect and the effect for the cause. For example, if I argue that spending more money on education will improve the economy because after all the countires that spend the most on education have the strongest economies, I may have reversed the cause and effect. It may be that nations with the strongest economies are able to spend more money on education. The ongoing argument about the relationship between violence on television and in movies and violence in society is a good example of possible reversed causation. Some say that the increased violence in the media causes more people to commit violent deeds, while others argue that the increased violence in movies and television is caused by the fact that we are becoming a more violent society.

Causation in Populations

Sometimes "X causes Y" refers to a causal relationship between two specific events.  At other times, "X causes Y" refers to causation in a population.  By this we mean that as the incidence of X in a population increases so too will the incidence of Y.  To put this differently if every member of a population is exposed to X, then there will be more cases of Y than if no member of the population is exposed to y.  X contributes to Y; or X increases the risk of Y.  When referring to a population, "X causes Y" does NOT mean that for every X we will find a Y.

We must also be careful to recognize that correlation is not causation.  Just because two events are correlated (that as one increases or decreases so does the other) does not guarantee that one causes the other.   In the example above which suggested that the increase of Baptist preachers caused the increase in public drunkenness correlation is mistaken for causation.    If I discover that people who drive red sports cars get more speeding tickets than people who drive all other cars, and then conclude that driving a red sport car causes a person to get speeding tickets, I am mistaking correlation from causation.

How do we determine if two correlated events are really linked in a causal relationship?

There experimental means for doing so.  These methods are fundamental to much of the research that goes on today in medicine and the social sciences.  If you major in any of these areas, you will learn much more about these experimental techniques.   The three methods are:  1)controlled cause-to-effect experiment; 2) non-experimental cause to effect studies; and 3) non-experimental effect-to- cause studies.

To describe these three different types of studies I am going to use a simple example.  Suppose I want to determine if chewing gum while taking exams will improve a student's test scores.

Controlled Cause-to-Effect Experiment

One way to test this hyposthesis is to do a "controlled cause-to-effect experiment."  In this experiment, I try to get two groups of people have approximately the same characteristics, expose one to the suspected cause (in this case, chewing gum)  and then test the frequency of the effect (in this case, doing well on an exam) in each group.  If the difference is statistically significant (a term we will discuss later), then I can have some degree of confidence that the suspected  cause does have the supposed effect.

How would we conduct our experiment.  We would first get a group of students, let's say 200, who have all completed the same course taught by the same teacher.   We then randomly separate them into two groups.  The random distribution of individuals to each group is designed to make sure that the variety of differences (some will be smarter than others, some will be better prepared for the test, etc) are evenly distributed.  One group will be asked to chew gum while they complete the final exam, while the other group will not be allow to chew gum.

The group that chews gum is called the "experimental group" because the suspected cause is given to these individuals.

The group that does not chew the gum is called the "control group."

After both groups have completed the exam, I must determine the difference (represented by "d") in the frequency of the effect.  I count the number of students in each group who made an A on the exam.   For the sake of discussion only, suppose I find that 22 people in the experimental group (remember, the ones who chewed gum) made an A on the exam, and that only 11 people in the control group (those who did not chew gum) made an A on the exam.  To state the difference (d) we must convert both results to percentages:

22% of experimental group made As

11% of control group made As.

The difference is stated in terms of percentage points.  In this case, d =11, (22 - 11).  Noting that the frequency of As in the experimental group was double the frequency of As in the control group, it would probably be tempting to conclude that chewing gum makes a difference in exam performance.

Before I make such a conclusion, I must be confident that the difference in the results were NOT the result of mere chance.  (Think about it, if you gave any two groups of people an exam, you would expect some difference in the scores of the two groups.)  Here we must rely on statisticians to give us some general guidelines on how much difference we must have to be confident that the difference was caused by the suspected cause or not.  Results that are NOT the product of chance are called "statistically significant."  In this case, with an experimental group of 100, statisticians tell us that the difference must be at least 13 to be statisically significant.  Hence my experiment would not support my hyposthesis that chewing the gum helps people to better on exams.

As we saw with generalization, these statistical determinations are stated in terms of a confidence level, which in most experiments is 95%.  In the above experiment, I can be 95% confident that the difference is not statistically significant.

As with generalizations, as the size of our experiemental group increase, the difference required for statistical significance decreases.  For example (here I am relying on Moore and Parker's Critical Thinking) if the experimental group is 10, a difference (d) of 40 percentage points is needed to ensure  statistical significance, at a confidence level of 95%.  If the experimental group increased to 50, a difference of 27 percentage points is needed to ensure statistical significance.  With an experimental group of 500, the difference required is six percentage points; while if the experimental group is 1500, a difference of 3 percentage points is required to determine statistical significance.

Non-Experimental Cause to Effect Study

Another way to test my hypothesis about chewing gum and test results would be to conduct a non-experimental cause to effect study.   The chief difference between the non-experimental study and the controlled experiment is that in the controlled experiment the researcher introduces the suspected cause into the experimental group.  (In the example above, I gave the chewing gum to the members of the experimental group.) In the non-experimental study, the researcher finds people who already have the suspected cause.

While such a study will not yield results as reliable as the controlled experiment, sometimes we have no choice, as when the suspected cause may be harmful.  It would be immoral to expose an experimental group to a drug that we suspected to be harmful.  Consider smoking.  Believing that smoking is bad for one's health, it would be immoral for me to ask an experimental group to smoke cigarettes for the purpose of letting me evaluate their effect on health.

