Drawing Causal Inferences

Whether it is inductive theorizing and research (trying to determine if there are general relationships by looking at samples, or specifics) or deductive theorizing and research (testing hypotheses; determining if proposed general relationships are found in specifics), we are likely to assert causal/functional propositions (i.e., to make causal inferences). However, as David Hume shows in A treatise of human nature, we cannot see causation directly. We only infer causal connection. Somehow, we feel more comfortable with the proposition "X causes Y" when the inference is drawn under certain evidentiary conditions, which are as follows:
1. Evidence that the alleged cause preceded the alleged effect ("temporal priority").

2. Empirical evidence that the alleged cause and effect occur together ("contiguity").

3. Logical evidence that ties them together ("constant conjunction”).

4. Evidence that alternative explanations (from extraneous variables) are implausible.

Let us examine each of these criteria.

Alleged Cause Precedes Alleged Effect.
Consider the following assertion. "An increase in teachers' authority to make curricular decisions (independent variable) fosters an increase in teachers' attachment to their school." This proposition (it could be an empirical generalization from research) seems plausible only if there is evidence that teachers' authority to make curricular decisions preceded an increase in teachers' attachment to their school. Evidence of temporal priority might be supplied by observation, experimental control, and/or commonsense reasoning (e.g., it is not likely that a house burned down and then someone smoked in bed).

Empirical Evidence of Association.
The inference that an increase in teachers' authority to make curricular decisions fosters an increase in teachers' attachment to their school, is more compelling if we have data showing that these two variables changed in close succession (V->Y: a proximal relationship) or in a sequence of variables that changed in close succession (V->W->X->Y: a distal relationship), and in the order asserted. Similarly, we can conclude that a family training program produced beneficial effects only if we have evidence of change in families and evidence that family members attended meetings, understood what was presented during meetings, and read and understood materials.

Evidence Provided by Inductive Logic.
Logical evidence is obtained by designing research, analyzing data, and interpreting findings such that we can apply one or more of John Stuart Mill's methods of inductive inference, as described in his A system of logic. These methods include: concomitant variation, agreement, difference, joint agreement and difference, and residues.

1. The method of concomitant variation. If two variables are changing with respect to one another (e.g., both are increasing, both are decreasing, or one is increasing and the other is decreasing) while everything else remains at about the same level, then we have logical evidence that one variable is a cause or an effect of the other (or they are both being changed by a third variable.)

For instance, an experiment was conducted in a class of 20 elementary school children to identify what affects the rate of children's aggression. During the first experimental period (A1 or Baseline), the teacher was asked to go about her business and handle the children's aggression (operationally defined as hitting, kicking, insulting, etc.) in her usual way. Prior observation showed that her usual way involved staring at the "offender," reminding the offender of the rules, telling the offender to stop, or even giving the offender an enjoyable activity to "distract him" or "settle him down."

In the next experimental period (B1), the teacher was coached to ignore aggression and, instead, to comfort and reinforce other children who were engaging in nonaggressive behavior at that time.

In the third experimental period (A2), called a "reversal," the teacher was asked to do what she used to do during A1 (which, again, meant that she tried to stop aggresssion). And during the final period (B2), she was asked to go back to ignoring aggression and reinforcing nonaggression.

Let's say that we graph the number of aggressive acts per day. Suppose we find that when the children received a lot of teacher contact following aggression (A1 and A2), the rate of aggression was high, and when the amount of teacher contact following aggression decreased (B1 and B2), the rate of aggression decreased. Since nothing else in the classroom was changing along with changes in the teacher's responses to aggression, it is plausible to infer that changes in the teacher's responses somehow caused changes in the children's rate of aggression. [Note that it would be important to try to determine how the teacher and the children made sense of what was happening--the subjective and intersubjective sides of the social system.]

2. The method of agreement. Imagine that we study twenty failed school reform efforts. Each school and each reform effort was a different configuration of variables (e.g., school size, socioeconomic status of school, location, teacher-student ratio, speed of reform). Despite these differences, however, all of the schools and failed reform efforts had one thing in common--staff did not fully understand and were not fully committed to the mission or the reform plans. Since nothing else in the schools and plans was common across the schools, it is reasonable to infer that the way in which they "agreed" (i.e., were the same) was the cause of the failed reform efforts.

3. The method of difference. Mill's method of difference is the form of inductive logic used in the typical pre-test, post-test, experimental-group, control-group study. Let us say that we have a pool of 50 families whom we randomly assign to two comparison groups. One group receives written materials, ten weekly group meetings, and weekly home visits aimed to improve family interaction and home teaching. The second group receives written materials only. We compare pre-test and post-test scores on the quality of family interaction and home teaching. Families in the first group have significantly larger pre-post-test differences. What can we infer? Since we randomly assigned families to the two groups, any personal and family differences that might have accounted for improvement or lack of improvement (e.g., religion, support network, expectations of success, initial teaching skill) had an equal chance of being in each group. Therefore, we can assume that the groups were fairly similar on these extraneous factors. (Of course, we could also measure those factors that we think are important and see how similar the two groups actually are.) Since the only other systematic difference between the two groups (which we know about) was group meetings and home visits, it seems likely that these two features of the training made the difference in the amounts of improvement.

4. The joint method of agreement and difference. This method combines the methods of agreement and difference. Let us take the above research on family training one step farther. We compared pre-post-test scores of families in the two groups which systematically differed only on whether they received written materials or received materials, meetings, and home visits. We used the method of difference to infer that the meetings and home visits accounted for the difference in improvement. Now imagine that, in addition, we obtain a large sample of families who differ in many ways (income, ethnicity, education, etc.). In each family we examine the quality of family interaction and teaching (dependent variables). We also examine whether each family reads materials on interaction and teaching (e.g., books, magazines), is part of some kind of group in which family interaction and teaching are discussed, or receives any in-home assistance or support (e.g., from relatives or other families) (independent variables). If we find that families who attend family-oriented meetings and receive home assistance also have higher quality family interaction and teaching, then we have logical evidence through the method of agreement that these variables make a difference. In summary, the combined use of the methods of agreement and difference provides compelling evidence.

5. The method of residues. Imagine a situation in which some phenomenon (Y) might be explained by four factors. We may be able plausibly to infer the one that is the cause through a process of elimination. If we know that factor 1 is a cause of Q, factor 2 is a cause of R, and factor 3 is a cause of S, then factor 4, the only one left, is likely to be the cause of Y. As Sherlock Holmes used to tell Dr. Watson, when you eliminate all of the other possible explanations, the one that remains, improbable though it may seem, must be the correct explanation.

Alternative Explanations (from extraneous variables) are Implausible.
This is done via research design. For example, using equivalent comparison groups (so that differences in outcome can’t logically be attributed to differences in groups); using validated instruments; checking reliability of measurements before and during the research; replicating the research with similar groups (to determine whether the findings are repeatable and likely to be “the way things really are”); replicating the research with different groups (to determine whether the findings are general or apply only to groups with certain characteristics)