Correlations

If two phenomena are generally found to occur together, they are said to be positively correlated. The identification of a correlation is often the first step towards the identification of a causal relationship. For example, we believe that smoking causes lung cancer because there has been found to be a significantly higher incidence of lung cancer among smokers than among non-smokers. Smoking is positively correlated with lung cancer.

Finding a correlation between two things, however, is not enough to establish a causal connection. We also need to be convinced that the causal explanation is the best explanation available.

Giving a causal argument involves:

 using statistical methods to find correlations

 considering whether the causal explanation is the best explanation for that correlation.

The first step towards establishing that there is a causal connection between two phenomena is to find that there is a correlation between them. It is not enough to show that one thing was followed by another, we need evidence of some regular correspondence between the two events to justify a claim that they are causally related.

To assume prematurely that X causes Y, merely because X happened then Y happened is to commit the post hoc fallacy (from the Latin post hoc, ergo propter hoc, "after this, therefore because of this").

This is a fallacy because mere temporal order is not enough to guarantee a genuine correlation between two types of events, and even if there is a correlation, there may be explanations which are not causal.

Research should be conducted in such a way that it establishes where genuine correlations occur, and, where possible, gives enough information about the correlation to justify the claim that the connection is a causal one. We will look first at the statistical methods used to establish correlations, and then at how we

can see whether any correlations which are found are evidence of the causal relationship we want to establish.

5.5.1.1 Samples and populations

Causal research generally proceeds like other statistical research. If we want to make a general claim about causes and effects in a population, we begin by finding the relationship between the supposed cause and effect in a sample.

As with other statistical research, the reliability of that generalisation will depend on the representativeness of the sample. Look for any relevant differences between the sample and population. These will weaken the inference.

Example:

Research conducted in Canada in 1977 found that 50% of laboratory rats fed large doses of saccharin developed bladder cancer. From this evidence about a sample, a conclusion was drawn that saccharin would also cause cancer in humans, and as a result the use of saccharin was banned or restricted in a number of countries. In the 1990s, these restrictions were lifted, when it was found that there was no correlation between saccharin consumption and cancer in humans, and that it was particular features of rat physiology which made them susceptible to saccharine-induced tumours.

The conclusion drawn about a population including humans from a sample of rats was unreliable in this case, because there turned out to be relevant differences between the sample and population.

5.5.1.2 Test groups and control groups

Suppose we want to show that X causes Y. It would not be enough to examine a sample of things with the property X, and show within that group there was a high incidence of property Y. To establish the correlation we would need to show that there are more Ys among Xs than among non Xs.

For example to show that smoking causes lung cancer, you would need to show not just that there was a significant incidence of lung cancer among the smokers, but that there was a higher incidence of lung cancer among smokers than among non-smokers. The observation of the smokers alone will tell you nothing unless you have something to compare them to.

For that reason, in causal research, the sample is divided into two parts - the test group and the control group.

The test group is the group which has the feature whose causal properties you want to investigate. The control group is the group which does not have that feature.

To make the comparison fair, and give the most accurate results, the test group and control group should be as similar as possible apart from the presence or absence of the suspected causal factor.

The test group and control group should be similar in all relevant ways, except that the test group has the suspected causal factor and the control group does not.

The selection of test groups and control groups can be either active or passive. For some purposes, we can actively construct the test and control groups by giving the alleged cause to one part of the sample and not the other. For other purposes, we must passively make observations of correlations already occurring.

5.5.1.2.1 Active test group selection

Test and control groups are actively selected when researchers randomly divide the sample in two, and give the supposed cause to one group, making that the test group. When it is possible to actively construct the

test and control groups, this allows researchers to have the most control, and helps to ensure that there will be no other relevant differences between the test group and control group.

Examples of research where the test and control groups can be actively constructed are experiments conducted in laboratories, where all the other factors can be controlled, and research using people where the causal factor is not considered harmful.

A blind study is one where even the subjects in the test and control groups do not know which group they are in. In medical research, for example, the test group may be given a drug which researchers want to test, and the control group is given a fake drug, or placebo. None of the subjects would know whether they had received the real drug or the placebo. This is to ensure that any differences measured between the test and control groups are the effect of the drug, and not psychological effects of people thinking they are being cured.

5.5.1.2.2 Passive test group selection

In some cases, however, it is not possible to construct test and control groups by providing the supposed cause to one group and not the other. In such cases, it is necessary to passively select a test group and control group by finding subjects with and without the supposed causal factor, to discover whether there is a higher incidence of what you take to be the effect in the former group than the latter. This may be necessary for practical or ethical reasons, for example:

(4a) If, for example, you wanted to work out whether unusually heavy rain had an effect on wheat yields, you cannot do this by 'giving' one area particularly heavy rain. You would have to find wheat-growing areas which had had heavy rain, and use them as your test group, comparing their yields with otherwise relevantly similar areas which had average amounts of rain.

(4b) If you want to find out whether people who had pets as children suffer from more respiratory problems in old age, it would be impractical to investigate this by giving people pets and waiting sixty or seventy years.

Even apart from the practicality, it would be unlikely that the test and control groups which were relevantly similar as children would still be relevantly similar as adults, since other aspects of their lives may ultimately have a greater effect on their respiratory health than whether they had pets as children. A better way to carry out this research would be to find elderly people, some of whom had had pets as children and some not, but who were similar in other relevant respects. This selection would be passive, in the sense that the researchers did not provide the alleged cause, but chose their test and control groups to have the properties they required.

In those two cases, it would be impossible to actively divide the sample into test and control groups for practical reasons. The active construction of a test group by providing the suspected cause may also be impossible in some cases for ethical reasons:

(4c) Research has been conducted recently into the question of whether painkillers taken during pregnancy increase the incidence of miscarriage. If this is suspected, it would be unethical to give pregnant women painkillers to see if they had miscarriages. But given that some women are taking painkillers, they can be used as a test group to see if they have a higher incidence of miscarriage than other women.

5.5.1.2.3 Are there any relevant differences between the test group and control group?

Just as it is important to try to make the sample representative of the population, it is important to try to make the control group and test group as similar as possible (apart from the presence in the test group of whatever you are investigating). Many flawed causal claims are made because there were differences between the test and control group other than the one which was being investigated, so that the differences which were subsequently observed may have been a result of something other than the suspected cause.

When you are evaluating a causal argument, think about whether there are likely to have been relevant differences between the test group and the control group, other than the one under investigation.

eg Researchers have found a correlation between body piercing and HIV infection, and this has led some to conclude that HIV may be transmitted through body piercings. Another explanation which has been suggested, however, is people who are inclined to have body piercings may also be more inclined than the rest of the population to engage in other behaviour such as IV drug use which would be relevant to the risk of HIV infection.

The suspicion, then, might be that the higher incidence of HIV among people with piercings is in fact a result of relevant differences between the test group of pierced people and the unpierced control group, and this is something which would have to be kept in mind in selecting those groups.

This is an situation where it would be unethical, and impractical, to actively construct a test group by

selecting a sample of people and then randomly piercing half of them. It would be unethical because if there is a suspicion that the action might lead to your test group becoming infected with HIV, it would be

unreasonable to expose them to that risk. It would also be impractical, because they would be unlikely to go along with it. In passively choosing your test and control groups, therefore, you would need to control for any other factors which might be relevant to HIV infection, which means that you would have to make sure that the test group and control groups were evenly matched with respect to these factors.

Taking these things into consideration, the methods of statistical research may be used to draw a conclusion about a correlation in a population from an observed correlation in a sample. The next step is to establish whether this correlation is evidence of a causal relationship.