To complete a non-experimental study about the effects of chewing gum, I would find a group of people who already have the habit of chewing gum while taking an exam.  This group would become my experimental group.  Then I would develop a control group comprised of individuals with approximately the same characteristics.   I would then compare their results on a common exam and try to determine if the difference is statistically significant.

A non-experimental study will not yield results as reliable as the controlled experiment because in such a study it is more difficult to know if the difference is the result of the suspected cause or the result of one or more other factors.  Perhaps, for example, people who chew gum are usually smarter (or dumber) than the average person.  This would diminish my confidence in the results of the experiment.

Non-experimental Effect-to-Cause Study

On other occasions, we may already have a group of people who have the effect we wish to study.  These individuals become our experimental group.  We then develop a group of people similar to those in the experimental group, with the exception of the effect being study.  We then compare the number of people in each group who have the suspected cause, and once again determine if the difference in the frequency of the suspected cause is statistically significant.

(Note that this type proceeds according the to pattern, "x is the common thread.")

If we were to complete a non-experimental effect to cause study to test my hypothesis about chewing gum and test performance, I would proceed by finding a group of students who made As on the final exam.  This group would be my experimental group.   I would then develop a control group by finding a group of people similar to the experimental group, except that they did not make an A on the final exam.   Then I would determine how many in each group chewed gum while taking the test.   If the number of A students who chewed gum was greater than the number of non-A students who chewed gum, and if this difference was statistically significant, then I could conclude that the chewing gum contributed to the better test scores.

A good example of a non-experimental effect-to-cause study is described by Diane Romain in Thinking Things Through.  One hundred and fifty years ago there were major outbreaks of cholera in Europe and the United States.    Cholera is a disease whose symptoms include diarrhea, vomiting, and muscular cramps.  It can lead to extreme dehydration and death within 48 hours.

Dr. John Snow in London hypothesized that the cholera was being spread through water contaminated by human waste.  He discovered that most of the people in London received their water from one of two water companies.   There were few other significant differences between the two groups besides their water supply.   He discovered that of the people who contracted cholera the vast majority used water from the same company.  This evidence convinced him that cholera was spread through contaminated water,and water sanitation would stop the spread of cholera.   After the city adopted his recommendations on cleaning the water, London never had another cholera epidemic.

Note Dr. Snow found people who had the effect, namely cholera, and looked to see which water company they received their water from.  Since the vast majority of cholera victims shared the same water company, he could conclude that the disease was being spread through contaminated water.

Exercises on Causation in Populations

Causation in Population - Case Study - A recent study in the New England Journal of Medicine provides a good example of a causal study.   These researchers wanted to test what has been generally accepted by health professionals, namely, that a low-fat, high fibre diet reduces the risk of colon cancer.    Since colon cancer often develops from  colorectal adenomas, or polyps, the researchers looked at the effect of a low-fat, high-fibre diet on individuals who had already had one poly.   The summary of the study is provided below:

Lack of Effect of a Low-Fat, High-Fiber Diet on the Recurrence of Colorectal Adenomas (polyp) New England Journal of Medicine, April 20, 2000

Arthur Schatzkin, Elaine Lanza, Donald Corle, Peter Lance, Frank Iber, Bette Caan, Moshe Shike, Joel Weissfeld, Randall Burt, M. Robert Cooper, J. Walter Kikendall, Jack Cahill, Laurence Freedman, James Marshall, Robert E. Schoen, Martha Slattery, the Polyp Prevention Trial Study Group

Background. We tested the hypothesis that dietary intervention can inhibit the development of recurrent colorectal adenomas (polyp), which are precursors of most large-bowel cancers.

Methods. We randomly assigned 2079 men and women who were 35 years of age or older and who had had one or more histologically confirmed colorectal adenomas removed within six months before randomization to one of two groups: 1) an intervention (experimental) group given intensive counseling and assigned to follow a diet that was low in fat (20 percent of total calories) and high in fiber (18 g of dietary fiber per 1000 kcal) and fruits and vegetables (3.5 servings per 1000 kcal), and 2) a control group given a standard brochure on healthy eating and assigned to follow their usual diet. Subjects entered the study after undergoing complete colonoscopy and removal of adenomatous polyps; they remained in the study for approximately four years, undergoing colonoscopy one and four years after randomization.

Results. A total of 1905 of the randomized subjects (91.6 percent) completed the study. Of the 958 subjects in the intervention (experimental) group and the 947 in the control group who completed the study, 39.7 percent and 39.5 percent, respectively, had at least one recurrent adenoma.

Conclusions. Adopting a diet that is low in fat and high in fiber, fruits, and vegetables does not influence the risk of recurrence of colorectal adenomas. (N Engl J Med 2000;342:1149-55.)

A. What is the causal claim being tested here?

B. What kind of study is this? (Controlled cause to effect experiment; non-experimental cause to effect study, c. non-experimental effect to cause study)

C. How were the experimental and control groups formed?

D. How were two groups similar?

E. What was different about the two groups?

F. What was the frequency of the effect in the experimental group? Control Group?

G. What was the difference in the frequency of the effect?

H. Do you suspect the difference is statistically significant?

I. Does the study support the conclusion?

J. What questions might be reasonably asked about the study? (Should physicians start telling their patients not to worry about eating low fat, high fibre diets?)